iProverMo---2.5-0.1.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SWV280-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Wed Jul 20 19:11:28 EDT 2022

% Result   : Unsatisfiable 174.38s 174.83s
% Output   : CNFRefutation 174.48s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

% Comments : 
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
    ! [X1,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X1,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble8,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__9_0) ).

fof(c_0_1,axiom,
    ! [X1,X68,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X1,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble7,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__8_0) ).

fof(c_0_2,axiom,
    ! [X1,X68,X69,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X1,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble6,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__7_0) ).

fof(c_0_3,axiom,
    ! [X1,X68,X69,X70,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X1,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble5,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__6_0) ).

fof(c_0_4,axiom,
    ! [X1,X68,X69,X70,X71,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X1,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble4,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__5_0) ).

fof(c_0_5,axiom,
    ! [X1,X68,X69,X70,X71,X72,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X1,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble3,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__4_0) ).

fof(c_0_6,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X1,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble2,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__3_0) ).

fof(c_0_7,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X1,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble1,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__2_0) ).

fof(c_0_8,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X4] : c_List_Onibble_Onibble__rec(X1,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble0,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__1_0) ).

fof(c_0_9,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X1,c_List_Onibble_ONibbleF,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__16_0) ).

fof(c_0_10,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X1,X75,c_List_Onibble_ONibbleE,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__15_0) ).

fof(c_0_11,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X1,X76,X75,c_List_Onibble_ONibbleD,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__14_0) ).

fof(c_0_12,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X1,X77,X76,X75,c_List_Onibble_ONibbleC,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__13_0) ).

fof(c_0_13,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X1,X78,X77,X76,X75,c_List_Onibble_ONibbleB,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__12_0) ).

fof(c_0_14,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X1,X79,X78,X77,X76,X75,c_List_Onibble_ONibbleA,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__11_0) ).

fof(c_0_15,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X1,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble9,X4) = X1,
    file('<stdin>',cls_List_Onibble_Orecs__10_0) ).

fof(c_0_16,axiom,
    ! [X1,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X1,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble8,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__9_0) ).

fof(c_0_17,axiom,
    ! [X1,X68,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X1,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble7,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__8_0) ).

fof(c_0_18,axiom,
    ! [X1,X68,X69,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X1,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble6,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__7_0) ).

fof(c_0_19,axiom,
    ! [X1,X68,X69,X70,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X1,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble5,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__6_0) ).

fof(c_0_20,axiom,
    ! [X1,X68,X69,X70,X71,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X1,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble4,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__5_0) ).

fof(c_0_21,axiom,
    ! [X1,X68,X69,X70,X71,X72,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X1,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble3,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__4_0) ).

fof(c_0_22,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X1,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble2,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__3_0) ).

fof(c_0_23,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X1,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble1,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__2_0) ).

fof(c_0_24,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X4] : c_List_Onibble_Onibble__case(X1,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble0,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__1_0) ).

fof(c_0_25,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X1,c_List_Onibble_ONibbleF,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__16_0) ).

fof(c_0_26,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X1,X75,c_List_Onibble_ONibbleE,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__15_0) ).

fof(c_0_27,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X1,X76,X75,c_List_Onibble_ONibbleD,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__14_0) ).

fof(c_0_28,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X1,X77,X76,X75,c_List_Onibble_ONibbleC,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__13_0) ).

fof(c_0_29,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X1,X78,X77,X76,X75,c_List_Onibble_ONibbleB,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__12_0) ).

fof(c_0_30,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X1,X79,X78,X77,X76,X75,c_List_Onibble_ONibbleA,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__11_0) ).

fof(c_0_31,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X1,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble9,X4) = X1,
    file('<stdin>',cls_List_Onibble_Ocases__10_0) ).

fof(c_0_32,axiom,
    ! [X31,X5,X6,X32,X3,X4] :
      ( ~ c_in(X31,c_Relation_Orel__comp(X6,X5,X32,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(c_Main_Orel__compE__1(X6,X5,X31,X32,X3,X4),c_Main_Orel__compE__2(X6,X5,X31,X32,X3,X4),X4,X32),X5,tc_prod(X4,X32)) ),
    file('<stdin>',cls_Relation_Orel__compE_1) ).

fof(c_0_33,axiom,
    ! [X31,X5,X6,X32,X3,X4] :
      ( ~ c_in(X31,c_Relation_Orel__comp(X6,X5,X32,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(c_Main_Orel__compE__2(X6,X5,X31,X32,X3,X4),c_Main_Orel__compE__3(X6,X5,X31,X32,X3,X4),X32,X3),X6,tc_prod(X32,X3)) ),
    file('<stdin>',cls_Relation_Orel__compE_0) ).

fof(c_0_34,axiom,
    ! [X31,X5,X6,X32,X3,X4] :
      ( ~ c_in(X31,c_Relation_Orel__comp(X6,X5,X32,X3,X4),tc_prod(X4,X3))
      | X31 = c_Pair(c_Main_Orel__compE__1(X6,X5,X31,X32,X3,X4),c_Main_Orel__compE__3(X6,X5,X31,X32,X3,X4),X4,X3) ),
    file('<stdin>',cls_Relation_Orel__compE_2) ).

fof(c_0_35,axiom,
    ! [X5,X6,X7,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X7 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X7,X6,X5,X4,X3),c_Main_OdprodE__2(X7,X6,X5,X4,X3),X4,X3),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X7,X6,X5,X4,X3),c_Main_OdprodE__4(X7,X6,X5,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodE_0) ).

fof(c_0_36,axiom,
    ! [X5,X6,X7,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdprodE__1(X7,X6,X5,X4,X3),c_Main_OdprodE__3(X7,X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodE_2) ).

fof(c_0_37,axiom,
    ! [X5,X6,X7,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdprodE__2(X7,X6,X5,X4,X3),c_Main_OdprodE__4(X7,X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodE_1) ).

fof(c_0_38,axiom,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__1(X6,X12,X4,X3),c_Main_OdsumE__2(X6,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__3(X5,X12,X4,X3),c_Main_OdsumE__4(X5,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_3) ).

fof(c_0_39,axiom,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__1(X6,X12,X4,X3),c_Main_OdsumE__2(X6,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X12 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X5,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X5,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_2) ).

fof(c_0_40,axiom,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__3(X5,X12,X4,X3),c_Main_OdsumE__4(X5,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X12 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_1) ).

fof(c_0_41,axiom,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X6,X24,X1,X26,X4),X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_Olistrel__Cons2_1) ).

fof(c_0_42,axiom,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X26,X4),X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X26,c_Main_Olistrel__Cons1__2(X6,X24,X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_Olistrel__Cons1_1) ).

fof(c_0_43,axiom,
    ! [X5,X6,X8,X9,X10,X11,X3,X4] :
      ( ~ c_in(c_Pair(X9,X8,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | ~ c_in(c_Pair(X11,X10,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X11,X9,X4,X3),c_Datatype__Universe_OScons(X10,X8,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodI_0) ).

fof(c_0_44,axiom,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X6,X24,X1,X26,X4),X1,X4,X4),X6,tc_prod(X4,X4)) ),
    file('<stdin>',cls_List_Olistrel__Cons2_2) ).

fof(c_0_45,axiom,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X26,X4),X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X6,X24,X1,X26,X4),X4,X4),X6,tc_prod(X4,X4)) ),
    file('<stdin>',cls_List_Olistrel__Cons1_2) ).

fof(c_0_46,axiom,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X12 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X12 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X5,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X5,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_0) ).

fof(c_0_47,axiom,
    ! [X6,X28,X14,X3,X4] :
      ( ~ c_in(X28,c_Relation_OImage(X6,X14,X3,X4),X4)
      | c_in(c_Pair(c_Main_OImageE__1(X14,X28,X6,X3,X4),X28,X3,X4),X6,tc_prod(X3,X4)) ),
    file('<stdin>',cls_Relation_OImageE_1) ).

fof(c_0_48,axiom,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X6,X24,X1,X26,X4),c_Main_Olistrel__Cons2__2(X6,X24,X1,X26,X4),X4) ),
    file('<stdin>',cls_List_Olistrel__Cons2_0) ).

fof(c_0_49,axiom,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X26,X4),X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X6,X24,X1,X26,X4),c_Main_Olistrel__Cons1__2(X6,X24,X1,X26,X4),X4) ),
    file('<stdin>',cls_List_Olistrel__Cons1_0) ).

fof(c_0_50,axiom,
    ! [X7,X13,X14,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X7 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X14,X13,X7,X4,X3),c_Main_OuprodE__2(X14,X13,X7,X4,X3),X4,X3) ),
    file('<stdin>',cls_Datatype__Universe_OuprodE_0) ).

fof(c_0_51,axiom,
    ! [X5,X6,X7,X28,X19,X32,X3,X4] :
      ( ~ c_in(c_Pair(X28,X7,X3,X32),X6,tc_prod(X3,X32))
      | ~ c_in(c_Pair(X19,X28,X4,X3),X5,tc_prod(X4,X3))
      | c_in(c_Pair(X19,X7,X4,X32),c_Relation_Orel__comp(X6,X5,X3,X32,X4),tc_prod(X4,X32)) ),
    file('<stdin>',cls_Relation_Orel__compI_0) ).

fof(c_0_52,axiom,
    ! [X1,X2,X48,X15] :
      ( ~ c_in(c_Pair(c_Pair(X2,X1,tc_nat,tc_nat),c_Pair(X15,X48,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_plus(X2,X48,tc_nat) = c_plus(X15,X1,tc_nat) ),
    file('<stdin>',cls_IntDef_Ointrel__iff_0) ).

fof(c_0_53,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('<stdin>',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).

fof(c_0_54,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('<stdin>',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).

fof(c_0_55,axiom,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('<stdin>',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).

fof(c_0_56,axiom,
    ! [X5,X6,X8,X9,X3,X4] :
      ( ~ c_in(c_Pair(X9,X8,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X9,X4,X3),c_Datatype__Universe_OIn1(X8,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    file('<stdin>',cls_Datatype__Universe_Odsum__In1I_0) ).

fof(c_0_57,axiom,
    ! [X5,X6,X10,X11,X3,X4] :
      ( ~ c_in(c_Pair(X11,X10,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X11,X4,X3),c_Datatype__Universe_OIn0(X10,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    file('<stdin>',cls_Datatype__Universe_Odsum__In0I_0) ).

fof(c_0_58,axiom,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('<stdin>',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).

fof(c_0_59,axiom,
    ! [X7,X13,X14,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OuprodE__1(X14,X13,X7,X4,X3),X14,tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OuprodE_2) ).

fof(c_0_60,axiom,
    ! [X7,X13,X14,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OuprodE__2(X14,X13,X7,X4,X3),X13,tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OuprodE_1) ).

fof(c_0_61,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Omod__pos__neg__number__of_0) ).

fof(c_0_62,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Omod__neg__neg__number__of_0) ).

fof(c_0_63,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odiv__pos__neg__number__of_0) ).

fof(c_0_64,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odiv__neg__neg__number__of_0) ).

fof(c_0_65,axiom,
    ! [X6,X28,X14,X3,X4] :
      ( ~ c_in(X28,c_Relation_OImage(X6,X14,X3,X4),X4)
      | c_in(c_Main_OImageE__1(X14,X28,X6,X3,X4),X14,X3) ),
    file('<stdin>',cls_Relation_OImageE_0) ).

fof(c_0_66,axiom,
    ! [X12] :
      ( ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).

fof(c_0_67,axiom,
    ! [X12] :
      ( ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).

fof(c_0_68,axiom,
    ! [X1,X2,X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X19,X2,X4),c_List_Olist_OCons(X28,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(X2,X1,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_Olexord__cons__cons_1) ).

fof(c_0_69,axiom,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X2,X1,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(X24,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_OCons__in__lex_1) ).

fof(c_0_70,axiom,
    ! [X1,X2] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X2,X1,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    file('<stdin>',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).

fof(c_0_71,axiom,
    ! [X1,X2,X48,X15] :
      ( c_plus(X2,X48,tc_nat) != c_plus(X15,X1,tc_nat)
      | c_in(c_Pair(c_Pair(X2,X1,tc_nat,tc_nat),c_Pair(X15,X48,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    file('<stdin>',cls_IntDef_Ointrel__iff_1) ).

fof(c_0_72,axiom,
    ! [X30,X6,X3,X4] :
      ( ~ c_in(X30,c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(c_Main_OconverseE__1(X6,X30,X3,X4),c_Main_OconverseE__2(X6,X30,X3,X4),X3,X4),X6,tc_prod(X3,X4)) ),
    file('<stdin>',cls_Relation_OconverseE_0) ).

fof(c_0_73,axiom,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__insert_1) ).

fof(c_0_74,axiom,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).

fof(c_0_75,axiom,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X24,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_Nat_Osize(X24,tc_List_Olist(X4)) = c_Nat_Osize(X26,tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_OCons__in__lex_3) ).

fof(c_0_76,axiom,
    ! [X1,X2,X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X19,X2,X4),c_List_Olist_OCons(X28,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | X19 = X28 ),
    file('<stdin>',cls_List_Olexord__cons__cons_0) ).

fof(c_0_77,axiom,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X2,X1,X4,X4),X6,tc_prod(X4,X4))
      | X2 = X1 ),
    file('<stdin>',cls_List_OCons__in__lex_0) ).

fof(c_0_78,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__1(X14,X15,X4,X3),X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__2(X13,X15,X4,X3),X13,tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_3) ).

fof(c_0_79,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__1(X14,X15,X4,X3),X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X15 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X15,X4,X3),X4,X3) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_2) ).

fof(c_0_80,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__2(X13,X15,X4,X3),X13,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X15 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X14,X15,X4,X3),X4,X3) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_1) ).

fof(c_0_81,axiom,
    ! [X1,X63,X2,X6,X4] :
      ( ~ c_in(c_Pair(X63,X1,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_List_Olist_OCons(X2,X63,X4),c_List_Olist_OCons(X2,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_Olexord__cons__cons_3) ).

fof(c_0_82,axiom,
    ! [X26,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(X24,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X2,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_OCons__in__lex_5) ).

fof(c_0_83,axiom,
    ! [X1,X2] :
      ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(X2,X1,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    file('<stdin>',cls_IntDef_Oequiv__intrel__iff_0) ).

fof(c_0_84,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X15 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X14,X15,X4,X3),X4,X3)
      | X15 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X15,X4,X3),X4,X3) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_0) ).

fof(c_0_85,axiom,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(X2,X1,X4,X4),X6,tc_prod(X4,X4))
      | c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X4))
      | c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_OCons__in__lex_4) ).

fof(c_0_86,axiom,
    ! [X1,X2] :
      ( ~ c_in(c_Pair(X2,X1,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    file('<stdin>',cls_IntDef_Oequiv__intrel__iff_1) ).

fof(c_0_87,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | X15 = c_Sum__Type_OInl(c_Main_OPlusE__1(X14,X15,X4,X3),X4,X3)
      | X15 = c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X15,X3,X4),X3,X4) ),
    file('<stdin>',cls_Sum__Type_OPlusE_0) ).

fof(c_0_88,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | c_in(c_Main_OPlusE__1(X14,X15,X4,X3),X14,X4)
      | X15 = c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X15,X3,X4),X3,X4) ),
    file('<stdin>',cls_Sum__Type_OPlusE_2) ).

fof(c_0_89,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | c_in(c_Main_OPlusE__2(X13,X15,X3,X4),X13,X3)
      | X15 = c_Sum__Type_OInl(c_Main_OPlusE__1(X14,X15,X4,X3),X4,X3) ),
    file('<stdin>',cls_Sum__Type_OPlusE_1) ).

fof(c_0_90,axiom,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | c_in(c_Main_OPlusE__1(X14,X15,X4,X3),X14,X4)
      | c_in(c_Main_OPlusE__2(X13,X15,X3,X4),X13,X3) ),
    file('<stdin>',cls_Sum__Type_OPlusE_3) ).

fof(c_0_91,axiom,
    ! [X17,X9,X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_OScons(X11,X9,X4,X3),X4,X3) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X17,X11,X4,X3),c_Datatype__Universe_Ontrunc(X17,X9,X4,X3),X4,X3),
    file('<stdin>',cls_Datatype__Universe_Ontrunc__Scons_0) ).

fof(c_0_92,axiom,
    ! [X1,X2,X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(c_List_Olist_OCons(X19,X2,X4),c_List_Olist_OCons(X28,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    file('<stdin>',cls_List_Olexord__cons__cons_2) ).

fof(c_0_93,axiom,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_Wellfounded__Recursion_Owf(X6,X4) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__insert_0) ).

fof(c_0_94,axiom,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_Wellfounded__Recursion_Oacyclic(X6,X4) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).

fof(c_0_95,axiom,
    ! [X6,X28,X3,X4] :
      ( ~ c_in(X28,c_Relation_ORange(X6,X3,X4),X4)
      | c_in(c_Pair(c_Main_ORangeE__1(X28,X6,X4,X3),X28,X3,X4),X6,tc_prod(X3,X4)) ),
    file('<stdin>',cls_Relation_ORangeE_0) ).

fof(c_0_96,axiom,
    ! [X6,X19,X3,X4] :
      ( ~ c_in(X19,c_Relation_ODomain(X6,X4,X3),X4)
      | c_in(c_Pair(X19,c_Main_ODomainE__1(X19,X6,X4,X3),X4,X3),X6,tc_prod(X4,X3)) ),
    file('<stdin>',cls_Relation_ODomainE_0) ).

fof(c_0_97,axiom,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__insert_2) ).

fof(c_0_98,axiom,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X6,X4)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).

fof(c_0_99,axiom,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(X28,c_Relation_OImage(X6,c_insert(X19,c_emptyset,X3),X3,X4),X4)
      | c_in(c_Pair(X19,X28,X3,X4),X6,tc_prod(X3,X4)) ),
    file('<stdin>',cls_Relation_OImage__singleton__iff_0) ).

fof(c_0_100,axiom,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X2 = X1
      | c_Nat_Osize(X24,tc_List_Olist(X4)) = c_Nat_Osize(X26,tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_OCons__in__lex_2) ).

fof(c_0_101,axiom,
    ! [X22,X16,X17] :
      ( ~ c_Divides_Oop_Advd(X17,c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X17,X22,tc_nat) ),
    file('<stdin>',cls_GCD_Ogcd__greatest__iff_1) ).

fof(c_0_102,axiom,
    ! [X22,X16,X17] :
      ( ~ c_Divides_Oop_Advd(X17,c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X17,X16,tc_nat) ),
    file('<stdin>',cls_GCD_Ogcd__greatest__iff_0) ).

fof(c_0_103,axiom,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X3,X4),X6,tc_prod(X3,X4))
      | c_in(X28,c_Relation_OImage(X6,c_insert(X19,c_emptyset,X3),X3,X4),X4) ),
    file('<stdin>',cls_Relation_OImage__singleton__iff_1) ).

fof(c_0_104,axiom,
    ! [X26,X24,X53,X54,X3,X4] :
      ( c_Nat_Osize(X26,tc_List_Olist(X4)) != c_Nat_Osize(X53,tc_List_Olist(X3))
      | c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X54,tc_List_Olist(X3))
      | c_List_Ozip(c_append(X24,X26,X4),c_append(X54,X53,X3),X4,X3) = c_append(c_List_Ozip(X24,X54,X4,X3),c_List_Ozip(X26,X53,X4,X3),tc_prod(X4,X3)) ),
    file('<stdin>',cls_List_Ozip__append_0) ).

fof(c_0_105,axiom,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X3),c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(X28,X19,X3,X4),X6,tc_prod(X3,X4)) ),
    file('<stdin>',cls_Relation_Oconverse__iff_0) ).

fof(c_0_106,axiom,
    ! [X5,X6,X3,X4] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X4,X3),
    file('<stdin>',cls_Datatype__Universe_ODomain__dsum_0) ).

fof(c_0_107,axiom,
    ! [X5,X6,X3,X4] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X4,X3),
    file('<stdin>',cls_Datatype__Universe_ODomain__dprod_0) ).

fof(c_0_108,axiom,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X28,X19,X3,X4),X6,tc_prod(X3,X4))
      | c_in(c_Pair(X19,X28,X4,X3),c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3)) ),
    file('<stdin>',cls_Relation_Oconverse__iff_1) ).

fof(c_0_109,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).

fof(c_0_110,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Omod__pos__pos__number__of_0) ).

fof(c_0_111,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Omod__neg__pos__number__of_0) ).

fof(c_0_112,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odiv__pos__pos__number__of_0) ).

fof(c_0_113,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odiv__neg__pos__number__of_0) ).

fof(c_0_114,axiom,
    ! [X22,X86,X42] : c_Nat_Opower(X86,c_Suc(X22),tc_set(tc_prod(X42,X42))) = c_Relation_Orel__comp(X86,c_Nat_Opower(X86,X22,tc_set(tc_prod(X42,X42))),X42,X42,X42),
    file('<stdin>',cls_Relation__Power_Orelpow_Osimps__2_0) ).

fof(c_0_115,axiom,
    ! [X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),c_Transitive__Closure_Otrancl(X6,X4),tc_prod(X4,X4))
      | c_in(c_Pair(X19,X28,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

fof(c_0_116,axiom,
    ! [X6,X28,X19,X14,X3,X4] :
      ( ~ c_in(X19,X14,X4)
      | ~ c_in(c_Pair(X19,X28,X4,X3),X6,tc_prod(X4,X3))
      | c_in(X28,c_Relation_OImage(X6,X14,X4,X3),X3) ),
    file('<stdin>',cls_Relation_OImageI_0) ).

fof(c_0_117,axiom,
    ! [X30,X6,X3,X4] :
      ( ~ c_in(X30,c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3))
      | X30 = c_Pair(c_Main_OconverseE__2(X6,X30,X3,X4),c_Main_OconverseE__1(X6,X30,X3,X4),X4,X3) ),
    file('<stdin>',cls_Relation_OconverseE_1) ).

fof(c_0_118,axiom,
    ! [X26,X1,X24,X2,X3,X4] : c_List_Ozip(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X3),X4,X3) = c_List_Olist_OCons(c_Pair(X2,X1,X4,X3),c_List_Ozip(X24,X26,X4,X3),tc_prod(X4,X3)),
    file('<stdin>',cls_List_Ozip__Cons__Cons_0) ).

fof(c_0_119,axiom,
    ! [X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(X19,X28,X4,X4),c_Transitive__Closure_Otrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

fof(c_0_120,axiom,
    ! [X9,X11,X13,X14,X3,X4] :
      ( ~ c_in(X9,X13,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | ~ c_in(X11,X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Datatype__Universe_OScons(X11,X9,X4,X3),c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_OuprodI_0) ).

fof(c_0_121,axiom,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).

fof(c_0_122,axiom,
    ! [X26,X24,X2,X3,X4] :
      ( ~ c_in(X2,c_List_Oset(X24,X4),X4)
      | c_Map_Omap__of(c_List_Ozip(X24,X26,X4,X3),X2,X4,X3) != c_Datatype_Ooption_ONone
      | c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X3)) ),
    file('<stdin>',cls_Map_Omap__of__zip__is__None_0) ).

fof(c_0_123,axiom,
    ! [X26,X24,X44,X3,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X26,tc_List_Olist(X3)),tc_nat)
      | ~ c_less(X44,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Onth(c_List_Ozip(X24,X26,X4,X3),X44,tc_prod(X4,X3)) = c_Pair(c_List_Onth(X24,X44,X4),c_List_Onth(X26,X44,X3),X4,X3) ),
    file('<stdin>',cls_List_Onth__zip_0) ).

fof(c_0_124,axiom,
    ! [X12] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).

fof(c_0_125,axiom,
    ! [X12] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).

fof(c_0_126,axiom,
    ! [X86,X4] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X86,X4),c_Transitive__Closure_Ortrancl(X86,X4),X4,X4,X4) = c_Transitive__Closure_Ortrancl(X86,X4),
    file('<stdin>',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).

fof(c_0_127,axiom,
    ! [X1,X3,X4] : c_Relation_Orel__comp(X1,c_Relation_OId,X4,X3,X4) = X1,
    file('<stdin>',cls_Relation_OR__O__Id_0) ).

fof(c_0_128,axiom,
    ! [X1,X3,X4] : c_Relation_Orel__comp(c_Relation_OId,X1,X3,X3,X4) = X1,
    file('<stdin>',cls_Relation_OId__O__R_0) ).

fof(c_0_129,axiom,
    ! [X22,X16,X17] :
      ( ~ c_Divides_Oop_Advd(X17,X22,tc_nat)
      | ~ c_Divides_Oop_Advd(X17,X16,tc_nat)
      | c_Divides_Oop_Advd(X17,c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),tc_nat) ),
    file('<stdin>',cls_GCD_Ogcd__greatest__iff_2) ).

fof(c_0_130,axiom,
    ! [X22,X16] : c_GCD_Ogcd(c_Pair(X16,c_plus(X22,X16,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),
    file('<stdin>',cls_GCD_Ogcd__add2_H_0) ).

fof(c_0_131,axiom,
    ! [X22,X16] : c_GCD_Ogcd(c_Pair(X16,c_plus(X16,X22,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),
    file('<stdin>',cls_GCD_Ogcd__add2_0) ).

fof(c_0_132,axiom,
    ! [X22,X16] : c_GCD_Ogcd(c_Pair(c_plus(X16,X22,tc_nat),X22,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),
    file('<stdin>',cls_GCD_Ogcd__add1_0) ).

fof(c_0_133,axiom,
    ! [X1,X2,X60,X44,X3,X4] : c_List_Ozip(c_List_Oreplicate(X44,X2,X4),c_List_Oreplicate(X60,X1,X3),X4,X3) = c_List_Oreplicate(c_Orderings_Omin(X44,X60,tc_nat),c_Pair(X2,X1,X4,X3),tc_prod(X4,X3)),
    file('<stdin>',cls_List_Ozip__replicate_0) ).

fof(c_0_134,axiom,
    ! [X1,X24,X2,X44,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Olist__update(c_List_Olist__update(X24,X44,X2,X4),X44,X1,X4) = c_List_Olist__update(X24,X44,X1,X4) ),
    file('<stdin>',cls_List_Olist__update__overwrite_0) ).

fof(c_0_135,axiom,
    ! [X1,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X1 = c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X4),c_Main_Olexord__Nil__left__2(X1,X4),X4) ),
    file('<stdin>',cls_List_Olexord__Nil__left_0) ).

fof(c_0_136,axiom,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).

fof(c_0_137,axiom,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X3),X6,tc_prod(X4,X3))
      | c_in(X28,c_Relation_ORange(X6,X4,X3),X3) ),
    file('<stdin>',cls_Relation_ORangeI_0) ).

fof(c_0_138,axiom,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X3),X6,tc_prod(X4,X3))
      | c_in(X19,c_Relation_ODomain(X6,X4,X3),X4) ),
    file('<stdin>',cls_Relation_ODomainI_0) ).

fof(c_0_139,axiom,
    ! [X22,X16] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),X22,tc_nat),
    file('<stdin>',cls_GCD_Ogcd__dvd2_0) ).

fof(c_0_140,axiom,
    ! [X22,X16] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),X16,tc_nat),
    file('<stdin>',cls_GCD_Ogcd__dvd1_0) ).

fof(c_0_141,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_8) ).

fof(c_0_142,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_8) ).

fof(c_0_143,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_8) ).

fof(c_0_144,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_8) ).

fof(c_0_145,axiom,
    ! [X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_ONil,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olistrel__Nil2_0) ).

fof(c_0_146,axiom,
    ! [X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olistrel__Nil1_0) ).

fof(c_0_147,axiom,
    ! [X2,X6,X4] : ~ c_in(c_Pair(X2,c_List_Olist_ONil,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    file('<stdin>',cls_List_Olexord__Nil__right_0) ).

fof(c_0_148,axiom,
    ! [X26,X6,X4] : ~ c_in(c_Pair(c_List_Olist_ONil,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    file('<stdin>',cls_List_ONil__notin__lex_0) ).

fof(c_0_149,axiom,
    ! [X24,X6,X4] : ~ c_in(c_Pair(X24,c_List_Olist_ONil,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    file('<stdin>',cls_List_ONil2__notin__lex_0) ).

fof(c_0_150,axiom,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).

fof(c_0_151,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_9) ).

fof(c_0_152,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_9) ).

fof(c_0_153,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,X19,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_9) ).

fof(c_0_154,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_0,X19,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_9) ).

fof(c_0_155,axiom,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_Nat_Opower(c_uminus(X19,X4),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X22,tc_nat),X4) = c_Nat_Opower(X19,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X22,tc_nat),X4) ),
    file('<stdin>',cls_NatBin_Opower__minus__even_0) ).

fof(c_0_156,axiom,
    ! [X1,X2] :
      ( ~ c_in(c_Pair(X2,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
      | c_less(X2,X1,tc_nat) ),
    file('<stdin>',cls_Wellfounded__Relations_Oless__than__iff_0) ).

fof(c_0_157,axiom,
    ! [X17,X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X17)),c_Datatype__Universe_OIn1(X11,X4,X3),X4,X3) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X17),X11,X4,X3),X4,X3),
    file('<stdin>',cls_Datatype__Universe_Ontrunc__In1_0) ).

fof(c_0_158,axiom,
    ! [X17,X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X17)),c_Datatype__Universe_OIn0(X11,X4,X3),X4,X3) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X17),X11,X4,X3),X4,X3),
    file('<stdin>',cls_Datatype__Universe_Ontrunc__In0_0) ).

fof(c_0_159,axiom,
    ! [X6,X19,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | ~ c_in(c_Pair(X19,X19,X4,X4),X6,tc_prod(X4,X4)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__not__refl_0) ).

fof(c_0_160,axiom,
    ! [X16] :
      ( ~ c_less(c_0,c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
      | c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1 ),
    file('<stdin>',cls_NatSimprocs_Omod2__gr__0_0) ).

fof(c_0_161,axiom,
    ! [X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),c_Relation_OId,tc_prod(X4,X4))
      | X19 = X28 ),
    file('<stdin>',cls_Relation_Opair__in__Id__conv_0) ).

fof(c_0_162,axiom,
    ! [X28] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X28,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X28,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_OnegDivAlg__minus1_0) ).

fof(c_0_163,axiom,
    ! [X9,X13,X14,X3,X4] :
      ( ~ c_in(X9,X13,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Datatype__Universe_OIn1(X9,X4,X3),c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_Ousum__In1I_0) ).

fof(c_0_164,axiom,
    ! [X11,X13,X14,X3,X4] :
      ( ~ c_in(X11,X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Datatype__Universe_OIn0(X11,X4,X3),c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    file('<stdin>',cls_Datatype__Universe_Ousum__In0I_0) ).

fof(c_0_165,axiom,
    ! [X87,X88,X89] : c_Message_Oparts(c_insert(c_Message_OHPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X88,X87),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oparts(c_insert(X87,X89,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__HPair_0) ).

fof(c_0_166,axiom,
    ! [X87,X88,X89] : c_Message_Oanalz(c_insert(c_Message_OHPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X88,X87),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(c_insert(X87,X89,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__insert__HPair_0) ).

fof(c_0_167,axiom,
    ! [X26,X24,X2,X3,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X3))
      | c_in(X2,c_List_Oset(X24,X4),X4)
      | c_Map_Omap__of(c_List_Ozip(X24,X26,X4,X3),X2,X4,X3) = c_Datatype_Ooption_ONone ),
    file('<stdin>',cls_Map_Omap__of__zip__is__None_1) ).

fof(c_0_168,axiom,
    ! [X87,X88,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X88,X87),c_Message_Oparts(c_insert(X88,c_insert(X87,X89,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__MPair_0) ).

fof(c_0_169,axiom,
    ! [X87,X88,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X88,X87),c_Message_Oanalz(c_insert(X88,c_insert(X87,X89,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__insert__MPair_0) ).

fof(c_0_170,axiom,
    ! [X6,X62,X25,X4] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X25,X62,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    file('<stdin>',cls_List_Olexord__Nil__left_1) ).

fof(c_0_171,axiom,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(c_minus(X14,c_insert(X19,X13,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_minus(X14,X13,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Diff__insert_0) ).

fof(c_0_172,axiom,
    ! [X26,X24,X22,X4] : c_List_Otake(X22,c_append(X24,X26,X4),X4) = c_append(c_List_Otake(X22,X24,X4),c_List_Otake(c_minus(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat),X26,X4),X4),
    file('<stdin>',cls_List_Otake__append_0) ).

fof(c_0_173,axiom,
    ! [X26,X24,X22,X4] : c_List_Odrop(X22,c_append(X24,X26,X4),X4) = c_append(c_List_Odrop(X22,X24,X4),c_List_Odrop(c_minus(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat),X26,X4),X4),
    file('<stdin>',cls_List_Odrop__append_0) ).

fof(c_0_174,axiom,
    ! [X85,X28,X43,X19,X3,X4] :
      ( c_Pair(X19,X28,X4,X3) != c_Pair(X43,X85,X4,X3)
      | X28 = X85 ),
    file('<stdin>',cls_Product__Type_OPair__eq_1) ).

fof(c_0_175,axiom,
    ! [X85,X28,X43,X19,X3,X4] :
      ( c_Pair(X19,X28,X4,X3) != c_Pair(X43,X85,X4,X3)
      | X19 = X43 ),
    file('<stdin>',cls_Product__Type_OPair__eq_0) ).

fof(c_0_176,axiom,
    ! [X8,X9,X10,X11,X3,X4] :
      ( c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OScons(X10,X8,X4,X3)
      | X9 = X8 ),
    file('<stdin>',cls_Datatype__Universe_OScons__Scons__eq_1) ).

fof(c_0_177,axiom,
    ! [X8,X9,X10,X11,X3,X4] :
      ( c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OScons(X10,X8,X4,X3)
      | X11 = X10 ),
    file('<stdin>',cls_Datatype__Universe_OScons__Scons__eq_0) ).

fof(c_0_178,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_less(X28,X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).

fof(c_0_179,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(X19,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).

fof(c_0_180,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_less(X28,X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).

fof(c_0_181,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(X19,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).

fof(c_0_182,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(X28,X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).

fof(c_0_183,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(X19,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).

fof(c_0_184,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(X28,X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).

fof(c_0_185,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(X19,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).

fof(c_0_186,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_4) ).

fof(c_0_187,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_1) ).

fof(c_0_188,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_4) ).

fof(c_0_189,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_1) ).

fof(c_0_190,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_4) ).

fof(c_0_191,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_1) ).

fof(c_0_192,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_4) ).

fof(c_0_193,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_1) ).

fof(c_0_194,axiom,
    ! [X16] :
      ( c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1
      | c_less(c_0,c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_NatSimprocs_Omod2__gr__0_1) ).

fof(c_0_195,axiom,
    ! [X26,X1,X24,X2,X4] : c_List_Olist__update(c_append(X24,c_List_Olist_OCons(X2,X26,X4),X4),c_Nat_Osize(X24,tc_List_Olist(X4)),X1,X4) = c_append(X24,c_List_Olist_OCons(X1,X26,X4),X4),
    file('<stdin>',cls_List_Olist__update__length_0) ).

fof(c_0_196,axiom,
    ! [X28,X13,X14,X3,X4] :
      ( ~ c_in(X28,X13,X4)
      | c_in(c_Sum__Type_OInr(X28,X4,X3),c_Sum__Type_OPlus(X14,X13,X3,X4),tc_sum(X3,X4)) ),
    file('<stdin>',cls_Sum__Type_OInrI_0) ).

fof(c_0_197,axiom,
    ! [X19,X13,X14,X3,X4] :
      ( ~ c_in(X19,X14,X4)
      | c_in(c_Sum__Type_OInl(X19,X4,X3),c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3)) ),
    file('<stdin>',cls_Sum__Type_OInlI_0) ).

fof(c_0_198,axiom,
    ! [X6,X50] : c_IntDiv_OnegateSnd(c_Pair(X50,X6,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X50,c_uminus(X6,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_OnegateSnd__eq_0) ).

fof(c_0_199,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_7) ).

fof(c_0_200,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_5) ).

fof(c_0_201,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_7) ).

fof(c_0_202,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_5) ).

fof(c_0_203,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,X19,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_7) ).

fof(c_0_204,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X19,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_5) ).

fof(c_0_205,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_0,X19,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_7) ).

fof(c_0_206,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X19,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_5) ).

fof(c_0_207,axiom,
    ! [X28] : c_IntDiv_OposDivAlg(c_Pair(c_0,X28,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_OposDivAlg__0_0) ).

fof(c_0_208,axiom,
    ! [X1,X22] : c_GCD_Ogcd(c_Pair(X1,c_times(X1,X22,tc_nat),tc_nat,tc_nat)) = X1,
    file('<stdin>',cls_GCD_Ogcd__mult_0) ).

fof(c_0_209,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_6) ).

fof(c_0_210,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_0) ).

fof(c_0_211,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_6) ).

fof(c_0_212,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_0) ).

fof(c_0_213,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_6) ).

fof(c_0_214,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_0) ).

fof(c_0_215,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_6) ).

fof(c_0_216,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_0) ).

fof(c_0_217,axiom,
    ! [X26,X24,X3,X4] : c_Nat_Osize(c_List_Ozip(X24,X26,X4,X3),tc_List_Olist(tc_prod(X4,X3))) = c_Orderings_Omin(c_Nat_Osize(X24,tc_List_Olist(X4)),c_Nat_Osize(X26,tc_List_Olist(X3)),tc_nat),
    file('<stdin>',cls_List_Olength__zip_0) ).

fof(c_0_218,axiom,
    ! [X1,X24,X44,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Onth(c_List_Olist__update(X24,X44,X1,X4),X44,X4) = X1 ),
    file('<stdin>',cls_List_Onth__list__update__eq_0) ).

fof(c_0_219,axiom,
    ! [X19,X14,X4] :
      ( ~ c_in(X19,X14,X4)
      | c_in(c_Pair(X19,X19,X4,X4),c_Relation_Odiag(X14,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Relation_OdiagI_0) ).

fof(c_0_220,axiom,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(c_minus(X14,X13,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_minus(X14,c_insert(X19,X13,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Diff__insert_1) ).

fof(c_0_221,axiom,
    ! [X24,X2,X48,X4] :
      ( c_List_Otake(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_minus(c_Numeral_Onumber__of(X48,tc_nat),c_1,tc_nat),X24,X4),X4)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    file('<stdin>',cls_List_Otake__Cons__number__of_1) ).

fof(c_0_222,axiom,
    ! [X1,X2] :
      ( ~ c_less(X2,X1,tc_nat)
      | c_in(c_Pair(X2,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    file('<stdin>',cls_Wellfounded__Relations_Oless__than__iff_1) ).

fof(c_0_223,axiom,
    ! [X2] :
      ( c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1 ),
    file('<stdin>',cls_Parity_Oneq__one__mod__two_1) ).

fof(c_0_224,axiom,
    ! [X7,X14,X4] :
      ( ~ c_in(X7,c_Relation_Odiag(X14,X4),tc_prod(X4,X4))
      | X7 = c_Pair(c_Main_OdiagE__1(X14,X7,X4),c_Main_OdiagE__1(X14,X7,X4),X4,X4) ),
    file('<stdin>',cls_Relation_OdiagE_0) ).

fof(c_0_225,axiom,
    ! [X24,X22,X44,X4] :
      ( ~ c_lessequals(c_plus(X22,X44,tc_nat),c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Onth(c_List_Odrop(X22,X24,X4),X44,X4) = c_List_Onth(X24,c_plus(X22,X44,tc_nat),X4) ),
    file('<stdin>',cls_List_Onth__drop_0) ).

fof(c_0_226,axiom,
    ! [X16] : c_div(c_Suc(c_Suc(X16)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    file('<stdin>',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).

fof(c_0_227,axiom,
    ! [X24,X2,X60,X44,X4] :
      ( X44 = X60
      | c_List_Onth(c_List_Olist__update(X24,X44,X2,X4),X60,X4) = c_List_Onth(X24,X60,X4) ),
    file('<stdin>',cls_List_Onth__list__update__neq_0) ).

fof(c_0_228,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_plus(X16,c_times(X22,X17,tc_nat),tc_nat),X22,tc_nat) = c_plus(X17,c_div(X16,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Divides_Odiv__mult__self2_0) ).

fof(c_0_229,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_plus(X16,c_times(X17,X22,tc_nat),tc_nat),X22,tc_nat) = c_plus(X17,c_div(X16,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Divides_Odiv__mult__self1_0) ).

fof(c_0_230,axiom,
    ! [X6,X19,X4] : c_in(c_Pair(X19,X19,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)),
    file('<stdin>',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

fof(c_0_231,axiom,
    ! [X48,X16] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X16))),c_Numeral_Onumber__of(X48,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X16,tc_nat),c_Numeral_Onumber__of(X48,tc_nat),tc_nat),
    file('<stdin>',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).

fof(c_0_232,axiom,
    ! [X48,X16] : c_div(c_Suc(c_Suc(c_Suc(X16))),c_Numeral_Onumber__of(X48,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X16,tc_nat),c_Numeral_Onumber__of(X48,tc_nat),tc_nat),
    file('<stdin>',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).

fof(c_0_233,axiom,
    ! [X103,X88,X13,X14] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X14,X13,X88),X103,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X88,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X103),tc_Message_Omsg),
    file('<stdin>',cls_Event_Oused__Says_0) ).

fof(c_0_234,axiom,
    ! [X36,X37,X3,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X36,X3)
      | ~ c_Wellfounded__Recursion_Owf(X37,X4)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X37,X36,X4,X3),tc_prod(X4,X3)) ),
    file('<stdin>',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

fof(c_0_235,axiom,
    ! [X34,X35,X3,X4] :
      ( ~ c_Relation_Otrans(X34,X3)
      | ~ c_Relation_Otrans(X35,X4)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X35,X34,X4,X3),tc_prod(X4,X3)) ),
    file('<stdin>',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

fof(c_0_236,axiom,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X93)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oanalz(c_insert(X88,X89,tc_Message_Omsg)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz__Crypt__if_0) ).

fof(c_0_237,axiom,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X28,X4)
      | ~ c_less(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4)
      | c_less(X2,X1,tc_nat) ),
    file('<stdin>',cls_Power_Opower__strict__increasing__iff_0) ).

fof(c_0_238,axiom,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X28,X4)
      | ~ c_lessequals(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4)
      | c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_Power_Opower__increasing__iff_0) ).

fof(c_0_239,axiom,
    ! [X48,X7,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Osemiring(X3)
      | c_times(c_Numeral_Onumber__of(X48,X3),c_plus(X28,X7,X3),X3) = c_plus(c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),c_times(c_Numeral_Onumber__of(X48,X3),X7,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oright__distrib__number__of_0) ).

fof(c_0_240,axiom,
    ! [X48,X7,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oring(X3)
      | c_times(c_Numeral_Onumber__of(X48,X3),c_minus(X28,X7,X3),X3) = c_minus(c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),c_times(c_Numeral_Onumber__of(X48,X3),X7,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).

fof(c_0_241,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Osemiring(X3)
      | c_times(c_plus(X19,X28,X3),c_Numeral_Onumber__of(X48,X3),X3) = c_plus(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oleft__distrib__number__of_0) ).

fof(c_0_242,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oring(X3)
      | c_times(c_minus(X19,X28,X3),c_Numeral_Onumber__of(X48,X3),X3) = c_minus(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).

fof(c_0_243,axiom,
    ! [X2,X4] : c_in(c_Pair(X2,X2,X4,X4),c_Relation_OId,tc_prod(X4,X4)),
    file('<stdin>',cls_Relation_Opair__in__Id__conv_1) ).

fof(c_0_244,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__15_0) ).

fof(c_0_245,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(X19,c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_2) ).

fof(c_0_246,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(X19,c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_2) ).

fof(c_0_247,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_2) ).

fof(c_0_248,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_0,X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_2) ).

fof(c_0_249,axiom,
    ! [X6,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X6,X4)
      | c_less(c_0,c_divide(X6,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X4),X4),X4) ),
    file('<stdin>',cls_NatSimprocs_Ohalf__gt__zero_0) ).

fof(c_0_250,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).

fof(c_0_251,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).

fof(c_0_252,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).

fof(c_0_253,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).

fof(c_0_254,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).

fof(c_0_255,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).

fof(c_0_256,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).

fof(c_0_257,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).

fof(c_0_258,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).

fof(c_0_259,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).

fof(c_0_260,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).

fof(c_0_261,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).

fof(c_0_262,axiom,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4))
      | c_lessequals(X60,X22,X4)
      | c_lessequals(X60,X44,X4) ),
    file('<stdin>',cls_SetInterval_Oivl__subset_1) ).

fof(c_0_263,axiom,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4))
      | c_lessequals(X16,X44,X4)
      | c_lessequals(X60,X44,X4) ),
    file('<stdin>',cls_SetInterval_Oivl__subset_0) ).

fof(c_0_264,axiom,
    ! [X1,X19,X3,X4] : c_snd(c_Pair(X19,X1,X3,X4),X3,X4) = X1,
    file('<stdin>',cls_Product__Type_Osnd__conv_0) ).

fof(c_0_265,axiom,
    ! [X1,X28,X3,X4] : c_fst(c_Pair(X1,X28,X4,X3),X4,X3) = X1,
    file('<stdin>',cls_Product__Type_Ofst__conv_0) ).

fof(c_0_266,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(X16,c_Suc(c_Suc(c_Suc(X22))),tc_nat) = c_Divides_Oop_Amod(X16,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X22,tc_nat),tc_nat),
    file('<stdin>',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).

fof(c_0_267,axiom,
    ! [X22,X16] : c_div(X16,c_Suc(c_Suc(c_Suc(X22))),tc_nat) = c_div(X16,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X22,tc_nat),tc_nat),
    file('<stdin>',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).

fof(c_0_268,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).

fof(c_0_269,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).

fof(c_0_270,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).

fof(c_0_271,axiom,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).

fof(c_0_272,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X17,tc_nat)
      | ~ c_lessequals(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Omult__le__cancel2_0) ).

fof(c_0_273,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X17,tc_nat)
      | ~ c_lessequals(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Omult__le__cancel1_0) ).

fof(c_0_274,axiom,
    ! [X24,X2,X59,X4] :
      ( ~ c_in(X2,c_List_Oset(c_List_Osublist(X24,X59,X4),X4),X4)
      | c_in(X2,c_List_Oset(X24,X4),X4) ),
    file('<stdin>',cls_List_Onotin__set__sublistI_0) ).

fof(c_0_275,axiom,
    ! [X1,X24,X2,X4] :
      ( ~ c_in(X2,c_List_Oset(c_List_Oremove1(X1,X24,X4),X4),X4)
      | c_in(X2,c_List_Oset(X24,X4),X4) ),
    file('<stdin>',cls_List_Onotin__set__remove1_0) ).

fof(c_0_276,axiom,
    ! [X7,X89,X20] :
      ( ~ c_in(X7,c_Message_Oparts(c_union(X20,X89,tc_Message_Omsg)),tc_Message_Omsg)
      | c_in(X7,c_Message_Oparts(X89),tc_Message_Omsg)
      | c_in(X7,c_Message_Oparts(X20),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oin__parts__UnE_0) ).

fof(c_0_277,axiom,
    ! [X24,X2,X44,X4] : c_Nat_Osize(c_List_Olist__update(X24,X44,X2,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olength__list__update_0) ).

fof(c_0_278,axiom,
    ! [X28,X19,X3,X4] : c_Nat_Osize(c_Pair(X19,X28,X4,X3),tc_prod(X4,X3)) = c_0,
    file('<stdin>',cls_Datatype_Oprod_Osize_0) ).

fof(c_0_279,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_1,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__13_1) ).

fof(c_0_280,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__less__divide__iff__number__of_0) ).

fof(c_0_281,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__le__divide__iff__number__of_0) ).

fof(c_0_282,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__0__iff__number__of_0) ).

fof(c_0_283,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__0__iff__number__of_0) ).

fof(c_0_284,axiom,
    ! [X16,X17,X60] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_minus(c_Suc(c_minus(X60,X17,tc_nat)),X16,tc_nat) = c_minus(c_Suc(X60),c_plus(X17,X16,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatArith_Odiff__Suc__diff__eq2_0) ).

fof(c_0_285,axiom,
    ! [X16,X17,X60] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_minus(X16,c_Suc(c_minus(X60,X17,tc_nat)),tc_nat) = c_minus(c_plus(X16,X17,tc_nat),c_Suc(X60),tc_nat) ),
    file('<stdin>',cls_NatArith_Odiff__Suc__diff__eq1_0) ).

fof(c_0_286,axiom,
    ! [X26,X1,X24,X2,X4] :
      ( c_append(X24,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) != c_append(X26,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4)
      | X2 = X1 ),
    file('<stdin>',cls_List_Oappend1__eq__conv_1) ).

fof(c_0_287,axiom,
    ! [X26,X1,X24,X2,X4] :
      ( c_append(X24,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) != c_append(X26,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4)
      | X24 = X26 ),
    file('<stdin>',cls_List_Oappend1__eq__conv_0) ).

fof(c_0_288,axiom,
    ! [X1,X44,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat)
      | c_List_Olist__update(X1,X44,c_List_Onth(X1,X44,X4),X4) = X1 ),
    file('<stdin>',cls_List_Olist__update__id_0) ).

fof(c_0_289,axiom,
    ! [X16] : c_GCD_Ogcd(c_Pair(c_Suc(c_0),X16,tc_nat,tc_nat)) = c_1,
    file('<stdin>',cls_GCD_Ogcd__1__left_0) ).

fof(c_0_290,axiom,
    ! [X16] : c_GCD_Ogcd(c_Pair(X16,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
    file('<stdin>',cls_GCD_Ogcd__1_0) ).

fof(c_0_291,axiom,
    ! [X12,X48,X28] :
      ( c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | X28 = c_Numeral_Obit_OB0
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X48,X28),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozdiv__number__of__BIT_2) ).

fof(c_0_292,axiom,
    ! [X1] : c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1,
    file('<stdin>',cls_GCD_Ogcd__self_0) ).

fof(c_0_293,axiom,
    ! [X1] : c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1,
    file('<stdin>',cls_GCD_Ogcd__0__left_0) ).

fof(c_0_294,axiom,
    ! [X1] : c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1,
    file('<stdin>',cls_GCD_Ogcd__0_0) ).

fof(c_0_295,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(c_0,X28,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__less__divide__iff__number__of_2) ).

fof(c_0_296,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(X28,c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__less__divide__iff__number__of_1) ).

fof(c_0_297,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(c_0,X28,X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__le__divide__iff__number__of_2) ).

fof(c_0_298,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__le__divide__iff__number__of_1) ).

fof(c_0_299,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(X28,c_0,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__0__iff__number__of_2) ).

fof(c_0_300,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(c_0,X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__0__iff__number__of_1) ).

fof(c_0_301,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__0__iff__number__of_2) ).

fof(c_0_302,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(c_0,X28,X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__0__iff__number__of_1) ).

fof(c_0_303,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4)
      | c_less(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__less__cancel__right_0) ).

fof(c_0_304,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4)
      | c_less(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__less__cancel__left_0) ).

fof(c_0_305,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__le__cancel__right_0) ).

fof(c_0_306,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__le__cancel__left_0) ).

fof(c_0_307,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__divide__eq__number__of_3) ).

fof(c_0_308,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__divide__eq__number__of_3) ).

fof(c_0_309,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__eq__number__of_3) ).

fof(c_0_310,axiom,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__eq__number__of_3) ).

fof(c_0_311,axiom,
    ! [X17,X9,X11,X3,X4] : c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_ONumb(X17,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OScons__not__Numb_0) ).

fof(c_0_312,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OLeaf(X19,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OScons__not__Leaf_0) ).

fof(c_0_313,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OAtom(X19,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OScons__not__Atom_0) ).

fof(c_0_314,axiom,
    ! [X17,X9,X11,X3,X4] : c_Datatype__Universe_ONumb(X17,X4,X3) != c_Datatype__Universe_OScons(X11,X9,X4,X3),
    file('<stdin>',cls_Datatype__Universe_ONumb__not__Scons_0) ).

fof(c_0_315,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OLeaf(X19,X4,X3) != c_Datatype__Universe_OScons(X11,X9,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OLeaf__not__Scons_0) ).

fof(c_0_316,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OAtom(X19,X4,X3) != c_Datatype__Universe_OScons(X11,X9,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OAtom__not__Scons_0) ).

fof(c_0_317,axiom,
    ! [X26,X24,X14,X4] :
      ( ~ c_in(X26,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | ~ c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(c_append(X24,X26,X4),c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Oappend__in__lists__conv_2) ).

fof(c_0_318,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_OHPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OHPair__synth__analz_2) ).

fof(c_0_319,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Onat__add__left__cancel__less_0) ).

fof(c_0_320,axiom,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Onat__add__left__cancel__le_0) ).

fof(c_0_321,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Omult__less__cancel2_1) ).

fof(c_0_322,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Omult__less__cancel1_1) ).

fof(c_0_323,axiom,
    ! [X49,X3,X4] : X49 = c_Pair(c_Main_Osurj__pair__1(X49,X4,X3),c_Main_Osurj__pair__2(X49,X4,X3),X4,X3),
    file('<stdin>',cls_Product__Type_Osurj__pair_0) ).

fof(c_0_324,axiom,
    ! [X1,X3,X4] : c_Pair(c_fst(X1,X4,X3),c_snd(X1,X4,X3),X4,X3) = X1,
    file('<stdin>',cls_Product__Type_Opair__collapse_0) ).

fof(c_0_325,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat)
      | c_less(c_0,X17,tc_nat) ),
    file('<stdin>',cls_Nat_Omult__less__cancel2_0) ).

fof(c_0_326,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat)
      | c_less(c_0,X17,tc_nat) ),
    file('<stdin>',cls_Nat_Omult__less__cancel1_0) ).

fof(c_0_327,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(X28,c_0,X3)
      | c_less(c_0,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__less__divide__iff__number__of_3) ).

fof(c_0_328,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_0,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__le__divide__iff__number__of_3) ).

fof(c_0_329,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(X28,c_0,X3)
      | c_less(c_0,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__0__iff__number__of_3) ).

fof(c_0_330,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_0,X28,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__0__iff__number__of_3) ).

fof(c_0_331,axiom,
    ! [X6,X4] : c_Relation_OImage(c_List_Olistrel(X6,X4),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X4)),tc_List_Olist(X4),tc_List_Olist(X4)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olistrel__Nil_0) ).

fof(c_0_332,axiom,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X60,X22,X4)
      | ~ c_lessequals(X16,X44,X4)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4)) ),
    file('<stdin>',cls_SetInterval_Oivl__subset_3) ).

fof(c_0_333,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | c_Numeral_Onumber__of(X2,X4) = c_1 ),
    file('<stdin>',cls_IntArith_Oarith__special__9_1) ).

fof(c_0_334,axiom,
    ! [X6,X3,X4] :
      ( ~ c_in(c_Relation_Oconverse(X6,X3,X4),c_Finite__Set_OFinites,tc_set(tc_prod(X4,X3)))
      | c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X3,X4))) ),
    file('<stdin>',cls_Finite__Set_Ofinite__converse_0) ).

fof(c_0_335,axiom,
    ! [X88,X93,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oparts(c_insert(X88,X89,tc_Message_Omsg)),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__Crypt_0) ).

fof(c_0_336,axiom,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(X2,X1,tc_nat)
      | ~ c_less(c_1,X28,X4)
      | c_less(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4) ),
    file('<stdin>',cls_Power_Opower__strict__increasing__iff_1) ).

fof(c_0_337,axiom,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X28,X4)
      | ~ c_lessequals(X2,X1,tc_nat)
      | c_lessequals(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4) ),
    file('<stdin>',cls_Power_Opower__increasing__iff_1) ).

fof(c_0_338,axiom,
    ! [X66,X61,X19,X42] :
      ( ~ c_in(X19,c_List_Oset(X66,X42),X42)
      | c_List_Olist__inter(c_List_Olist_OCons(X19,X61,X42),X66,X42) = c_List_Olist_OCons(X19,c_List_Olist__inter(X61,X66,X42),X42) ),
    file('<stdin>',cls_List_Olist__inter_Osimps__2_0) ).

fof(c_0_339,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X2)),X4),X4)
      | ~ c_lessequals(c_Numeral_Onumber__of(X2,X4),c_1,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__17_0) ).

fof(c_0_340,axiom,
    ! [X22,X16,X44] :
      ( ~ c_lessequals(c_plus(X44,X16,tc_nat),X22,tc_nat)
      | c_List_Otake(X16,c_List_Oupt(X44,X22),tc_nat) = c_List_Oupt(X44,c_plus(X44,X16,tc_nat)) ),
    file('<stdin>',cls_List_Otake__upt_0) ).

fof(c_0_341,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_0,X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__less__divide__iff__number__of_5) ).

fof(c_0_342,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X28,X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__less__divide__iff__number__of_4) ).

fof(c_0_343,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_0,X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__le__divide__iff__number__of_5) ).

fof(c_0_344,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X28,X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ozero__le__divide__iff__number__of_4) ).

fof(c_0_345,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X28,X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__0__iff__number__of_5) ).

fof(c_0_346,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_0,X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__less__0__iff__number__of_4) ).

fof(c_0_347,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X28,X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__0__iff__number__of_5) ).

fof(c_0_348,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_0,X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    file('<stdin>',cls_NatSimprocs_Odivide__le__0__iff__number__of_4) ).

fof(c_0_349,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_0,X2,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Ozero__less__power__eq__number__of_0) ).

fof(c_0_350,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(X2,c_Main_OMin__gr__iff__1(X14,X2,X4),X4)
      | c_less(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__gr__iff_2) ).

fof(c_0_351,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X14,X2,X4),X4)
      | c_lessequals(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__ge__iff_2) ).

fof(c_0_352,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(c_Main_OMax__less__iff__1(X14,X2,X4),X2,X4)
      | c_less(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__less__iff_2) ).

fof(c_0_353,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(c_Main_OMax__le__iff__1(X14,X2,X4),X2,X4)
      | c_lessequals(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__le__iff_2) ).

fof(c_0_354,axiom,
    ! [X19,X14,X4] : c_insert(X19,c_minus(X14,c_insert(X19,c_emptyset,X4),tc_set(X4)),X4) = c_insert(X19,X14,X4),
    file('<stdin>',cls_Set_Oinsert__Diff__single_0) ).

fof(c_0_355,axiom,
    ! [X26,X1,X4] : c_List_Orev(c_append(c_List_Orev(X26,X4),c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4),X4) = c_List_Olist_OCons(X1,X26,X4),
    file('<stdin>',cls_List_Orev__eq__Cons__iff_1) ).

fof(c_0_356,axiom,
    ! [X19,X13,X14,X4] : c_inter(c_insert(X19,X14,X4),c_insert(X19,X13,X4),X4) = c_insert(X19,c_inter(X14,X13,X4),X4),
    file('<stdin>',cls_Set_Oinsert__inter__insert_0) ).

fof(c_0_357,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X15,X27,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).

fof(c_0_358,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_0,X2,X4) ),
    file('<stdin>',cls_Parity_Ozero__le__power__eq__number__of_0) ).

fof(c_0_359,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(X2,c_0,X4) ),
    file('<stdin>',cls_Parity_Opower__le__zero__eq__number__of_2) ).

fof(c_0_360,axiom,
    ! [X103,X88,X14] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X14,X88),X103,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X88,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X103),tc_Message_Omsg),
    file('<stdin>',cls_Event_Oused__Notes_0) ).

fof(c_0_361,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(X16,X22,tc_nat)
      | ~ c_less(c_0,X17,tc_nat)
      | c_less(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Omult__less__cancel2_2) ).

fof(c_0_362,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(X16,X22,tc_nat)
      | ~ c_less(c_0,X17,tc_nat)
      | c_less(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Omult__less__cancel1_2) ).

fof(c_0_363,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X15,c_plus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).

fof(c_0_364,axiom,
    ! [X29,X4] :
      ( ~ c_in(X29,c_Relation_OId,tc_prod(X4,X4))
      | X29 = c_Pair(c_Main_OIdE__1(X29,X4),c_Main_OIdE__1(X29,X4),X4,X4) ),
    file('<stdin>',cls_Relation_OIdE_0) ).

fof(c_0_365,axiom,
    ! [X22,X16,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X44,X22,X4)
      | c_minus(c_SetInterval_OatLeastLessThan(X44,X16,X4),c_SetInterval_OatLeastLessThan(X44,X22,X4),tc_set(X4)) = c_SetInterval_OatLeastLessThan(X22,X16,X4) ),
    file('<stdin>',cls_SetInterval_Oivl__diff_0) ).

fof(c_0_366,axiom,
    ! [X16] : c_Divides_Oop_Amod(c_Suc(c_Suc(X16)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    file('<stdin>',cls_NatSimprocs_Omod2__Suc__Suc_0) ).

fof(c_0_367,axiom,
    ! [X22,X16,X17] : c_Divides_Oop_Amod(c_plus(X16,c_times(X22,X17,tc_nat),tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    file('<stdin>',cls_Divides_Omod__mult__self2_0) ).

fof(c_0_368,axiom,
    ! [X22,X16,X17] : c_Divides_Oop_Amod(c_plus(X16,c_times(X17,X22,tc_nat),tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    file('<stdin>',cls_Divides_Omod__mult__self1_0) ).

fof(c_0_369,axiom,
    ! [X27,X19,X14,X4] :
      ( ~ c_in(X19,X14,X4)
      | ~ c_in(X27,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(c_List_Olist_OCons(X19,X27,X4),c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Olists_OCons_0) ).

fof(c_0_370,axiom,
    ! [X17,X44,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_ONumb(X44,X4,X3),X4,X3) = c_Datatype__Universe_ONumb(X44,X4,X3),
    file('<stdin>',cls_Datatype__Universe_Ontrunc__Numb_0) ).

fof(c_0_371,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_OLeaf(X19,X4,X3),X4,X3) = c_Datatype__Universe_OLeaf(X19,X4,X3),
    file('<stdin>',cls_Datatype__Universe_Ontrunc__Leaf_0) ).

fof(c_0_372,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_OAtom(X19,X4,X3),X4,X3) = c_Datatype__Universe_OAtom(X19,X4,X3),
    file('<stdin>',cls_Datatype__Universe_Ontrunc__Atom_0) ).

fof(c_0_373,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_1,X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__13_0) ).

fof(c_0_374,axiom,
    ! [X26,X1,X24,X4] : c_List_Onth(c_append(X24,c_List_Olist_OCons(X1,X26,X4),X4),c_Nat_Osize(X24,tc_List_Olist(X4)),X4) = X1,
    file('<stdin>',cls_List_Onth__append__length_0) ).

fof(c_0_375,axiom,
    ! [X12,X48,X28] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X48,X28),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozdiv__number__of__BIT_1) ).

fof(c_0_376,axiom,
    ! [X103,X88,X13,X14] : c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X14,X13,X88),X103,tc_Event_Oevent)) = c_insert(X88,c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg),
    file('<stdin>',cls_Event_Oknows__Spy__Says_0) ).

fof(c_0_377,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_less(c_1,c_divide(X28,X19,X4),X4)
      | c_less(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oless__divide__eq__1__pos_0) ).

fof(c_0_378,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_less(c_1,c_divide(X28,X19,X4),X4)
      | c_less(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oless__divide__eq__1__neg_0) ).

fof(c_0_379,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(c_1,c_divide(X28,X19,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ole__divide__eq__1__pos_0) ).

fof(c_0_380,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(c_1,c_divide(X28,X19,X4),X4)
      | c_lessequals(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ole__divide__eq__1__neg_0) ).

fof(c_0_381,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_less(c_divide(X28,X19,X4),c_1,X4)
      | c_less(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__less__eq__1__pos_0) ).

fof(c_0_382,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_less(c_divide(X28,X19,X4),c_1,X4)
      | c_less(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__less__eq__1__neg_0) ).

fof(c_0_383,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(c_divide(X28,X19,X4),c_1,X4)
      | c_lessequals(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__le__eq__1__pos_0) ).

fof(c_0_384,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(c_divide(X28,X19,X4),c_1,X4)
      | c_lessequals(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__le__eq__1__neg_0) ).

fof(c_0_385,axiom,
    ! [X12,X48,X7,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_minus(X7,c_Numeral_Onumber__of(X12,X4),X4),X4) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X12)),X4),X7,X4) ),
    file('<stdin>',cls_Numeral_Oadd__number__of__diff2_0) ).

fof(c_0_386,axiom,
    ! [X2] :
      ( c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
      | c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1 ),
    file('<stdin>',cls_Parity_Oneq__one__mod__two_0) ).

fof(c_0_387,axiom,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Ozero__less__power__eq__number__of_1) ).

fof(c_0_388,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4)
      | c_less(c_1,c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__11_1) ).

fof(c_0_389,axiom,
    ! [X24,X2,X48,X4] :
      ( c_List_Onth(c_List_Olist_OCons(X2,X24,X4),c_Numeral_Onumber__of(X48,tc_nat),X4) = c_List_Onth(X24,c_minus(c_Numeral_Onumber__of(X48,tc_nat),c_1,tc_nat),X4)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    file('<stdin>',cls_List_Onth__Cons__number__of_1) ).

fof(c_0_390,axiom,
    ! [X24,X2,X48,X4] :
      ( c_List_Odrop(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X48,tc_nat),c_1,tc_nat),X24,X4)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    file('<stdin>',cls_List_Odrop__Cons__number__of_1) ).

fof(c_0_391,axiom,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_less(c_0,c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Ozero__less__power__eq__number__of_2) ).

fof(c_0_392,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_less(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__less__iff__less__neg_0) ).

fof(c_0_393,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_less(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__less__iff__less_0) ).

fof(c_0_394,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_lessequals(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__le__iff__le__neg_0) ).

fof(c_0_395,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_lessequals(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__le__iff__le_0) ).

fof(c_0_396,axiom,
    ! [X17,X60,X44] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_minus(X44,c_minus(X60,X17,tc_nat),tc_nat) = c_minus(c_plus(X44,X17,tc_nat),X60,tc_nat) ),
    file('<stdin>',cls_NatArith_Odiff__diff__right_0) ).

fof(c_0_397,axiom,
    ! [X17,X60,X44] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_plus(X44,c_minus(X60,X17,tc_nat),tc_nat) = c_minus(c_plus(X44,X60,tc_nat),X17,tc_nat) ),
    file('<stdin>',cls_NatArith_Oadd__diff__assoc_0) ).

fof(c_0_398,axiom,
    ! [X17,X60,X44] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_plus(c_minus(X60,X17,tc_nat),X44,tc_nat) = c_minus(c_plus(X60,X44,tc_nat),X17,tc_nat) ),
    file('<stdin>',cls_NatArith_Oadd__diff__assoc2_0) ).

fof(c_0_399,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | X2 = c_0 ),
    file('<stdin>',cls_Parity_Opower__le__zero__eq__number__of_1) ).

fof(c_0_400,axiom,
    ! [X26,X24,X22,X4] : c_List_Onth(c_append(X24,X26,X4),c_plus(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat),X4) = c_List_Onth(X26,X22,X4),
    file('<stdin>',cls_List_Onth__append__length__plus_0) ).

fof(c_0_401,axiom,
    ! [X7,X28,X19] :
      ( ~ c_less(c_0,X7,tc_nat)
      | c_div(c_times(X19,X7,tc_nat),c_times(X28,X7,tc_nat),tc_nat) = c_div(X19,X28,tc_nat) ),
    file('<stdin>',cls_Divides_Odiv__mult__mult2_0) ).

fof(c_0_402,axiom,
    ! [X7,X28,X19] :
      ( ~ c_less(c_0,X7,tc_nat)
      | c_div(c_times(X7,X19,tc_nat),c_times(X7,X28,tc_nat),tc_nat) = c_div(X19,X28,tc_nat) ),
    file('<stdin>',cls_Divides_Odiv__mult__mult1_0) ).

fof(c_0_403,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | ~ c_less(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4) ),
    file('<stdin>',cls_Parity_Opower__less__zero__eq__number__of_0) ).

fof(c_0_404,axiom,
    ! [X6,X3,X4] :
      ( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X3,X4)))
      | c_in(c_Relation_Oconverse(X6,X3,X4),c_Finite__Set_OFinites,tc_set(tc_prod(X4,X3))) ),
    file('<stdin>',cls_Finite__Set_Ofinite__converse_1) ).

fof(c_0_405,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OHash__synth__analz_0) ).

fof(c_0_406,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_lessequals(X2,c_0,X4)
      | X2 = c_0 ),
    file('<stdin>',cls_Parity_Opower__le__zero__eq__number__of_3) ).

fof(c_0_407,axiom,
    ! [X89,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X89,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X89,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__synth__Un_0) ).

fof(c_0_408,axiom,
    ! [X1,X2,X44,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X44,tc_nat)
      | c_List_Olist__update(X1,X44,X2,X4) = X1 ),
    file('<stdin>',cls_List_Olist__update__beyond_0) ).

fof(c_0_409,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_less(X2,c_0,X4) ),
    file('<stdin>',cls_Parity_Opower__less__zero__eq__number__of_1) ).

fof(c_0_410,axiom,
    ! [X26,X24,X14,X4] :
      ( ~ c_in(c_append(X24,X26,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X26,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Oappend__in__lists__conv_1) ).

fof(c_0_411,axiom,
    ! [X26,X24,X14,X4] :
      ( ~ c_in(c_append(X24,X26,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Oappend__in__lists__conv_0) ).

fof(c_0_412,axiom,
    ! [X2,X27,X14,X4] :
      ( ~ c_in(c_List_Olist_OCons(X2,X27,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X27,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_OlistsE_0) ).

fof(c_0_413,axiom,
    ! [X48] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).

fof(c_0_414,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OHash__synth__analz_1) ).

fof(c_0_415,axiom,
    ! [X2,X12] :
      ( ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),tc_nat),tc_nat)
      | c_less(c_0,X2,tc_nat)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).

fof(c_0_416,axiom,
    ! [X17,X60,X44] :
      ( ~ c_less(c_plus(X44,X17,tc_nat),X60,tc_nat)
      | c_List_Onth(c_List_Oupt(X44,X60),X17,tc_nat) = c_plus(X44,X17,tc_nat) ),
    file('<stdin>',cls_List_Onth__upt_0) ).

fof(c_0_417,axiom,
    ! [X49,X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_Numeral_Onumber__of(X48,X4),c_times(c_Numeral_Onumber__of(X12,X4),X49,X4),X4) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X48,X12),X4),X49,X4) ),
    file('<stdin>',cls_Numeral_Omult__number__of__left_0) ).

fof(c_0_418,axiom,
    ! [X49,X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_plus(c_Numeral_Onumber__of(X12,X4),X49,X4),X4) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,X12),X4),X49,X4) ),
    file('<stdin>',cls_Numeral_Oadd__number__of__left_0) ).

fof(c_0_419,axiom,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(X2,c_Finite__Set_OMin(X14,X4),X4)
      | c_less(X2,X25,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__gr__iff_0) ).

fof(c_0_420,axiom,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(X2,c_Finite__Set_OMin(X14,X4),X4)
      | c_lessequals(X2,X25,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__ge__iff_0) ).

fof(c_0_421,axiom,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(c_Finite__Set_OMax(X14,X4),X2,X4)
      | c_less(X25,X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__less__iff_0) ).

fof(c_0_422,axiom,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(c_Finite__Set_OMax(X14,X4),X2,X4)
      | c_lessequals(X25,X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__le__iff_0) ).

fof(c_0_423,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    file('<stdin>',cls_NatBin_Omod__nat__number__of_2) ).

fof(c_0_424,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | c_lessequals(c_1,c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__15_1) ).

fof(c_0_425,axiom,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X60,X44,X4)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4)) ),
    file('<stdin>',cls_SetInterval_Oivl__subset_2) ).

fof(c_0_426,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__less__iff__less__neg_1) ).

fof(c_0_427,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__less__iff__less_1) ).

fof(c_0_428,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__le__iff__le__neg_1) ).

fof(c_0_429,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__le__iff__le_1) ).

fof(c_0_430,axiom,
    ! [X2,X14,X4] :
      ( ~ c_lessequals(X14,c_insert(X2,c_emptyset,X4),tc_set(X4))
      | c_insert(X2,X14,X4) = c_insert(X2,c_emptyset,X4) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_H_2) ).

fof(c_0_431,axiom,
    ! [X2,X14,X4] :
      ( ~ c_lessequals(X14,c_insert(X2,c_emptyset,X4),tc_set(X4))
      | c_insert(X2,c_emptyset,X4) = c_insert(X2,X14,X4) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_2) ).

fof(c_0_432,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X4),X4)
      | ~ c_lessequals(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__13_0) ).

fof(c_0_433,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_union(X14,X13,X4),X4)
      | c_in(X7,X13,X4)
      | c_in(X7,X14,X4) ),
    file('<stdin>',cls_Set_OUn__iff_0) ).

fof(c_0_434,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__less__cancel__right_1) ).

fof(c_0_435,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__less__cancel__left_1) ).

fof(c_0_436,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__le__cancel__right_1) ).

fof(c_0_437,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oadd__le__cancel__left_1) ).

fof(c_0_438,axiom,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X13,X33,tc_set(X4))
      | ~ c_lessequals(X14,X33,tc_set(X4))
      | c_lessequals(c_union(X14,X13,X4),X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OUn__subset__iff_2) ).

fof(c_0_439,axiom,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X33,X13,tc_set(X4))
      | ~ c_lessequals(X33,X14,tc_set(X4))
      | c_lessequals(X33,c_inter(X14,X13,X4),tc_set(X4)) ),
    file('<stdin>',cls_Set_OInt__subset__iff_2) ).

fof(c_0_440,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X13,X4)
      | ~ c_in(X7,c_minus(X14,X13,tc_set(X4)),X4) ),
    file('<stdin>',cls_Set_ODiff__iff_1) ).

fof(c_0_441,axiom,
    ! [X2,X27,X14,X4] :
      ( ~ c_in(c_List_Olist_OCons(X2,X27,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X2,X14,X4) ),
    file('<stdin>',cls_List_OlistsE_1) ).

fof(c_0_442,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) != c_0 ),
    file('<stdin>',cls_Parity_Opower__le__zero__eq__number__of_0) ).

fof(c_0_443,axiom,
    ! [X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X11,X4,X3),X4,X3) = c_emptyset,
    file('<stdin>',cls_Datatype__Universe_Ontrunc__one__In1_0) ).

fof(c_0_444,axiom,
    ! [X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X11,X4,X3),X4,X3) = c_emptyset,
    file('<stdin>',cls_Datatype__Universe_Ontrunc__one__In0_0) ).

fof(c_0_445,axiom,
    ! [X20,X21,X4] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_in(X21,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_union(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Un_2) ).

fof(c_0_446,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(X2,c_0,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Opower__le__zero__eq__number__of_4) ).

fof(c_0_447,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X84),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatBin_Oless__nat__number__of_4) ).

fof(c_0_448,axiom,
    ! [X2,X13,X14,X4] :
      ( ~ c_in(X2,X13,X4)
      | ~ c_lessequals(X14,X13,tc_set(X4))
      | c_lessequals(c_insert(X2,X14,X4),X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_Oinsert__subset_2) ).

fof(c_0_449,axiom,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Power_Orecpower(X3)
      | c_Nat_Opower(c_Numeral_Onumber__of(X12,X3),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3) = c_times(c_Numeral_Onumber__of(X12,X3),c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatBin_Opower2__eq__square__number__of_0) ).

fof(c_0_450,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_plus(X16,X22,tc_nat),tc_nat)
      | c_less(c_0,X22,tc_nat)
      | c_less(c_0,X16,tc_nat) ),
    file('<stdin>',cls_Nat_Oadd__gr__0_0) ).

fof(c_0_451,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_1,c_divide(X28,X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oless__divide__eq__1__pos_1) ).

fof(c_0_452,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_1,c_divide(X28,X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oless__divide__eq__1__neg_1) ).

fof(c_0_453,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_1,c_divide(X28,X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Ole__divide__eq__1__pos_1) ).

fof(c_0_454,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_1,c_divide(X28,X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Ole__divide__eq__1__neg_1) ).

fof(c_0_455,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_divide(X28,X19,X4),c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__less__eq__1__pos_1) ).

fof(c_0_456,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,X28,X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_divide(X28,X19,X4),c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__less__eq__1__neg_1) ).

fof(c_0_457,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_divide(X28,X19,X4),c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__le__eq__1__pos_1) ).

fof(c_0_458,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_divide(X28,X19,X4),c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__le__eq__1__neg_1) ).

fof(c_0_459,axiom,
    ! [X22,X16,X17] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Onat__add__left__cancel__less_1) ).

fof(c_0_460,axiom,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Onat__add__left__cancel__le_1) ).

fof(c_0_461,axiom,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Omult__le__cancel2_2) ).

fof(c_0_462,axiom,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Omult__le__cancel1_2) ).

fof(c_0_463,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMin__gr__iff__1(X14,X2,X4),X14,X4)
      | c_less(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__gr__iff_1) ).

fof(c_0_464,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMin__ge__iff__1(X14,X2,X4),X14,X4)
      | c_lessequals(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__ge__iff_1) ).

fof(c_0_465,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMax__less__iff__1(X14,X2,X4),X14,X4)
      | c_less(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__less__iff_1) ).

fof(c_0_466,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMax__le__iff__1(X14,X2,X4),X14,X4)
      | c_lessequals(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__le__iff_1) ).

fof(c_0_467,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_OHPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OHPair__synth__analz_0) ).

fof(c_0_468,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X44,X15,X4)
      | ~ c_less(X27,X44,X4)
      | c_in(X44,c_SetInterval_OgreaterThanLessThan(X27,X15,X4),X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThanLessThan__iff_2) ).

fof(c_0_469,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X27,X44,X4)
      | ~ c_lessequals(X44,X15,X4)
      | c_in(X44,c_SetInterval_OgreaterThanAtMost(X27,X15,X4),X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThanAtMost__iff_2) ).

fof(c_0_470,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X44,X15,X4)
      | ~ c_lessequals(X27,X44,X4)
      | c_in(X44,c_SetInterval_OatLeastLessThan(X27,X15,X4),X4) ),
    file('<stdin>',cls_SetInterval_OatLeastLessThan__iff_2) ).

fof(c_0_471,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_lessequals(X44,X15,X4)
      | ~ c_lessequals(X27,X44,X4)
      | c_in(X44,c_SetInterval_OatLeastAtMost(X27,X15,X4),X4) ),
    file('<stdin>',cls_SetInterval_OatLeastAtMost__iff_2) ).

fof(c_0_472,axiom,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X1,X49,X3)
      | ~ c_lessequals(X2,X49,X3)
      | c_lessequals(c_Orderings_Omax(X2,X1,X3),X49,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).

fof(c_0_473,axiom,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,X49,X3)
      | ~ c_lessequals(X2,X1,X3)
      | c_lessequals(X2,c_Orderings_Omin(X1,X49,X3),X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).

fof(c_0_474,axiom,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X49,X1,X4)
      | ~ c_less(X49,X2,X4)
      | c_less(X49,c_Orderings_Omin(X2,X1,X4),X4) ),
    file('<stdin>',cls_Orderings_Omin__less__iff__conj_2) ).

fof(c_0_475,axiom,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X1,X49,X4)
      | ~ c_less(X2,X49,X4)
      | c_less(c_Orderings_Omax(X2,X1,X4),X49,X4) ),
    file('<stdin>',cls_Orderings_Omax__less__iff__conj_2) ).

fof(c_0_476,axiom,
    ! [X24,X14,X4] :
      ( ~ c_in(c_Main_Oin__listsI__1(X14,X24,X4),X14,X4)
      | c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Oin__listsI_1) ).

fof(c_0_477,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_Message_Osynth(c_Message_Oanalz(c_insert(X88,X89,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X89)) ),
    file('<stdin>',cls_Message_OFake__analz__eq_0) ).

fof(c_0_478,axiom,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(X19,X13,X4)
      | c_emptyset != c_inter(c_insert(X19,X14,X4),X13,X4) ),
    file('<stdin>',cls_Set_Oinsert__disjoint__2_0) ).

fof(c_0_479,axiom,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(X19,X13,X4)
      | c_inter(c_insert(X19,X14,X4),X13,X4) != c_emptyset ),
    file('<stdin>',cls_Set_Oinsert__disjoint__1_0) ).

fof(c_0_480,axiom,
    ! [X28,X13,X14,X4] :
      ( ~ c_in(X28,X14,X4)
      | c_emptyset != c_inter(X14,c_insert(X28,X13,X4),X4) ),
    file('<stdin>',cls_Set_Odisjoint__insert__2_0) ).

fof(c_0_481,axiom,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(X19,X13,X4)
      | c_inter(X13,c_insert(X19,X14,X4),X4) != c_emptyset ),
    file('<stdin>',cls_Set_Odisjoint__insert__1_0) ).

fof(c_0_482,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,X2,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    file('<stdin>',cls_Parity_Ozero__less__power__eq__number__of_5) ).

fof(c_0_483,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,X2,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    file('<stdin>',cls_Parity_Ozero__le__power__eq__number__of_2) ).

fof(c_0_484,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(X2,c_0,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4) ),
    file('<stdin>',cls_Parity_Opower__less__zero__eq__number__of_2) ).

fof(c_0_485,axiom,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X4),X22,X4),X4)
      | X22 = c_0 ),
    file('<stdin>',cls_Power_Ozero__less__power__abs__iff_0) ).

fof(c_0_486,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X19,X7,X4),c_times(X28,X7,X4),X4) = c_divide(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__right__if_1) ).

fof(c_0_487,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X7,X19,X4),c_times(X7,X28,X4),X4) = c_divide(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__left__if_1) ).

fof(c_0_488,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_plus(c_HOL_Oabs(X19,X4),c_HOL_Oabs(X28,X4),X4),X4) = c_plus(c_HOL_Oabs(X19,X4),c_HOL_Oabs(X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__add__abs_0) ).

fof(c_0_489,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_divide(X28,X7,X4),X4) = c_divide(c_times(X19,X7,X4),X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__divide__eq__right_0) ).

fof(c_0_490,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_divide(X19,X28,X4),X7,X4) = c_divide(X19,c_times(X28,X7,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__divide__eq__left_0) ).

fof(c_0_491,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | ~ c_in(X28,c_IntDef_ONats,X4)
      | ~ c_in(X19,c_IntDef_ONats,X4)
      | c_in(c_times(X19,X28,X4),c_IntDef_ONats,X4) ),
    file('<stdin>',cls_IntDef_ONats__mult_0) ).

fof(c_0_492,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | ~ c_in(X28,c_IntDef_ONats,X4)
      | ~ c_in(X19,c_IntDef_ONats,X4)
      | c_in(c_plus(X19,X28,X4),c_IntDef_ONats,X4) ),
    file('<stdin>',cls_IntDef_ONats__add_0) ).

fof(c_0_493,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X28,c_IntDef_OInts,X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_times(X19,X28,X4),c_IntDef_OInts,X4) ),
    file('<stdin>',cls_IntDef_OInts__mult_0) ).

fof(c_0_494,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X28,c_IntDef_OInts,X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_minus(X19,X28,X4),c_IntDef_OInts,X4) ),
    file('<stdin>',cls_IntDef_OInts__diff_0) ).

fof(c_0_495,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X28,c_IntDef_OInts,X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_plus(X19,X28,X4),c_IntDef_OInts,X4) ),
    file('<stdin>',cls_IntDef_OInts__add_0) ).

fof(c_0_496,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__11_0) ).

fof(c_0_497,axiom,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Main_OInter__iff__1(X14,X33,X4),X4)
      | c_in(X14,c_Inter(X33,X4),X4) ),
    file('<stdin>',cls_Set_OInter__iff_2) ).

fof(c_0_498,axiom,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Main_OInterI__1(X14,X33,X4),X4)
      | c_in(X14,c_Inter(X33,X4),X4) ),
    file('<stdin>',cls_Set_OInterI_1) ).

fof(c_0_499,axiom,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(X26,X4)
      | ~ c_List_Odistinct(X24,X4)
      | c_inter(c_List_Oset(X24,X4),c_List_Oset(X26,X4),X4) != c_emptyset
      | c_List_Odistinct(c_append(X24,X26,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__append_3) ).

fof(c_0_500,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X13,X4)
      | ~ c_in(X7,X14,X4)
      | c_in(X7,c_inter(X14,X13,X4),X4) ),
    file('<stdin>',cls_Set_OInt__iff_2) ).

fof(c_0_501,axiom,
    ! [X12,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_nat),tc_IntDef_Oint)) ),
    file('<stdin>',cls_NatBin_Opower__nat__number__of__number__of_1) ).

fof(c_0_502,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    file('<stdin>',cls_NatBin_Odiv__nat__number__of_1) ).

fof(c_0_503,axiom,
    ! [X24,X2,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Oset(c_List_Oremove1(X2,X24,X4),X4) = c_minus(c_List_Oset(X24,X4),c_insert(X2,c_emptyset,X4),tc_set(X4)) ),
    file('<stdin>',cls_List_Oset__remove1__eq_0) ).

fof(c_0_504,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X19,X14,X4) != c_insert(X28,c_emptyset,X4)
      | c_lessequals(X14,c_insert(X28,c_emptyset,X4),tc_set(X4)) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_H_1) ).

fof(c_0_505,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X28,c_emptyset,X4) != c_insert(X19,X14,X4)
      | c_lessequals(X14,c_insert(X28,c_emptyset,X4),tc_set(X4)) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_1) ).

fof(c_0_506,axiom,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(tc_set(X4)))
      | ~ c_in(c_Main_Ofinite__Union__1(X14,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Union(X14,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Union_1) ).

fof(c_0_507,axiom,
    ! [X22,X16,X17] : c_minus(c_minus(c_Suc(X16),X22,tc_nat),c_Suc(X17),tc_nat) = c_minus(c_minus(X16,X22,tc_nat),X17,tc_nat),
    file('<stdin>',cls_Nat_OSuc__diff__diff_0) ).

fof(c_0_508,axiom,
    ! [X24,X22,X4] :
      ( ~ c_less(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_in(c_List_Onth(X24,X22,X4),c_List_Oset(X24,X4),X4) ),
    file('<stdin>',cls_List_Onth__mem_0) ).

fof(c_0_509,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_divide(X28,X7,X4),X19,X4) = c_divide(c_times(X28,X19,X4),X7,X4) ),
    file('<stdin>',cls_Ring__and__Field_Otimes__divide__eq__2_0) ).

fof(c_0_510,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X19,c_divide(X28,X7,X4),X4) = c_divide(c_times(X19,X28,X4),X7,X4) ),
    file('<stdin>',cls_Ring__and__Field_Otimes__divide__eq__1_0) ).

fof(c_0_511,axiom,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3)
      | c_less(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).

fof(c_0_512,axiom,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3)
      | c_lessequals(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).

fof(c_0_513,axiom,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).

fof(c_0_514,axiom,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).

fof(c_0_515,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4)
      | c_1 = c_Numeral_Onumber__of(X1,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__7_1) ).

fof(c_0_516,axiom,
    ! [X1,X24,X4] : c_List_Olast(c_append(X24,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4),X4) = X1,
    file('<stdin>',cls_List_Olast__snoc_0) ).

fof(c_0_517,axiom,
    ! [X1,X2,X4] : c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4),X4) = X1,
    file('<stdin>',cls_List_Obutlast__snoc_0) ).

fof(c_0_518,axiom,
    ! [X7,X14,X4] :
      ( ~ c_in(X7,c_Relation_Odiag(X14,X4),tc_prod(X4,X4))
      | c_in(c_Main_OdiagE__1(X14,X7,X4),X14,X4) ),
    file('<stdin>',cls_Relation_OdiagE_1) ).

fof(c_0_519,axiom,
    ! [X24,X2,X22,X4] : c_List_Otake(c_Suc(X22),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X22,X24,X4),X4),
    file('<stdin>',cls_List_Otake__Suc__Cons_0) ).

fof(c_0_520,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_minus(X14,X13,tc_set(X4)),X4)
      | c_in(X7,X14,X4) ),
    file('<stdin>',cls_Set_ODiff__iff_0) ).

fof(c_0_521,axiom,
    ! [X13,X14,X4] : c_Relation_OImage(c_Relation_Odiag(X14,X4),X13,X4,X4) = c_inter(X14,X13,X4),
    file('<stdin>',cls_Relation_OImage__diag_0) ).

fof(c_0_522,axiom,
    ! [X1,X2] :
      ( ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | c_IntDef_OAbs__Integ(X2) != c_IntDef_OAbs__Integ(X1)
      | X2 = X1 ),
    file('<stdin>',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).

fof(c_0_523,axiom,
    ! [X103,X88,X14] :
      ( ~ c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X14,X88),X103,tc_Event_Oevent)) = c_insert(X88,c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg) ),
    file('<stdin>',cls_Event_Oknows__Spy__Notes_0) ).

fof(c_0_524,axiom,
    ! [X1,X24,X2,X42] :
      ( X2 = X1
      | c_List_Oremove1(X2,c_List_Olist_OCons(X1,X24,X42),X42) = c_List_Olist_OCons(X1,c_List_Oremove1(X2,X24,X42),X42) ),
    file('<stdin>',cls_List_Oremove1_Osimps__2_1) ).

fof(c_0_525,axiom,
    ! [X2,X13,X14,X4] :
      ( ~ c_lessequals(c_insert(X2,X14,X4),X13,tc_set(X4))
      | c_lessequals(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_Oinsert__subset_1) ).

fof(c_0_526,axiom,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(c_union(X14,X13,X4),X33,tc_set(X4))
      | c_lessequals(X13,X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OUn__subset__iff_1) ).

fof(c_0_527,axiom,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(c_union(X14,X13,X4),X33,tc_set(X4))
      | c_lessequals(X14,X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OUn__subset__iff_0) ).

fof(c_0_528,axiom,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X33,c_inter(X14,X13,X4),tc_set(X4))
      | c_lessequals(X33,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_OInt__subset__iff_1) ).

fof(c_0_529,axiom,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X33,c_inter(X14,X13,X4),tc_set(X4))
      | c_lessequals(X33,X14,tc_set(X4)) ),
    file('<stdin>',cls_Set_OInt__subset__iff_0) ).

fof(c_0_530,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(c_1,X22,tc_nat)
      | ~ c_lessequals(c_1,X16,tc_nat)
      | c_lessequals(c_Suc(c_0),c_times(X16,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Oone__le__mult__iff_2) ).

fof(c_0_531,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | ~ c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__synth__analz_2) ).

fof(c_0_532,axiom,
    ! [X88,X93,X89] :
      ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X93)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz__Crypt__if_1) ).

fof(c_0_533,axiom,
    ! [X19,X13,X14,X4] : c_union(X14,c_insert(X19,X13,X4),X4) = c_insert(X19,c_union(X14,X13,X4),X4),
    file('<stdin>',cls_Set_OUn__insert__right_0) ).

fof(c_0_534,axiom,
    ! [X19,X33,X13,X4] : c_union(c_insert(X19,X13,X4),X33,X4) = c_insert(X19,c_union(X13,X33,X4),X4),
    file('<stdin>',cls_Set_OUn__insert__left_0) ).

fof(c_0_535,axiom,
    ! [X26,X24,X2,X42] : c_append(c_List_Olist_OCons(X2,X24,X42),X26,X42) = c_List_Olist_OCons(X2,c_append(X24,X26,X42),X42),
    file('<stdin>',cls_List_Oop_A_64_Oappend__Cons_0) ).

fof(c_0_536,axiom,
    ! [X26,X24,X2,X42] : c_List_Oitrev(c_List_Olist_OCons(X2,X24,X42),X26,X42) = c_List_Oitrev(X24,c_List_Olist_OCons(X2,X26,X42),X42),
    file('<stdin>',cls_List_Oitrev_Osimps__2_0) ).

fof(c_0_537,axiom,
    ! [X52,X26,X24,X4] : c_append(c_append(X24,X26,X4),X52,X4) = c_append(X24,c_append(X26,X52,X4),X4),
    file('<stdin>',cls_List_Oappend__assoc_0) ).

fof(c_0_538,axiom,
    ! [X19,X14,X4] :
      ( ~ c_in(c_insert(X19,X14,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X14,c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__insert_0) ).

fof(c_0_539,axiom,
    ! [X20,X21,X4] :
      ( ~ c_in(c_union(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X20,c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Un_1) ).

fof(c_0_540,axiom,
    ! [X20,X21,X4] :
      ( ~ c_in(c_union(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X21,c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Un_0) ).

fof(c_0_541,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X16,tc_nat)
      | ~ c_less(c_0,X22,tc_nat)
      | c_less(c_minus(X16,X22,tc_nat),X16,tc_nat) ),
    file('<stdin>',cls_NatArith_Odiff__less_0) ).

fof(c_0_542,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X16,tc_nat)
      | ~ c_less(c_1,X22,tc_nat)
      | c_less(c_div(X16,X22,tc_nat),X16,tc_nat) ),
    file('<stdin>',cls_Divides_Odiv__less__dividend_0) ).

fof(c_0_543,axiom,
    ! [X24,X22,X16,X4] : c_List_Otake(X22,c_List_Otake(X16,X24,X4),X4) = c_List_Otake(c_Orderings_Omin(X22,X16,tc_nat),X24,X4),
    file('<stdin>',cls_List_Otake__take_0) ).

fof(c_0_544,axiom,
    ! [X2,X17,X44,X4] : c_List_Otake(X44,c_List_Oreplicate(X17,X2,X4),X4) = c_List_Oreplicate(c_Orderings_Omin(X44,X17,tc_nat),X2,X4),
    file('<stdin>',cls_List_Otake__replicate_0) ).

fof(c_0_545,axiom,
    ! [X2,X17,X44,X4] : c_List_Odrop(X44,c_List_Oreplicate(X17,X2,X4),X4) = c_List_Oreplicate(c_minus(X17,X44,tc_nat),X2,X4),
    file('<stdin>',cls_List_Odrop__replicate_0) ).

fof(c_0_546,axiom,
    ! [X24,X22,X16,X4] : c_List_Odrop(X22,c_List_Odrop(X16,X24,X4),X4) = c_List_Odrop(c_plus(X22,X16,tc_nat),X24,X4),
    file('<stdin>',cls_List_Odrop__drop_0) ).

fof(c_0_547,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ class_Orderings_Olinorder(X4)
      | ~ c_less(c_plus(X19,X19,X4),c_0,X4)
      | c_less(X19,c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).

fof(c_0_548,axiom,
    ! [X2,X13,X14,X4] :
      ( ~ c_lessequals(c_insert(X2,X14,X4),X13,tc_set(X4))
      | c_in(X2,X13,X4) ),
    file('<stdin>',cls_Set_Oinsert__subset_0) ).

fof(c_0_549,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | ~ c_less(c_0,X16,tc_nat)
      | c_less(c_0,c_times(X16,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Onat__0__less__mult__iff_2) ).

fof(c_0_550,axiom,
    ! [X24,X25,X14,X4] :
      ( ~ c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | ~ c_in(X25,c_List_Oset(X24,X4),X4)
      | c_in(X25,X14,X4) ),
    file('<stdin>',cls_List_Oin__listsD__dest_0) ).

fof(c_0_551,axiom,
    ! [X24,X2,X42] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X2,X24,X42),X42)
      | ~ c_in(X2,c_List_Oset(X24,X42),X42) ),
    file('<stdin>',cls_List_Odistinct_Osimps__2_0) ).

fof(c_0_552,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanLessThan(X27,X15,X4),X4)
      | c_less(X44,X15,X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThanLessThan__iff_1) ).

fof(c_0_553,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanLessThan(X27,X15,X4),X4)
      | c_less(X27,X44,X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThanLessThan__iff_0) ).

fof(c_0_554,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanAtMost(X27,X15,X4),X4)
      | c_lessequals(X44,X15,X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThanAtMost__iff_1) ).

fof(c_0_555,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanAtMost(X27,X15,X4),X4)
      | c_less(X27,X44,X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThanAtMost__iff_0) ).

fof(c_0_556,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastLessThan(X27,X15,X4),X4)
      | c_less(X44,X15,X4) ),
    file('<stdin>',cls_SetInterval_OatLeastLessThan__iff_1) ).

fof(c_0_557,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastLessThan(X27,X15,X4),X4)
      | c_lessequals(X27,X44,X4) ),
    file('<stdin>',cls_SetInterval_OatLeastLessThan__iff_0) ).

fof(c_0_558,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastAtMost(X27,X15,X4),X4)
      | c_lessequals(X44,X15,X4) ),
    file('<stdin>',cls_SetInterval_OatLeastAtMost__iff_1) ).

fof(c_0_559,axiom,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastAtMost(X27,X15,X4),X4)
      | c_lessequals(X27,X44,X4) ),
    file('<stdin>',cls_SetInterval_OatLeastAtMost__iff_0) ).

fof(c_0_560,axiom,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_Orderings_Omax(X2,X1,X3),X49,X3)
      | c_lessequals(X1,X49,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).

fof(c_0_561,axiom,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_Orderings_Omax(X2,X1,X3),X49,X3)
      | c_lessequals(X2,X49,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).

fof(c_0_562,axiom,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,c_Orderings_Omin(X1,X49,X3),X3)
      | c_lessequals(X2,X49,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).

fof(c_0_563,axiom,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,c_Orderings_Omin(X1,X49,X3),X3)
      | c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).

fof(c_0_564,axiom,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X49,c_Orderings_Omin(X2,X1,X4),X4)
      | c_less(X49,X1,X4) ),
    file('<stdin>',cls_Orderings_Omin__less__iff__conj_1) ).

fof(c_0_565,axiom,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X49,c_Orderings_Omin(X2,X1,X4),X4)
      | c_less(X49,X2,X4) ),
    file('<stdin>',cls_Orderings_Omin__less__iff__conj_0) ).

fof(c_0_566,axiom,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(c_Orderings_Omax(X2,X1,X4),X49,X4)
      | c_less(X1,X49,X4) ),
    file('<stdin>',cls_Orderings_Omax__less__iff__conj_1) ).

fof(c_0_567,axiom,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(c_Orderings_Omax(X2,X1,X4),X49,X4)
      | c_less(X2,X49,X4) ),
    file('<stdin>',cls_Orderings_Omax__less__iff__conj_0) ).

fof(c_0_568,axiom,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oanalz(X89),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X93)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz_ODecrypt__dest_0) ).

fof(c_0_569,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_lessequals(X22,X16,tc_nat)
      | c_NatArith_Oof__nat(c_minus(X16,X22,tc_nat),X4) = c_minus(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__diff_0) ).

fof(c_0_570,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | c_in(X7,X13,X4)
      | c_in(X7,c_minus(X14,X13,tc_set(X4)),X4) ),
    file('<stdin>',cls_Set_ODiff__iff_2) ).

fof(c_0_571,axiom,
    ! [X13,X14,X4] :
      ( ~ c_in(c_Main_OsubsetI__1(X14,X13,X4),X13,X4)
      | c_lessequals(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_OsubsetI_1) ).

fof(c_0_572,axiom,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).

fof(c_0_573,axiom,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).

fof(c_0_574,axiom,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3)
      | c_less(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).

fof(c_0_575,axiom,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3)
      | c_lessequals(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).

fof(c_0_576,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,c_divide(c_1,X28,X4),X4)
      | c_less(c_0,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ozero__less__divide__1__iff_0) ).

fof(c_0_577,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,c_divide(c_1,X28,X4),X4)
      | c_lessequals(c_0,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ozero__le__divide__1__iff_0) ).

fof(c_0_578,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_divide(c_1,X28,X4),c_0,X4)
      | c_less(X28,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__less__0__1__iff_0) ).

fof(c_0_579,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_divide(c_1,X28,X4),c_0,X4)
      | c_lessequals(X28,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__le__0__1__iff_0) ).

fof(c_0_580,axiom,
    ! [X2,X13,X14,X4] :
      ( ~ c_in(X2,X13,X4)
      | c_minus(c_insert(X2,X14,X4),X13,tc_set(X4)) = c_minus(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_Oinsert__Diff1_0) ).

fof(c_0_581,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_9) ).

fof(c_0_582,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_12) ).

fof(c_0_583,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_minus(X19,X28,X4),c_0,X4)
      | c_less(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).

fof(c_0_584,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_minus(X19,X28,X4),c_0,X4)
      | c_lessequals(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).

fof(c_0_585,axiom,
    ! [X17,X60,X44] : c_minus(c_minus(X44,X60,tc_nat),X17,tc_nat) = c_minus(X44,c_plus(X60,X17,tc_nat),tc_nat),
    file('<stdin>',cls_Nat_Odiff__diff__left_0) ).

fof(c_0_586,axiom,
    ! [X28,X19] :
      ( X19 = c_0
      | c_div(c_plus(X28,X19,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_plus(c_div(X28,X19,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozdiv__zadd__self2_0) ).

fof(c_0_587,axiom,
    ! [X28,X19] :
      ( X19 = c_0
      | c_div(c_plus(X19,X28,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_plus(c_div(X28,X19,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozdiv__zadd__self1_0) ).

fof(c_0_588,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X2)),X4),X4)
      | ~ c_lessequals(c_Numeral_Onumber__of(X2,X4),c_0,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__16_0) ).

fof(c_0_589,axiom,
    ! [X22,X16,X17] :
      ( c_less(c_0,X17,tc_nat)
      | c_lessequals(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Omult__le__cancel2_1) ).

fof(c_0_590,axiom,
    ! [X22,X16,X17] :
      ( c_less(c_0,X17,tc_nat)
      | c_lessequals(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Omult__le__cancel1_1) ).

fof(c_0_591,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,c_plus(X19,X19,X4),X4)
      | c_lessequals(c_0,X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).

fof(c_0_592,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_plus(X19,X19,X4),c_0,X4)
      | c_lessequals(X19,c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).

fof(c_0_593,axiom,
    ! [X28,X19,X14,X4] :
      ( ~ c_in(X19,c_insert(X28,X14,X4),X4)
      | c_in(X19,X14,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Set_Oinsert__iff_0) ).

fof(c_0_594,axiom,
    ! [X26,X1,X2,X42] :
      ( ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X26,X42),X42)
      | c_List_Oop_Amem(X2,X26,X42)
      | X1 = X2 ),
    file('<stdin>',cls_List_Oop_Amem_Osimps__2_0) ).

fof(c_0_595,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatBin_Oless__nat__number__of_2) ).

fof(c_0_596,axiom,
    ! [X19,X13,X14,X4] :
      ( c_emptyset != c_inter(c_insert(X19,X14,X4),X13,X4)
      | c_emptyset = c_inter(X14,X13,X4) ),
    file('<stdin>',cls_Set_Oinsert__disjoint__2_1) ).

fof(c_0_597,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(c_insert(X19,X14,X4),X13,X4) != c_emptyset
      | c_inter(X14,X13,X4) = c_emptyset ),
    file('<stdin>',cls_Set_Oinsert__disjoint__1_1) ).

fof(c_0_598,axiom,
    ! [X28,X13,X14,X4] :
      ( c_emptyset != c_inter(X14,c_insert(X28,X13,X4),X4)
      | c_emptyset = c_inter(X14,X13,X4) ),
    file('<stdin>',cls_Set_Odisjoint__insert__2_1) ).

fof(c_0_599,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(X13,c_insert(X19,X14,X4),X4) != c_emptyset
      | c_inter(X13,X14,X4) = c_emptyset ),
    file('<stdin>',cls_Set_Odisjoint__insert__1_1) ).

fof(c_0_600,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_inter(X14,X13,X4),X4)
      | c_in(X7,X13,X4) ),
    file('<stdin>',cls_Set_OInt__iff_1) ).

fof(c_0_601,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_inter(X14,X13,X4),X4)
      | c_in(X7,X14,X4) ),
    file('<stdin>',cls_Set_OInt__iff_0) ).

fof(c_0_602,axiom,
    ! [X22] :
      ( ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | X22 = c_0 ),
    file('<stdin>',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).

fof(c_0_603,axiom,
    ! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X1,
    file('<stdin>',cls_NatSimprocs_Oadd__self__div__2_0) ).

fof(c_0_604,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(X2,X4) != c_1
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__9_0) ).

fof(c_0_605,axiom,
    ! [X24,X2,X42] : c_List_Orev(c_List_Olist_OCons(X2,X24,X42),X42) = c_append(c_List_Orev(X24,X42),c_List_Olist_OCons(X2,c_List_Olist_ONil,X42),X42),
    file('<stdin>',cls_List_Orev_Osimps__2_0) ).

fof(c_0_606,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__6_1) ).

fof(c_0_607,axiom,
    ! [X84,X48] :
      ( ~ c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oless__nat__number__of_1) ).

fof(c_0_608,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(c_Suc(c_0),c_times(X16,X22,tc_nat),tc_nat)
      | c_lessequals(c_1,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Oone__le__mult__iff_1) ).

fof(c_0_609,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(c_Suc(c_0),c_times(X16,X22,tc_nat),tc_nat)
      | c_lessequals(c_1,X16,tc_nat) ),
    file('<stdin>',cls_Nat_Oone__le__mult__iff_0) ).

fof(c_0_610,axiom,
    ! [X2,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Finite__Set_OMin(c_insert(X2,X14,X3),X3) = c_Orderings_Omin(X2,c_Finite__Set_OMin(X14,X3),X3) ),
    file('<stdin>',cls_Finite__Set_OMin__insert_0) ).

fof(c_0_611,axiom,
    ! [X2,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Finite__Set_OMax(c_insert(X2,X14,X3),X3) = c_Orderings_Omax(X2,c_Finite__Set_OMax(X14,X3),X3) ),
    file('<stdin>',cls_Finite__Set_OMax__insert_0) ).

fof(c_0_612,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__14_0) ).

fof(c_0_613,axiom,
    ! [X19,X13,X14,X4] :
      ( c_emptyset != c_inter(X14,X13,X4)
      | c_in(X19,X13,X4)
      | c_emptyset = c_inter(c_insert(X19,X14,X4),X13,X4) ),
    file('<stdin>',cls_Set_Oinsert__disjoint__2_2) ).

fof(c_0_614,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(X14,X13,X4) != c_emptyset
      | c_in(X19,X13,X4)
      | c_inter(c_insert(X19,X14,X4),X13,X4) = c_emptyset ),
    file('<stdin>',cls_Set_Oinsert__disjoint__1_2) ).

fof(c_0_615,axiom,
    ! [X28,X13,X14,X4] :
      ( c_emptyset != c_inter(X14,X13,X4)
      | c_in(X28,X14,X4)
      | c_emptyset = c_inter(X14,c_insert(X28,X13,X4),X4) ),
    file('<stdin>',cls_Set_Odisjoint__insert__2_2) ).

fof(c_0_616,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(X13,X14,X4) != c_emptyset
      | c_in(X19,X13,X4)
      | c_inter(X13,c_insert(X19,X14,X4),X4) = c_emptyset ),
    file('<stdin>',cls_Set_Odisjoint__insert__1_2) ).

fof(c_0_617,axiom,
    ! [X24,X22,X44,X4] :
      ( ~ c_less(X44,X22,tc_nat)
      | c_List_Onth(c_List_Otake(X22,X24,X4),X44,X4) = c_List_Onth(X24,X44,X4) ),
    file('<stdin>',cls_List_Onth__take_0) ).

fof(c_0_618,axiom,
    ! [X2,X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X2,X14,X4)
      | c_Finite__Set_Ocard(c_insert(X2,X14,X4),X4) = c_Suc(c_Finite__Set_Ocard(X14,X4)) ),
    file('<stdin>',cls_Finite__Set_Ocard__insert__disjoint_0) ).

fof(c_0_619,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__6_0) ).

fof(c_0_620,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_minus(X22,X16,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Ozero__less__diff_0) ).

fof(c_0_621,axiom,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(c_append(X24,X26,X4),X4)
      | c_inter(c_List_Oset(X24,X4),c_List_Oset(X26,X4),X4) = c_emptyset ),
    file('<stdin>',cls_List_Odistinct__append_2) ).

fof(c_0_622,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_OHPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OHPair__synth__analz_1) ).

fof(c_0_623,axiom,
    ! [X66,X61,X19,X42] :
      ( c_in(X19,c_List_Oset(X66,X42),X42)
      | c_List_Olist__inter(c_List_Olist_OCons(X19,X61,X42),X66,X42) = c_List_Olist__inter(X61,X66,X42) ),
    file('<stdin>',cls_List_Olist__inter_Osimps__2_1) ).

fof(c_0_624,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_times(X16,X22,tc_nat),tc_nat)
      | c_less(c_0,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Onat__0__less__mult__iff_1) ).

fof(c_0_625,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_times(X16,X22,tc_nat),tc_nat)
      | c_less(c_0,X16,tc_nat) ),
    file('<stdin>',cls_Nat_Onat__0__less__mult__iff_0) ).

fof(c_0_626,axiom,
    ! [X49,X12] :
      ( ~ c_lessequals(X12,c_minus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(X12,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Ozle__diff1__eq_0) ).

fof(c_0_627,axiom,
    ! [X49,X12] :
      ( ~ c_less(X12,c_plus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(X12,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Ozle__add1__eq__le_0) ).

fof(c_0_628,axiom,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(c_Main_OUnion__iff__1(X14,X33,X4),X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OUnion__iff_0) ).

fof(c_0_629,axiom,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(c_Main_OUnionE__1(X14,X33,X4),X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OUnionE_0) ).

fof(c_0_630,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_7) ).

fof(c_0_631,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_5) ).

fof(c_0_632,axiom,
    ! [X26,X1,X24,X4] :
      ( c_List_Orev(X24,X4) != c_List_Olist_OCons(X1,X26,X4)
      | X24 = c_append(c_List_Orev(X26,X4),c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) ),
    file('<stdin>',cls_List_Orev__eq__Cons__iff_0) ).

fof(c_0_633,axiom,
    ! [X2,X14,X4] :
      ( ~ c_in(c_0,X14,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X14,X4) = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) ),
    file('<stdin>',cls_List_Osublist__singleton_0) ).

fof(c_0_634,axiom,
    ! [X100,X102] : c_Nat_Osize(c_Message_Omsg_OMPair(X102,X100),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X102,tc_Message_Omsg),c_Nat_Osize(X100,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
    file('<stdin>',cls_Message_Omsg_Osize__6_0) ).

fof(c_0_635,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X2)),X4),X4)
      | c_lessequals(c_Numeral_Onumber__of(X2,X4),c_1,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__17_1) ).

fof(c_0_636,axiom,
    ! [X12,X48] : c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X48,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdiv__number__of__BIT_0) ).

fof(c_0_637,axiom,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(X14,c_Main_OUnion__iff__1(X14,X33,X4),X4) ),
    file('<stdin>',cls_Set_OUnion__iff_1) ).

fof(c_0_638,axiom,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(X14,c_Main_OUnionE__1(X14,X33,X4),X4) ),
    file('<stdin>',cls_Set_OUnionE_1) ).

fof(c_0_639,axiom,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Opower__le__zero__eq__number__of_5) ).

fof(c_0_640,axiom,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(tc_set(X4)))
      | c_in(c_Main_Ofinite__Union__1(X14,X4),X14,tc_set(X4))
      | c_in(c_Union(X14,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Union_0) ).

fof(c_0_641,axiom,
    ! [X60,X44] :
      ( ~ c_lessequals(X44,X60,tc_nat)
      | c_List_Oupt(X44,c_Suc(X60)) = c_append(c_List_Oupt(X44,X60),c_List_Olist_OCons(X60,c_List_Olist_ONil,tc_nat),tc_nat) ),
    file('<stdin>',cls_List_Oupt_Oupt__Suc_0) ).

fof(c_0_642,axiom,
    ! [X93,X89] :
      ( ~ c_in(X93,c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat)
      | c_in(X93,c_Message_OkeysFor(X89),tc_nat)
      | c_in(c_Message_Omsg_OKey(v_sko__uhi(X89,X93)),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Event_OkeysFor__synth_H_0) ).

fof(c_0_643,axiom,
    ! [X2,X13,X14,X4] :
      ( c_in(X2,X14,X4)
      | c_minus(X14,c_insert(X2,X13,X4),tc_set(X4)) = c_minus(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_ODiff__insert0_0) ).

fof(c_0_644,axiom,
    ! [X2,X12] :
      ( ~ c_less(c_0,X2,tc_nat)
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).

fof(c_0_645,axiom,
    ! [X24,X2,X42] :
      ( c_in(X2,c_List_Oset(X24,X42),X42)
      | c_List_Oremdups(c_List_Olist_OCons(X2,X24,X42),X42) = c_List_Olist_OCons(X2,c_List_Oremdups(X24,X42),X42) ),
    file('<stdin>',cls_List_Oremdups_Osimps__2_1) ).

fof(c_0_646,axiom,
    ! [X48] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    file('<stdin>',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).

fof(c_0_647,axiom,
    ! [X103,X28,X14] :
      ( ~ c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X28,X14))),c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg) ),
    file('<stdin>',cls_Public_OSpy__spies__bad__privateKey_0) ).

fof(c_0_648,axiom,
    ! [X24,X22,X4] :
      ( ~ c_less(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Olast(c_List_Odrop(X22,X24,X4),X4) = c_List_Olast(X24,X4) ),
    file('<stdin>',cls_List_Olast__drop_0) ).

fof(c_0_649,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | X2 = c_0 ),
    file('<stdin>',cls_Parity_Ozero__less__power__eq__number__of_4) ).

fof(c_0_650,axiom,
    ! [X25,X33,X14,X4] :
      ( ~ c_in(X25,X33,tc_set(X4))
      | ~ c_in(X14,c_Inter(X33,X4),X4)
      | c_in(X14,X25,X4) ),
    file('<stdin>',cls_Set_OInter__iff_0) ).

fof(c_0_651,axiom,
    ! [X2,X22,X4] :
      ( X22 = c_0
      | c_List_Otl(c_List_Oreplicate(X22,X2,X4),X4) = c_List_Oreplicate(c_minus(X22,c_1,tc_nat),X2,X4) ),
    file('<stdin>',cls_List_Otl__replicate_0) ).

fof(c_0_652,axiom,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),tc_set(X4))
      | c_lessequals(X13,X14,tc_set(X4)) ),
    file('<stdin>',cls_Set_OCompl__subset__Compl__iff_0) ).

fof(c_0_653,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(X19,c_0,X4),c_times(X28,c_0,X4),X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__right__if_0) ).

fof(c_0_654,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(c_0,X19,X4),c_times(c_0,X28,X4),X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__left__if_0) ).

fof(c_0_655,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    file('<stdin>',cls_Parity_Ozero__le__power__eq__number__of_1) ).

fof(c_0_656,axiom,
    ! [X12,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | X19 = c_divide(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0 ),
    file('<stdin>',cls_NatSimprocs_Oeq__divide__eq__number__of_3) ).

fof(c_0_657,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0
      | c_times(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) = X28 ),
    file('<stdin>',cls_NatSimprocs_Oeq__divide__eq__number__of_0) ).

fof(c_0_658,axiom,
    ! [X12,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0
      | c_divide(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) = X19 ),
    file('<stdin>',cls_NatSimprocs_Odivide__eq__eq__number__of_3) ).

fof(c_0_659,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | X28 = c_times(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0 ),
    file('<stdin>',cls_NatSimprocs_Odivide__eq__eq__number__of_0) ).

fof(c_0_660,axiom,
    ! [X24,X14,X4] :
      ( c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(c_Main_Oin__listsI__1(X14,X24,X4),c_List_Oset(X24,X4),X4) ),
    file('<stdin>',cls_List_Oin__listsI_0) ).

fof(c_0_661,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__synth_1) ).

fof(c_0_662,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X87,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__synth_0) ).

fof(c_0_663,axiom,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OCrypt__synth__eq_0) ).

fof(c_0_664,axiom,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OCrypt__synth_1) ).

fof(c_0_665,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_3) ).

fof(c_0_666,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(X87,c_Message_Osynth(X89),tc_Message_Omsg)
      | ~ c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Osynth_OMPair_0) ).

fof(c_0_667,axiom,
    ! [X88,X93,X89] :
      ( ~ c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Osynth_OCrypt_0) ).

fof(c_0_668,axiom,
    ! [X22,X16,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X19,X4)
      | c_Nat_Opower(X19,X16,X4) != c_Nat_Opower(X19,X22,X4)
      | X16 = X22 ),
    file('<stdin>',cls_Power_Opower__inject__exp_0) ).

fof(c_0_669,axiom,
    ! [X47,X13,X4] :
      ( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_minus(X13,X47,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Diff_0) ).

fof(c_0_670,axiom,
    ! [X1,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X1,X14,X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Orderings_Omax(X1,c_Finite__Set_OMin(X14,X3),X3) = X1 ),
    file('<stdin>',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).

fof(c_0_671,axiom,
    ! [X1,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X1,X14,X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Orderings_Omin(X1,c_Finite__Set_OMax(X14,X3),X3) = X1 ),
    file('<stdin>',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).

fof(c_0_672,axiom,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OCrypt__synth__eq_1) ).

fof(c_0_673,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X2,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_lessequals(c_Finite__Set_OMin(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__le_0) ).

fof(c_0_674,axiom,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X2,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_lessequals(X2,c_Finite__Set_OMax(X14,X4),X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__ge_0) ).

fof(c_0_675,axiom,
    ! [X1,X22,X4] : c_append(c_List_Otake(X22,X1,X4),c_List_Odrop(X22,X1,X4),X4) = X1,
    file('<stdin>',cls_List_Oappend__take__drop__id_0) ).

fof(c_0_676,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_less(c_0,c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__10_1) ).

fof(c_0_677,axiom,
    ! [X84] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    file('<stdin>',cls_NatBin_Oone__mod__nat__number__of_1) ).

fof(c_0_678,axiom,
    ! [X25,X33,X14,X4] :
      ( ~ c_in(X14,X25,X4)
      | ~ c_in(X25,X33,tc_set(X4))
      | c_in(X14,c_Union(X33,X4),X4) ),
    file('<stdin>',cls_Set_OUnion__iff_2) ).

fof(c_0_679,axiom,
    ! [X24,X2,X42] :
      ( ~ c_in(X2,c_List_Oset(X24,X42),X42)
      | c_List_Oremdups(c_List_Olist_OCons(X2,X24,X42),X42) = c_List_Oremdups(X24,X42) ),
    file('<stdin>',cls_List_Oremdups_Osimps__2_0) ).

fof(c_0_680,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X84),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oless__nat__number__of_0) ).

fof(c_0_681,axiom,
    ! [X20,X21,X4] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_inter(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Int_1) ).

fof(c_0_682,axiom,
    ! [X20,X21,X4] :
      ( ~ c_in(X21,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_inter(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Int_0) ).

fof(c_0_683,axiom,
    ! [X19,X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_insert(X19,X14,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_OFinites_OinsertI_0) ).

fof(c_0_684,axiom,
    ! [X24,X2,X48,X4] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_List_Odrop(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_OCons(X2,X24,X4) ),
    file('<stdin>',cls_List_Odrop__Cons__number__of_0) ).

fof(c_0_685,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_plus(X19,X19,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).

fof(c_0_686,axiom,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oeq__divide__eq__number__of_4) ).

fof(c_0_687,axiom,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_divide(c_times(c_0,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) = c_0 ),
    file('<stdin>',cls_NatSimprocs_Odivide__eq__eq__number__of_4) ).

fof(c_0_688,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__12_1) ).

fof(c_0_689,axiom,
    ! [X13,X14,X4] : c_uminus(c_union(X14,X13,X4),tc_set(X4)) = c_inter(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),X4),
    file('<stdin>',cls_Set_OCompl__Un_0) ).

fof(c_0_690,axiom,
    ! [X13,X14,X4] : c_uminus(c_inter(X14,X13,X4),tc_set(X4)) = c_union(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),X4),
    file('<stdin>',cls_Set_OCompl__Int_0) ).

fof(c_0_691,axiom,
    ! [X93,X89] :
      ( c_in(X93,c_Message_OkeysFor(c_Message_Oanalz(X89)),tc_nat)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X93),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz__insert__Key_0) ).

fof(c_0_692,axiom,
    ! [X26,X24,X4] : c_Nat_Osize(c_append(X24,X26,X4),tc_List_Olist(X4)) = c_plus(c_Nat_Osize(X24,tc_List_Olist(X4)),c_Nat_Osize(X26,tc_List_Olist(X4)),tc_nat),
    file('<stdin>',cls_List_Olength__append_0) ).

fof(c_0_693,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | c_less(c_0,c_divide(c_1,X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Ozero__less__divide__1__iff_1) ).

fof(c_0_694,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,X28,X4)
      | c_lessequals(c_0,c_divide(c_1,X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Ozero__le__divide__1__iff_1) ).

fof(c_0_695,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | c_less(c_divide(c_1,X28,X4),c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__less__0__1__iff_1) ).

fof(c_0_696,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(X28,c_0,X4)
      | c_lessequals(c_divide(c_1,X28,X4),c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__le__0__1__iff_1) ).

fof(c_0_697,axiom,
    ! [X1,X2] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) != c_0
      | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).

fof(c_0_698,axiom,
    ! [X1,X2] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0 ),
    file('<stdin>',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).

fof(c_0_699,axiom,
    ! [X1,X2] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).

fof(c_0_700,axiom,
    ! [X1,X2] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    file('<stdin>',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).

fof(c_0_701,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_minus(X19,X28,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).

fof(c_0_702,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_minus(X19,X28,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).

fof(c_0_703,axiom,
    ! [X28,X19,X4] :
      ( ~ c_in(X28,c_insert(X19,c_emptyset,X4),X4)
      | X28 = X19 ),
    file('<stdin>',cls_Set_OsingletonD__dest_0) ).

fof(c_0_704,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_Nat_Opower(c_HOL_Oabs(X2,X4),c_Numeral_Onumber__of(X12,tc_nat),X4) = c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4) ),
    file('<stdin>',cls_Parity_Opower__even__abs__number__of_0) ).

fof(c_0_705,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,X19,X4)
      | c_lessequals(c_0,c_plus(X19,X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).

fof(c_0_706,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_lessequals(c_plus(X19,X19,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).

fof(c_0_707,axiom,
    ! [X22,X44] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_minus(X22,c_Suc(X44),tc_nat),X22,tc_nat) ),
    file('<stdin>',cls_Nat_Odiff__Suc__less_0) ).

fof(c_0_708,axiom,
    ! [X17,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | c_minus(c_insert(X17,c_emptyset,X4),c_SetInterval_OlessThan(X17,X4),tc_set(X4)) = c_insert(X17,c_emptyset,X4) ),
    file('<stdin>',cls_SetInterval_Osingle__Diff__lessThan_0) ).

fof(c_0_709,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__10_0) ).

fof(c_0_710,axiom,
    ! [X33,X14,X4] :
      ( c_in(X14,c_Inter(X33,X4),X4)
      | c_in(c_Main_OInter__iff__1(X14,X33,X4),X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OInter__iff_1) ).

fof(c_0_711,axiom,
    ! [X33,X14,X4] :
      ( c_in(X14,c_Inter(X33,X4),X4)
      | c_in(c_Main_OInterI__1(X14,X33,X4),X33,tc_set(X4)) ),
    file('<stdin>',cls_Set_OInterI_0) ).

fof(c_0_712,axiom,
    ! [X28,X19,X14,X4] :
      ( ~ c_in(X19,X14,X4)
      | c_in(X19,c_insert(X28,X14,X4),X4) ),
    file('<stdin>',cls_Set_Oinsert__iff_2) ).

fof(c_0_713,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X13,X4)
      | c_in(X7,c_union(X14,X13,X4),X4) ),
    file('<stdin>',cls_Set_OUn__iff_2) ).

fof(c_0_714,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | c_in(X7,c_union(X14,X13,X4),X4) ),
    file('<stdin>',cls_Set_OUn__iff_1) ).

fof(c_0_715,axiom,
    ! [X26,X1,X2,X42] :
      ( ~ c_List_Oop_Amem(X2,X26,X42)
      | c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X26,X42),X42) ),
    file('<stdin>',cls_List_Oop_Amem_Osimps__2_2) ).

fof(c_0_716,axiom,
    ! [X1,X46,X4] : c_Public_Okeymode_Okeymode__rec(X46,X1,c_Public_Okeymode_OEncryption,X4) = X1,
    file('<stdin>',cls_Public_Okeymode_Orecs__2_0) ).

fof(c_0_717,axiom,
    ! [X1,X45,X4] : c_Public_Okeymode_Okeymode__rec(X1,X45,c_Public_Okeymode_OSignature,X4) = X1,
    file('<stdin>',cls_Public_Okeymode_Orecs__1_0) ).

fof(c_0_718,axiom,
    ! [X1,X46,X4] : c_Public_Okeymode_Okeymode__case(X46,X1,c_Public_Okeymode_OEncryption,X4) = X1,
    file('<stdin>',cls_Public_Okeymode_Ocases__2_0) ).

fof(c_0_719,axiom,
    ! [X1,X45,X4] : c_Public_Okeymode_Okeymode__case(X1,X45,c_Public_Okeymode_OSignature,X4) = X1,
    file('<stdin>',cls_Public_Okeymode_Ocases__1_0) ).

fof(c_0_720,axiom,
    ! [X1,X4] : c_Relation_OImage(c_Relation_OId,X1,X4,X4) = X1,
    file('<stdin>',cls_Relation_OImage__Id_0) ).

fof(c_0_721,axiom,
    ! [X1,X46,X4] : c_Numeral_Obit_Obit__rec(X46,X1,c_Numeral_Obit_OB1,X4) = X1,
    file('<stdin>',cls_Numeral_Obit_Orecs__2_0) ).

fof(c_0_722,axiom,
    ! [X1,X45,X4] : c_Numeral_Obit_Obit__rec(X1,X45,c_Numeral_Obit_OB0,X4) = X1,
    file('<stdin>',cls_Numeral_Obit_Orecs__1_0) ).

fof(c_0_723,axiom,
    ! [X1,X46,X4] : c_Numeral_Obit_Obit__case(X46,X1,c_Numeral_Obit_OB1,X4) = X1,
    file('<stdin>',cls_Numeral_Obit_Ocases__2_0) ).

fof(c_0_724,axiom,
    ! [X1,X45,X4] : c_Numeral_Obit_Obit__case(X1,X45,c_Numeral_Obit_OB0,X4) = X1,
    file('<stdin>',cls_Numeral_Obit_Ocases__1_0) ).

fof(c_0_725,axiom,
    ! [X1,X46,X4] : c_Extraction_Osumbool_Osumbool__rec(X46,X1,c_Extraction_Osumbool_ORight,X4) = X1,
    file('<stdin>',cls_Extraction_Osumbool_Orecs__2_0) ).

fof(c_0_726,axiom,
    ! [X1,X45,X4] : c_Extraction_Osumbool_Osumbool__rec(X1,X45,c_Extraction_Osumbool_OLeft,X4) = X1,
    file('<stdin>',cls_Extraction_Osumbool_Orecs__1_0) ).

fof(c_0_727,axiom,
    ! [X1,X46,X4] : c_Extraction_Osumbool_Osumbool__case(X46,X1,c_Extraction_Osumbool_ORight,X4) = X1,
    file('<stdin>',cls_Extraction_Osumbool_Ocases__2_0) ).

fof(c_0_728,axiom,
    ! [X1,X45,X4] : c_Extraction_Osumbool_Osumbool__case(X1,X45,c_Extraction_Osumbool_OLeft,X4) = X1,
    file('<stdin>',cls_Extraction_Osumbool_Ocases__1_0) ).

fof(c_0_729,axiom,
    ! [X60,X44] : ~ c_less(c_plus(X60,X44,tc_nat),X44,tc_nat),
    file('<stdin>',cls_Nat_Onot__add__less2_0) ).

fof(c_0_730,axiom,
    ! [X60,X44] : ~ c_less(c_plus(X44,X60,tc_nat),X44,tc_nat),
    file('<stdin>',cls_Nat_Onot__add__less1_0) ).

fof(c_0_731,axiom,
    ! [X86,X3,X4] : c_Relation_OImage(X86,c_emptyset,X3,X4) = c_emptyset,
    file('<stdin>',cls_Relation_OImage__empty_0) ).

fof(c_0_732,axiom,
    ! [X26,X3,X4] : c_List_Ozip(c_List_Olist_ONil,X26,X4,X3) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Ozip__Nil_0) ).

fof(c_0_733,axiom,
    ! [X24,X83,X42] : c_List_Ozip(X24,c_List_Olist_ONil,X42,X83) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Ozip_Osimps__1_0) ).

fof(c_0_734,axiom,
    ! [X1,X22,X44,X4] :
      ( ~ c_less(X44,X22,tc_nat)
      | c_List_Onth(c_List_Oreplicate(X22,X1,X4),X44,X4) = X1 ),
    file('<stdin>',cls_List_Onth__replicate_0) ).

fof(c_0_735,axiom,
    ! [X48,X44,X42] : c_List_Olist__update(c_List_Olist_ONil,X44,X48,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Olist__update_Osimps__1_0) ).

fof(c_0_736,axiom,
    ! [X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_0,X11,X4,X3) = c_emptyset,
    file('<stdin>',cls_Datatype__Universe_Ontrunc__0_0) ).

fof(c_0_737,axiom,
    ! [X3,X4] : c_Sum__Type_OPlus(c_UNIV,c_UNIV,X4,X3) = c_UNIV,
    file('<stdin>',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).

fof(c_0_738,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__12_0) ).

fof(c_0_739,axiom,
    ! [X1,X22] :
      ( ~ c_lessequals(X22,X1,tc_nat)
      | c_plus(X22,c_minus(X1,X22,tc_nat),tc_nat) = X1 ),
    file('<stdin>',cls_Nat_Ole__add__diff__inverse_0) ).

fof(c_0_740,axiom,
    ! [X1,X22] :
      ( ~ c_lessequals(X22,X1,tc_nat)
      | c_plus(c_minus(X1,X22,tc_nat),X22,tc_nat) = X1 ),
    file('<stdin>',cls_Nat_Ole__add__diff__inverse2_0) ).

fof(c_0_741,axiom,
    ! [X1,X22] :
      ( ~ c_lessequals(X1,X22,tc_nat)
      | c_minus(X22,c_minus(X22,X1,tc_nat),tc_nat) = X1 ),
    file('<stdin>',cls_NatArith_Odiff__diff__cancel_0) ).

fof(c_0_742,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_times(X19,X28,X4),X4) = c_times(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__mult__distrib_0) ).

fof(c_0_743,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_HOL_Oabs(c_divide(X19,X28,X4),X4) = c_divide(c_HOL_Oabs(X19,X4),c_HOL_Oabs(X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oabs__divide_0) ).

fof(c_0_744,axiom,
    ! [X22,X44] :
      ( ~ c_lessequals(c_1,X44,tc_nat)
      | c_lessequals(c_Suc(c_0),c_Nat_Opower(X44,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Power_Onat__one__le__power_0) ).

fof(c_0_745,axiom,
    ! [X22] :
      ( ~ c_less(c_0,c_Nat_Opower(c_0,X22,tc_nat),tc_nat)
      | X22 = c_0 ),
    file('<stdin>',cls_Power_Onat__zero__less__power__iff_0) ).

fof(c_0_746,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Numeral_Onumber__of(X12,tc_nat) != c_0
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    file('<stdin>',cls_Parity_Ozero__less__power__eq__number__of_3) ).

fof(c_0_747,axiom,
    ! [X13,X14,X4] : c_minus(c_minus(X14,X13,tc_set(X4)),X13,tc_set(X4)) = c_minus(X14,X13,tc_set(X4)),
    file('<stdin>',cls_Set_ODiff__idemp_0) ).

fof(c_0_748,axiom,
    ! [X13,X14,X4] : c_Union(c_union(X14,X13,tc_set(X4)),X4) = c_union(c_Union(X14,X4),c_Union(X13,X4),X4),
    file('<stdin>',cls_Set_OUnion__Un__distrib_0) ).

fof(c_0_749,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OlessThan(X2,X4),c_SetInterval_OlessThan(X1,X4),tc_set(X4))
      | c_lessequals(X2,X1,X4) ),
    file('<stdin>',cls_SetInterval_OlessThan__subset__iff_0) ).

fof(c_0_750,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X4),c_SetInterval_OgreaterThan(X1,X4),tc_set(X4))
      | c_lessequals(X1,X2,X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__subset__iff_0) ).

fof(c_0_751,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(c_SetInterval_OatMost(X2,X4),c_SetInterval_OatMost(X1,X4),tc_set(X4))
      | c_lessequals(X2,X1,X4) ),
    file('<stdin>',cls_SetInterval_OatMost__subset__iff_0) ).

fof(c_0_752,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(c_SetInterval_OatLeast(X2,X4),c_SetInterval_OatLeast(X1,X4),tc_set(X4))
      | c_lessequals(X1,X2,X4) ),
    file('<stdin>',cls_SetInterval_OatLeast__subset__iff_0) ).

fof(c_0_753,axiom,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_0,c_minus(X22,X16,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Ozero__less__diff_1) ).

fof(c_0_754,axiom,
    ! [X26,X24,X4] : c_List_Oconcat(c_append(X24,X26,tc_List_Olist(X4)),X4) = c_append(c_List_Oconcat(X24,X4),c_List_Oconcat(X26,X4),X4),
    file('<stdin>',cls_List_Oconcat__append_0) ).

fof(c_0_755,axiom,
    ! [X1,X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_times(X1,X22,tc_nat),X22,tc_nat) = X1 ),
    file('<stdin>',cls_Divides_Odiv__mult__self__is__m_0) ).

fof(c_0_756,axiom,
    ! [X1,X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_times(X22,X1,tc_nat),X22,tc_nat) = X1 ),
    file('<stdin>',cls_Divides_Odiv__mult__self1__is__m_0) ).

fof(c_0_757,axiom,
    ! [X1,X4] :
      ( X1 = c_List_Olist_ONil
      | c_append(c_List_Obutlast(X1,X4),c_List_Olist_OCons(c_List_Olast(X1,X4),c_List_Olist_ONil,X4),X4) = X1 ),
    file('<stdin>',cls_List_Oappend__butlast__last__id_0) ).

fof(c_0_758,axiom,
    ! [X28,X19] :
      ( ~ c_less(c_0,X28,tc_IntDef_Oint)
      | c_less(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Opos__mod__bound_0) ).

fof(c_0_759,axiom,
    ! [X28,X19] :
      ( ~ c_less(X28,c_0,tc_IntDef_Oint)
      | c_less(X28,c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Oneg__mod__bound_0) ).

fof(c_0_760,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) ),
    file('<stdin>',cls_Divides_Omod__less__divisor_0) ).

fof(c_0_761,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_lessequals(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) ),
    file('<stdin>',cls_Divides_Omod__le__divisor_0) ).

fof(c_0_762,axiom,
    ! [X49,X12] :
      ( ~ c_less(X12,X49,tc_IntDef_Oint)
      | c_lessequals(X12,c_minus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Ozle__diff1__eq_1) ).

fof(c_0_763,axiom,
    ! [X49,X12] :
      ( ~ c_lessequals(X12,X49,tc_IntDef_Oint)
      | c_less(X12,c_plus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Ozle__add1__eq__le_1) ).

fof(c_0_764,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X4),X4)
      | c_lessequals(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__13_1) ).

fof(c_0_765,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X54,tc_List_Olist(X4)) != c_Nat_Osize(X53,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X54 = X53 ),
    file('<stdin>',cls_List_Oappend__eq__append__conv_3) ).

fof(c_0_766,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X54,tc_List_Olist(X4)) != c_Nat_Osize(X53,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X24 = X26 ),
    file('<stdin>',cls_List_Oappend__eq__append__conv_2) ).

fof(c_0_767,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X54 = X53 ),
    file('<stdin>',cls_List_Oappend__eq__append__conv_1) ).

fof(c_0_768,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X24 = X26 ),
    file('<stdin>',cls_List_Oappend__eq__append__conv_0) ).

fof(c_0_769,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_0,c_plus(X16,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Oadd__gr__0_2) ).

fof(c_0_770,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_0,X16,tc_nat)
      | c_less(c_0,c_plus(X16,X22,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Oadd__gr__0_1) ).

fof(c_0_771,axiom,
    ! [X28,X19] :
      ( ~ c_less(c_0,X28,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Opos__mod__sign_0) ).

fof(c_0_772,axiom,
    ! [X28,X19] :
      ( ~ c_less(X28,c_0,tc_IntDef_Oint)
      | c_lessequals(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Oneg__mod__sign_0) ).

fof(c_0_773,axiom,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | ~ c_lessequals(X14,X13,tc_set(X4))
      | c_in(X7,X13,X4) ),
    file('<stdin>',cls_Set_OsubsetD_0) ).

fof(c_0_774,axiom,
    ! [X2,X22] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,X22,tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__power_1) ).

fof(c_0_775,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat)
      | c_less(c_0,X1,tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__power_1) ).

fof(c_0_776,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_uminus(c_LOrder_Omeet(X19,X28,X4),X4) = c_LOrder_Ojoin(c_uminus(X19,X4),c_uminus(X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__meet__eq__join_0) ).

fof(c_0_777,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_uminus(c_LOrder_Ojoin(X19,X28,X4),X4) = c_LOrder_Omeet(c_uminus(X19,X4),c_uminus(X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__join__eq__meet_0) ).

fof(c_0_778,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_plus(X19,X28,X4),X4) = c_plus(c_uminus(X19,X4),c_uminus(X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Ominus__add__distrib_0) ).

fof(c_0_779,axiom,
    ! [X6,X29,X4] :
      ( ~ c_in(X29,X6,tc_prod(X4,X4))
      | c_in(X29,c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    file('<stdin>',cls_Transitive__Closure_Or__into__rtrancl_0) ).

fof(c_0_780,axiom,
    ! [X13,X14,X4] : c_Pow(c_inter(X14,X13,X4),X4) = c_inter(c_Pow(X14,X4),c_Pow(X13,X4),tc_set(X4)),
    file('<stdin>',cls_Set_OPow__Int__eq_0) ).

fof(c_0_781,axiom,
    ! [X13,X14,X4] : c_List_Olists(c_inter(X14,X13,X4),X4) = c_inter(c_List_Olists(X14,X4),c_List_Olists(X13,X4),tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olists__Int__eq_0) ).

fof(c_0_782,axiom,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X13,X14,tc_set(X4))
      | c_lessequals(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),tc_set(X4)) ),
    file('<stdin>',cls_Set_OCompl__subset__Compl__iff_1) ).

fof(c_0_783,axiom,
    ! [X103,X88,X14] :
      ( c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X14,X88),X103,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X103) ),
    file('<stdin>',cls_Event_Oknows__Spy__Notes_1) ).

fof(c_0_784,axiom,
    ! [X7,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | ~ c_in(X7,c_uminus(X14,tc_set(X4)),X4) ),
    file('<stdin>',cls_Set_OCompl__iff_0) ).

fof(c_0_785,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_uminus(c_Numeral_Onumber__of(X12,X4),X4),X49,X4) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X12),X4),X49,X4) ),
    file('<stdin>',cls_Numeral_Ominus__number__of__mult_0) ).

fof(c_0_786,axiom,
    ! [X13,X14,X4] : c_uminus(c_minus(X14,X13,tc_set(X4)),tc_set(X4)) = c_union(c_uminus(X14,tc_set(X4)),X13,X4),
    file('<stdin>',cls_Set_OCompl__Diff__eq_0) ).

fof(c_0_787,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_NatArith_Oof__nat(c_times(X16,X22,tc_nat),X4) = c_times(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__mult_0) ).

fof(c_0_788,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_NatArith_Oof__nat(c_plus(X16,X22,tc_nat),X4) = c_plus(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__add_0) ).

fof(c_0_789,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_times(X12,X49,tc_IntDef_Oint),X4) = c_times(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__mult_0) ).

fof(c_0_790,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_minus(X12,X49,tc_IntDef_Oint),X4) = c_minus(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__diff_0) ).

fof(c_0_791,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_plus(X12,X49,tc_IntDef_Oint),X4) = c_plus(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__add_0) ).

fof(c_0_792,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X84),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatBin_Oless__nat__number__of_3) ).

fof(c_0_793,axiom,
    ! [X49,X12] :
      ( ~ c_less(X12,X49,tc_IntDef_Oint)
      | ~ c_less(c_0,X49,tc_IntDef_Oint)
      | c_less(c_IntDef_Onat(X12),c_IntDef_Onat(X49),tc_nat) ),
    file('<stdin>',cls_IntDef_Ozless__nat__conj_2) ).

fof(c_0_794,axiom,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(X7,c_times(X28,X7,X4),X4) = c_divide(c_1,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__right__if1_1) ).

fof(c_0_795,axiom,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(X7,c_times(X7,X28,X4),X4) = c_divide(c_1,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__left__if1_1) ).

fof(c_0_796,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_uminus(X28,X4),c_uminus(X19,X4),X4)
      | c_less(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__less__iff__less_0) ).

fof(c_0_797,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_uminus(X28,X4),c_uminus(X19,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__le__iff__le_0) ).

fof(c_0_798,axiom,
    ! [X84] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)),
    file('<stdin>',cls_NatBin_Oone__div__nat__number__of_0) ).

fof(c_0_799,axiom,
    ! [X12,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatBin_Opower__nat__number__of__number__of_0) ).

fof(c_0_800,axiom,
    ! [X2,X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_Parity_Oeven(X22,tc_nat)
      | c_Nat_Opower(c_uminus(X2,X4),X22,X4) = c_uminus(c_Nat_Opower(X2,X22,X4),X4) ),
    file('<stdin>',cls_Parity_Opower__minus__odd_0) ).

fof(c_0_801,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_NatArith_Oof__nat__less__iff_0) ).

fof(c_0_802,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4)
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_NatArith_Oof__nat__le__iff_0) ).

fof(c_0_803,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4)
      | c_less(X12,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Oof__int__less__iff_0) ).

fof(c_0_804,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4)
      | c_lessequals(X12,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Oof__int__le__iff_0) ).

fof(c_0_805,axiom,
    ! [X89,X20] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X89,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X89,tc_Message_Omsg)),
    file('<stdin>',cls_Message_Oanalz__analz__Un_0) ).

fof(c_0_806,axiom,
    ! [X13,X14,X4] : c_union(X14,c_minus(X13,X14,tc_set(X4)),X4) = c_union(X14,X13,X4),
    file('<stdin>',cls_Set_OUn__Diff__cancel_0) ).

fof(c_0_807,axiom,
    ! [X13,X14,X4] : c_union(c_minus(X13,X14,tc_set(X4)),X14,X4) = c_union(X13,X14,X4),
    file('<stdin>',cls_Set_OUn__Diff__cancel2_0) ).

fof(c_0_808,axiom,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X19,X4),X22,X4),X4)
      | X19 = c_0 ),
    file('<stdin>',cls_Power_Ozero__less__power__abs__iff_1) ).

fof(c_0_809,axiom,
    ! [X26,X24,X4] : c_List_Oset(c_append(X24,X26,X4),X4) = c_union(c_List_Oset(X24,X4),c_List_Oset(X26,X4),X4),
    file('<stdin>',cls_List_Oset__append_0) ).

fof(c_0_810,axiom,
    ! [X26,X24,X4] : c_List_Orev(c_append(X24,X26,X4),X4) = c_append(c_List_Orev(X26,X4),c_List_Orev(X24,X4),X4),
    file('<stdin>',cls_List_Orev__append_0) ).

fof(c_0_811,axiom,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X19,X4),X22,X4),X4) ),
    file('<stdin>',cls_Power_Ozero__le__power__abs_0) ).

fof(c_0_812,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_1 != c_Numeral_Onumber__of(X1,X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__7_0) ).

fof(c_0_813,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__synth__analz_1) ).

fof(c_0_814,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__synth__analz_0) ).

fof(c_0_815,axiom,
    ! [X88,X93,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X93),c_Message_OkeysFor(X89),tc_nat),
    file('<stdin>',cls_Message_OkeysFor__insert__Crypt_0) ).

fof(c_0_816,axiom,
    ! [X103,X7] :
      ( ~ c_in(X7,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X103)),tc_Message_Omsg)
      | c_in(X7,c_Event_Oused(X103),tc_Message_Omsg) ),
    file('<stdin>',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).

fof(c_0_817,axiom,
    ! [X24,X2,X42] :
      ( ~ c_List_Odistinct(X24,X42)
      | c_List_Odistinct(c_List_Olist_OCons(X2,X24,X42),X42)
      | c_in(X2,c_List_Oset(X24,X42),X42) ),
    file('<stdin>',cls_List_Odistinct_Osimps__2_2) ).

fof(c_0_818,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X15,X27,tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).

fof(c_0_819,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X15,X27,tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).

fof(c_0_820,axiom,
    ! [X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X19,X4),c_0,X4),X4) ),
    file('<stdin>',cls_Power_Ozero__less__power__abs__iff_2) ).

fof(c_0_821,axiom,
    ! [X84,X48] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_Numeral_Onumber__of(X84,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_2) ).

fof(c_0_822,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omax(X2,c_Orderings_Omax(X2,X1,X3),X3) = c_Orderings_Omax(X2,X1,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).

fof(c_0_823,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omin(X2,c_Orderings_Omin(X2,X1,X3),X3) = c_Orderings_Omin(X2,X1,X3) ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).

fof(c_0_824,axiom,
    ! [X13,X14,X4] :
      ( c_in(c_Main_OsubsetI__1(X14,X13,X4),X14,X4)
      | c_lessequals(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_OsubsetI_0) ).

fof(c_0_825,axiom,
    ! [X88,X89] :
      ( ~ c_in(c_Message_Omsg_OHash(X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OHash__synth_0) ).

fof(c_0_826,axiom,
    ! [X2,X22,X42] : c_List_Oreplicate(c_Suc(X22),X2,X42) = c_List_Olist_OCons(X2,c_List_Oreplicate(X22,X2,X42),X42),
    file('<stdin>',cls_List_Oreplicate_Oreplicate__Suc_0) ).

fof(c_0_827,axiom,
    ! [X24,X2,X22,X4] : c_List_Onth(c_List_Olist_OCons(X2,X24,X4),c_Suc(X22),X4) = c_List_Onth(X24,X22,X4),
    file('<stdin>',cls_List_Onth__Cons__Suc_0) ).

fof(c_0_828,axiom,
    ! [X24,X2,X22,X4] : c_List_Odrop(c_Suc(X22),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Odrop(X22,X24,X4),
    file('<stdin>',cls_List_Odrop__Suc__Cons_0) ).

fof(c_0_829,axiom,
    ! [X2,X12] :
      ( c_Numeral_Onumber__of(X12,tc_nat) != c_0
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).

fof(c_0_830,axiom,
    ! [X65,X19,X4] : c_Nat_Osize(c_List_Olist_OCons(X19,X65,X4),tc_List_Olist(X4)) = c_plus(c_Nat_Osize(X65,tc_List_Olist(X4)),c_Suc(c_0),tc_nat),
    file('<stdin>',cls_List_Olist_Osize__2_0) ).

fof(c_0_831,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X2,X4),X4) = c_uminus(c_Numeral_Onumber__of(X2,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__6_0) ).

fof(c_0_832,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_Numeral_Onumber__of(X2,X4) = c_Numeral_Onumber__of(X1,X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__1_1) ).

fof(c_0_833,axiom,
    ! [X2,X22] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | ~ c_less(c_0,X22,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X2,X22,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__power_2) ).

fof(c_0_834,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | ~ c_less(c_0,X1,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__power_2) ).

fof(c_0_835,axiom,
    ! [X24,X22,X4] : c_Nat_Osize(c_List_Otake(X22,X24,X4),tc_List_Olist(X4)) = c_Orderings_Omin(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat),
    file('<stdin>',cls_List_Olength__take_0) ).

fof(c_0_836,axiom,
    ! [X24,X22,X4] : c_Nat_Osize(c_List_Odrop(X22,X24,X4),tc_List_Olist(X4)) = c_minus(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat),
    file('<stdin>',cls_List_Olength__drop_0) ).

fof(c_0_837,axiom,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_minus(c_Numeral_Onumber__of(X48,X4),c_1,X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__5_0) ).

fof(c_0_838,axiom,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(X19,X3),c_1,X3)
      | c_less(c_uminus(c_1,X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__less__iff__1_0) ).

fof(c_0_839,axiom,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(X19,X3),c_1,X3)
      | c_lessequals(c_uminus(c_1,X3),X19,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__le__iff__1_0) ).

fof(c_0_840,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X2,X4) = c_uminus(c_divide(c_1,X2,X4),X4) ),
    file('<stdin>',cls_NatSimprocs_Ominus1__divide_0) ).

fof(c_0_841,axiom,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_1,c_uminus(X28,X3),X3)
      | c_less(X28,c_uminus(c_1,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__minus__iff__1_0) ).

fof(c_0_842,axiom,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_1,c_uminus(X28,X3),X3)
      | c_lessequals(X28,c_uminus(c_1,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__minus__iff__1_0) ).

fof(c_0_843,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__sum_1) ).

fof(c_0_844,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__sum_0) ).

fof(c_0_845,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X1,tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__sum_1) ).

fof(c_0_846,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X2,tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__sum_0) ).

fof(c_0_847,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__difference_1) ).

fof(c_0_848,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__difference_0) ).

fof(c_0_849,axiom,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(c_1,X3),X19,X3)
      | c_less(c_uminus(X19,X3),c_1,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__less__iff__1_1) ).

fof(c_0_850,axiom,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(c_1,X3),X19,X3)
      | c_lessequals(c_uminus(X19,X3),c_1,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__le__iff__1_1) ).

fof(c_0_851,axiom,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(X28,c_uminus(c_1,X3),X3)
      | c_less(c_1,c_uminus(X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oless__minus__iff__1_1) ).

fof(c_0_852,axiom,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(X28,c_uminus(c_1,X3),X3)
      | c_lessequals(c_1,c_uminus(X28,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Ole__minus__iff__1_1) ).

fof(c_0_853,axiom,
    ! [X13,X14,X4] : c_union(X14,c_union(X13,X14,X4),X4) = c_union(X13,X14,X4),
    file('<stdin>',cls_Message_Ostrange__Un__eq_0) ).

fof(c_0_854,axiom,
    ! [X2,X14,X4] : c_insert(X2,c_insert(X2,X14,X4),X4) = c_insert(X2,X14,X4),
    file('<stdin>',cls_Set_Oinsert__absorb2_0) ).

fof(c_0_855,axiom,
    ! [X29,X22] : c_Nat_Opower(X29,c_Suc(X22),tc_nat) = c_times(X29,c_Nat_Opower(X29,X22,tc_nat),tc_nat),
    file('<stdin>',cls_Power_Opower_Osimps__2_0) ).

fof(c_0_856,axiom,
    ! [X22,X16] : c_times(c_Suc(X16),X22,tc_nat) = c_plus(X22,c_times(X16,X22,tc_nat),tc_nat),
    file('<stdin>',cls_Nat_Oop_A_K_Omult__Suc_0) ).

fof(c_0_857,axiom,
    ! [X22,X16] : c_times(X16,c_Suc(X22),tc_nat) = c_plus(X16,c_times(X16,X22,tc_nat),tc_nat),
    file('<stdin>',cls_Nat_Omult__Suc__right_0) ).

fof(c_0_858,axiom,
    ! [X29,X22] : c_Nat_Opower(X29,c_Suc(X22),tc_IntDef_Oint) = c_times(X29,c_Nat_Opower(X29,X22,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Opower_Osimps__2_0) ).

fof(c_0_859,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_uminus(X28,X4),X4) = c_uminus(c_divide(X19,X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__minus__right_0) ).

fof(c_0_860,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_uminus(X19,tc_IntDef_Oint),c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozmod__zminus__zminus_0) ).

fof(c_0_861,axiom,
    ! [X19,X13,X4] : c_Union(c_insert(X19,X13,tc_set(X4)),X4) = c_union(X19,c_Union(X13,X4),X4),
    file('<stdin>',cls_Set_OUnion__insert_0) ).

fof(c_0_862,axiom,
    ! [X19,X13,X4] : c_Inter(c_insert(X19,X13,tc_set(X4)),X4) = c_inter(X19,c_Inter(X13,X4),X4),
    file('<stdin>',cls_Set_OInter__insert_0) ).

fof(c_0_863,axiom,
    ! [X67,X14,X42] : c_List_Olistset(c_List_Olist_OCons(X14,X67,tc_set(X42)),X42) = c_List_Oset__Cons(X14,c_List_Olistset(X67,X42),X42),
    file('<stdin>',cls_List_Olistset_Osimps__2_0) ).

fof(c_0_864,axiom,
    ! [X24,X2,X42] : c_List_Oconcat(c_List_Olist_OCons(X2,X24,tc_List_Olist(X42)),X42) = c_append(X2,c_List_Oconcat(X24,X42),X42),
    file('<stdin>',cls_List_Oconcat_Osimps__2_0) ).

fof(c_0_865,axiom,
    ! [X14,X4] :
      ( ~ c_in(c_Pow(X14,X4),c_Finite__Set_OFinites,tc_set(tc_set(X4)))
      | c_in(X14,c_Finite__Set_OFinites,tc_set(X4)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Pow__iff_0) ).

fof(c_0_866,axiom,
    ! [X12,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,c_Numeral_Onumber__of(X12,tc_nat),X4) != c_0
      | c_less(c_0,c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Opower__eq__0__iff__number__of_1) ).

fof(c_0_867,axiom,
    ! [X22] : c_plus(X22,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(X22)),
    file('<stdin>',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).

fof(c_0_868,axiom,
    ! [X22] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X22,tc_nat) = c_Suc(c_Suc(X22)),
    file('<stdin>',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).

fof(c_0_869,axiom,
    ! [X2,X14,X4] :
      ( c_in(c_0,X14,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X14,X4) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Osublist__singleton_1) ).

fof(c_0_870,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_plus(X28,X19,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_Divides_Oop_Amod(X28,X19,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozmod__zadd__self2_0) ).

fof(c_0_871,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_plus(X19,X28,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_Divides_Oop_Amod(X28,X19,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozmod__zadd__self1_0) ).

fof(c_0_872,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Omod__mod__trivial_0) ).

fof(c_0_873,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    file('<stdin>',cls_Divides_Onat__mod__mod__trivial_0) ).

fof(c_0_874,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_plus(X16,X22,tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    file('<stdin>',cls_Divides_Omod__add__self2_0) ).

fof(c_0_875,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_plus(X22,X16,tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    file('<stdin>',cls_Divides_Omod__add__self1_0) ).

fof(c_0_876,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__product_0) ).

fof(c_0_877,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_times(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X1,tc_nat)
      | c_Parity_Oeven(X2,tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__product_0) ).

fof(c_0_878,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,X84),tc_nat) ),
    file('<stdin>',cls_NatBin_Oadd__nat__number__of_2) ).

fof(c_0_879,axiom,
    ! [X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | c_lessequals(c_Finite__Set_OMin(X14,X3),c_Finite__Set_OMax(X14,X3),X3)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).

fof(c_0_880,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oring(X4)
      | c_times(X19,c_uminus(X28,X4),X4) = c_uminus(c_times(X19,X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__minus__right_0) ).

fof(c_0_881,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oring(X4)
      | c_times(c_uminus(X19,X4),X28,X4) = c_uminus(c_times(X19,X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__minus__left_0) ).

fof(c_0_882,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_uminus(X19,X4),X28,X4) = c_uminus(c_divide(X19,X28,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__minus__left_0) ).

fof(c_0_883,axiom,
    ! [X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X4) = c_0 ),
    file('<stdin>',cls_NatBin_Ozero__power2_0) ).

fof(c_0_884,axiom,
    ! [X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X4) = c_1 ),
    file('<stdin>',cls_NatBin_Oone__power2_0) ).

fof(c_0_885,axiom,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4) = c_0 ),
    file('<stdin>',cls_Parity_Opower__eq__0__iff__number__of_2) ).

fof(c_0_886,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X2,X1,X4)
      | c_lessequals(c_SetInterval_OlessThan(X2,X4),c_SetInterval_OlessThan(X1,X4),tc_set(X4)) ),
    file('<stdin>',cls_SetInterval_OlessThan__subset__iff_1) ).

fof(c_0_887,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X1,X2,X4)
      | c_lessequals(c_SetInterval_OgreaterThan(X2,X4),c_SetInterval_OgreaterThan(X1,X4),tc_set(X4)) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__subset__iff_1) ).

fof(c_0_888,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X2,X1,X4)
      | c_lessequals(c_SetInterval_OatMost(X2,X4),c_SetInterval_OatMost(X1,X4),tc_set(X4)) ),
    file('<stdin>',cls_SetInterval_OatMost__subset__iff_1) ).

fof(c_0_889,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X1,X2,X4)
      | c_lessequals(c_SetInterval_OatLeast(X2,X4),c_SetInterval_OatLeast(X1,X4),tc_set(X4)) ),
    file('<stdin>',cls_SetInterval_OatLeast__subset__iff_1) ).

fof(c_0_890,axiom,
    ! [X24,X2,X48,X4] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_List_Onth(c_List_Olist_OCons(X2,X24,X4),c_Numeral_Onumber__of(X48,tc_nat),X4) = X2 ),
    file('<stdin>',cls_List_Onth__Cons__number__of_0) ).

fof(c_0_891,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg)
      | c_Message_Oparts(c_insert(X88,X89,tc_Message_Omsg)) = c_Message_Oparts(X89) ),
    file('<stdin>',cls_Message_Oparts__cut__eq_0) ).

fof(c_0_892,axiom,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X4,X4),X4)
      | c_Wellfounded__Recursion_Oacyclic(X6,X4) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).

fof(c_0_893,axiom,
    ! [X24,X22,X4] :
      ( ~ c_List_Odistinct(c_List_Orotate(X22,X24,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    file('<stdin>',cls_List_Odistinct__rotate_0) ).

fof(c_0_894,axiom,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(c_append(X24,X26,X4),X4)
      | c_List_Odistinct(X26,X4) ),
    file('<stdin>',cls_List_Odistinct__append_1) ).

fof(c_0_895,axiom,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(c_append(X24,X26,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    file('<stdin>',cls_List_Odistinct__append_0) ).

fof(c_0_896,axiom,
    ! [X24,X2,X42] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X2,X24,X42),X42)
      | c_List_Odistinct(X24,X42) ),
    file('<stdin>',cls_List_Odistinct_Osimps__2_1) ).

fof(c_0_897,axiom,
    ! [X24,X2,X48,X4] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_List_Otake(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Otake__Cons__number__of_0) ).

fof(c_0_898,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X2)),X4),X4)
      | c_lessequals(c_Numeral_Onumber__of(X2,X4),c_0,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__16_1) ).

fof(c_0_899,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(X48,tc_nat) ),
    file('<stdin>',cls_NatBin_Omod__nat__number__of_1) ).

fof(c_0_900,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(X48,tc_nat) ),
    file('<stdin>',cls_NatBin_Oadd__nat__number__of_1) ).

fof(c_0_901,axiom,
    ! [X93,X89] :
      ( ~ c_in(X93,c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat)
      | c_in(X93,c_Message_OkeysFor(X89),tc_nat)
      | X93 = c_Message_OinvKey(v_sko__uhi(X89,X93)) ),
    file('<stdin>',cls_Event_OkeysFor__synth_H_1) ).

fof(c_0_902,axiom,
    ! [X26,X24,X4] :
      ( X24 = c_List_Olist_ONil
      | c_List_Otl(c_append(X24,X26,X4),X4) = c_append(c_List_Otl(X24,X4),X26,X4) ),
    file('<stdin>',cls_List_Otl__append2_0) ).

fof(c_0_903,axiom,
    ! [X24,X2,X42] :
      ( X24 = c_List_Olist_ONil
      | c_List_Obutlast(c_List_Olist_OCons(X2,X24,X42),X42) = c_List_Olist_OCons(X2,c_List_Obutlast(X24,X42),X42) ),
    file('<stdin>',cls_List_Obutlast_Osimps__2_1) ).

fof(c_0_904,axiom,
    ! [X2,X22] :
      ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,tc_IntDef_Oint),X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | X2 = c_0 ),
    file('<stdin>',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).

fof(c_0_905,axiom,
    ! [X24,X2,X42] : c_List_Oset(c_List_Olist_OCons(X2,X24,X42),X42) = c_insert(X2,c_List_Oset(X24,X42),X42),
    file('<stdin>',cls_List_Oset_Osimps__2_0) ).

fof(c_0_906,axiom,
    ! [X2,X22] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X2,tc_IntDef_Oint),X22,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozero__le__zpower__abs_0) ).

fof(c_0_907,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_OrderedGroup_Opprt(X19,X4),c_OrderedGroup_Opprt(X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Opprt__mono_0) ).

fof(c_0_908,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_OrderedGroup_Onprt(X19,X4),c_OrderedGroup_Onprt(X28,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Onprt__mono_0) ).

fof(c_0_909,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_uminus(X28,X4),c_uminus(X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__less__iff__less_1) ).

fof(c_0_910,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_uminus(X28,X4),c_uminus(X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__le__iff__le_1) ).

fof(c_0_911,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X12,X2),X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__12_0) ).

fof(c_0_912,axiom,
    ! [X1,X22,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X22,tc_nat)
      | c_List_Otake(X22,X1,X4) = X1 ),
    file('<stdin>',cls_List_Otake__all_0) ).

fof(c_0_913,axiom,
    ! [X1,X22,X4] :
      ( c_Divides_Oop_Amod(X22,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) != c_0
      | c_List_Orotate(X22,X1,X4) = X1 ),
    file('<stdin>',cls_List_Orotate__id_0) ).

fof(c_0_914,axiom,
    ! [X24,X22,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat)
      | c_List_Odrop(X22,X24,X4) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Odrop__eq__Nil_1) ).

fof(c_0_915,axiom,
    ! [X2] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).

fof(c_0_916,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__14_1) ).

fof(c_0_917,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(X16,X22,tc_nat)
      | c_less(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__less__iff_1) ).

fof(c_0_918,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__le__iff_1) ).

fof(c_0_919,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(X12,X49,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__less__iff_1) ).

fof(c_0_920,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(X12,X49,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__le__iff_1) ).

fof(c_0_921,axiom,
    ! [X13,X14,X4] :
      ( ~ c_in(X14,c_Pow(X13,X4),tc_set(X4))
      | c_lessequals(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_OPow__iff_0) ).

fof(c_0_922,axiom,
    ! [X1,X2,X23,X4] :
      ( ~ c_Infinite__Set_Oatmost__one(X23,X4)
      | ~ c_in(X1,X23,X4)
      | ~ c_in(X2,X23,X4)
      | X1 = X2 ),
    file('<stdin>',cls_Infinite__Set_Oatmost__one__unique_0) ).

fof(c_0_923,axiom,
    ! [X1,X22,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),c_1,tc_nat)
      | c_List_Orotate(X22,X1,X4) = X1 ),
    file('<stdin>',cls_List_Orotate__length01_0) ).

fof(c_0_924,axiom,
    ! [X16,X60,X44] : c_List_Odrop(X16,c_List_Oupt(X44,X60),tc_nat) = c_List_Oupt(c_plus(X44,X16,tc_nat),X60),
    file('<stdin>',cls_List_Odrop__upt_0) ).

fof(c_0_925,axiom,
    ! [X1] :
      ( ~ c_less(c_0,X1,tc_nat)
      | c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1 ),
    file('<stdin>',cls_Nat_OSuc__pred_0) ).

fof(c_0_926,axiom,
    ! [X103,X25] :
      ( ~ c_in(c_Message_Omsg_ONonce(X25),c_Event_Oused(X103),tc_Message_Omsg)
      | ~ c_lessequals(v_sko__urX(X103),X25,tc_nat) ),
    file('<stdin>',cls_Public_ONonce__supply__lemma_0) ).

fof(c_0_927,axiom,
    ! [X2,X22] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__power_0) ).

fof(c_0_928,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X2,tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__power_0) ).

fof(c_0_929,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_0 = c_Numeral_Onumber__of(X1,X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__6_1) ).

fof(c_0_930,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_8) ).

fof(c_0_931,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_11) ).

fof(c_0_932,axiom,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X13,X14,tc_set(X4))
      | ~ c_lessequals(X14,X13,tc_set(X4))
      | X14 = X13 ),
    file('<stdin>',cls_Set_Osubset__antisym_0) ).

fof(c_0_933,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Event_Oused(X89),tc_Message_Omsg)
      | c_in(X88,c_Event_Oused(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Public_OMPair__used_1) ).

fof(c_0_934,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Event_Oused(X89),tc_Message_Omsg)
      | c_in(X87,c_Event_Oused(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Public_OMPair__used_0) ).

fof(c_0_935,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__analz_1) ).

fof(c_0_936,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X87,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__analz_0) ).

fof(c_0_937,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oparts(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__parts_1) ).

fof(c_0_938,axiom,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oparts(X89),tc_Message_Omsg)
      | c_in(X87,c_Message_Oparts(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OMPair__parts_0) ).

fof(c_0_939,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,c_HOL_Oinverse(X19,X4),X4)
      | c_less(c_0,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__positive__iff__positive_0) ).

fof(c_0_940,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_HOL_Oinverse(X19,X4),c_0,X4)
      | c_lessequals(X19,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0) ).

fof(c_0_941,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,c_HOL_Oinverse(X19,X4),X4)
      | c_lessequals(c_0,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0) ).

fof(c_0_942,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_HOL_Oinverse(X19,X4),c_0,X4)
      | c_less(X19,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__negative__iff__negative_0) ).

fof(c_0_943,axiom,
    ! [X13,X14,X4] :
      ( ~ c_less(X14,X13,tc_set(X4))
      | ~ c_lessequals(X13,X14,tc_set(X4)) ),
    file('<stdin>',cls_Set_OpsubsetE_0) ).

fof(c_0_944,axiom,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Pow(X14,X4),c_Finite__Set_OFinites,tc_set(tc_set(X4))) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Pow__iff_1) ).

fof(c_0_945,axiom,
    ! [X24,X2,X42] : ~ c_List_Onull(c_List_Olist_OCons(X2,X24,X42),X42),
    file('<stdin>',cls_List_Onull_Osimps__2_0) ).

fof(c_0_946,axiom,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),X4),X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__4_0) ).

fof(c_0_947,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_divide(X19,X28,X4),X4) = c_divide(X28,X19,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__divide_0) ).

fof(c_0_948,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,X7,X4) != c_divide(X28,X7,X4)
      | X19 = X28
      | X7 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__cancel__right_0) ).

fof(c_0_949,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X7,X19,X4) != c_divide(X7,X28,X4)
      | X19 = X28
      | X7 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__cancel__left_0) ).

fof(c_0_950,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OlessThan(X17,X4),X4)
      | c_less(X44,X17,X4) ),
    file('<stdin>',cls_SetInterval_OlessThan__iff_0) ).

fof(c_0_951,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThan(X17,X4),X4)
      | c_less(X17,X44,X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__iff_0) ).

fof(c_0_952,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatMost(X17,X4),X4)
      | c_lessequals(X44,X17,X4) ),
    file('<stdin>',cls_SetInterval_OatMost__iff_0) ).

fof(c_0_953,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeast(X17,X4),X4)
      | c_lessequals(X17,X44,X4) ),
    file('<stdin>',cls_SetInterval_OatLeast__iff_0) ).

fof(c_0_954,axiom,
    ! [X22,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X22,X4),X4) = c_1 ),
    file('<stdin>',cls_IntArith_Oabs__power__minus__one_0) ).

fof(c_0_955,axiom,
    ! [X48] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X48,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X48,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Oint__eq__iff__number__of_2) ).

fof(c_0_956,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | c_Numeral_Onumber__of(X2,X4) = c_0 ),
    file('<stdin>',cls_IntArith_Oarith__special__8_1) ).

fof(c_0_957,axiom,
    ! [X9,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X9),c_Message_Oparts(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__Number_0) ).

fof(c_0_958,axiom,
    ! [X9,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X9),c_Message_Oparts(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__Nonce_0) ).

fof(c_0_959,axiom,
    ! [X93,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X93),c_Message_Oparts(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__Key_0) ).

fof(c_0_960,axiom,
    ! [X88,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X88),c_Message_Oparts(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__Hash_0) ).

fof(c_0_961,axiom,
    ! [X111,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X111),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X111),c_Message_Oparts(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__insert__Agent_0) ).

fof(c_0_962,axiom,
    ! [X9,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X9),c_Message_Oanalz(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__insert__Number_0) ).

fof(c_0_963,axiom,
    ! [X9,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X9),c_Message_Oanalz(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__insert__Nonce_0) ).

fof(c_0_964,axiom,
    ! [X88,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X88),c_Message_Oanalz(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__insert__Hash_0) ).

fof(c_0_965,axiom,
    ! [X111,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X111),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X111),c_Message_Oanalz(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__insert__Agent_0) ).

fof(c_0_966,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_uminus(X19,X4),c_0,X4)
      | c_less(c_0,X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).

fof(c_0_967,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_uminus(X19,X4),c_0,X4)
      | c_lessequals(c_0,X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).

fof(c_0_968,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_0,c_uminus(X19,X4),X4)
      | c_less(X19,c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).

fof(c_0_969,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_0,c_uminus(X19,X4),X4)
      | c_lessequals(X19,c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).

fof(c_0_970,axiom,
    ! [X6,X4] : c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X4,X4)),X4) = c_Transitive__Closure_Ortrancl(X6,X4),
    file('<stdin>',cls_Transitive__Closure_Otrancl__reflcl_0) ).

fof(c_0_971,axiom,
    ! [X86,X4] : c_Transitive__Closure_Ortrancl(c_union(X86,c_Relation_OId,tc_prod(X4,X4)),X4) = c_Transitive__Closure_Ortrancl(X86,X4),
    file('<stdin>',cls_Transitive__Closure_Ortrancl__reflcl_0) ).

fof(c_0_972,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_0,c_NatArith_Oof__nat(X22,X4),X4)
      | c_less(c_0,X22,tc_nat) ),
    file('<stdin>',cls_NatArith_Oof__nat__0__less__iff_0) ).

fof(c_0_973,axiom,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_IntDef_Oof__int(X12,X4),c_0,X4)
      | c_less(X12,c_0,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Oof__int__less__0__iff_0) ).

fof(c_0_974,axiom,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_IntDef_Oof__int(X12,X4),c_0,X4)
      | c_lessequals(X12,c_0,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Oof__int__le__0__iff_0) ).

fof(c_0_975,axiom,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_IntDef_Oof__int(X49,X4),X4)
      | c_less(c_0,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Oof__int__0__less__iff_0) ).

fof(c_0_976,axiom,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,c_IntDef_Oof__int(X49,X4),X4)
      | c_lessequals(c_0,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Oof__int__0__le__iff_0) ).

fof(c_0_977,axiom,
    ! [X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Finite__Set_OMin(X14,X4),X14,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMin__in_0) ).

fof(c_0_978,axiom,
    ! [X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Finite__Set_OMax(X14,X4),X14,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_OMax__in_0) ).

fof(c_0_979,axiom,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X14,X13,tc_set(X4))
      | c_in(X14,c_Pow(X13,X4),tc_set(X4)) ),
    file('<stdin>',cls_Set_OPow__iff_1) ).

fof(c_0_980,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_minus(X19,X28,X4),X4) = c_minus(X28,X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Ominus__diff__eq_0) ).

fof(c_0_981,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X19,X7,X4) != c_times(X28,X7,X4)
      | X19 = X28
      | X7 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).

fof(c_0_982,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X7,X19,X4) != c_times(X7,X28,X4)
      | X19 = X28
      | X7 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).

fof(c_0_983,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X28,X14))),c_Event_Oused(X103),tc_Message_Omsg),
    file('<stdin>',cls_Public_OprivateKey__into__used_0) ).

fof(c_0_984,axiom,
    ! [X28,X14] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X28,X14))),c_Event_OinitState(X14),tc_Message_Omsg),
    file('<stdin>',cls_Public_OpriK__in__initState_0) ).

fof(c_0_985,axiom,
    ! [X24,X22,X4] : c_List_Orotate(c_Suc(X22),X24,X4) = c_List_Orotate1(c_List_Orotate(X22,X24,X4),X4),
    file('<stdin>',cls_List_Orotate__Suc_0) ).

fof(c_0_986,axiom,
    ! [X24,X4] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X24,X4),tc_List_Olist(X4)),c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat),
    file('<stdin>',cls_List_Olength__remdups__leq_0) ).

fof(c_0_987,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
      | c_plus(X28,X19,X4) != c_plus(X7,X19,X4)
      | X28 = X7 ),
    file('<stdin>',cls_OrderedGroup_Oadd__right__cancel_0) ).

fof(c_0_988,axiom,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
      | c_plus(X19,X28,X4) != c_plus(X19,X7,X4)
      | X28 = X7 ),
    file('<stdin>',cls_OrderedGroup_Oadd__left__cancel_0) ).

fof(c_0_989,axiom,
    ! [X103,X88,X14] : c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X14,X88),X103,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X103),
    file('<stdin>',cls_Event_Oknows__Spy__Gets_0) ).

fof(c_0_990,axiom,
    ! [X51,X25,X4] :
      ( ~ c_in(X25,c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Oconcat(X51,X4) != c_List_Olist_ONil
      | X25 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oconcat__eq__Nil__conv_0) ).

fof(c_0_991,axiom,
    ! [X51,X25,X4] :
      ( ~ c_in(X25,c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Olist_ONil != c_List_Oconcat(X51,X4)
      | X25 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__eq__concat__conv_0) ).

fof(c_0_992,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(X19,c_divide(X28,X19,X4),X4) = X28 ),
    file('<stdin>',cls_Ring__and__Field_Otimes__divide__self__right_1) ).

fof(c_0_993,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(c_divide(X28,X19,X4),X19,X4) = X28 ),
    file('<stdin>',cls_Ring__and__Field_Otimes__divide__self__left_1) ).

fof(c_0_994,axiom,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X19,X7,X4),X7,X4) = X19 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__right__if2_1) ).

fof(c_0_995,axiom,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X7,X19,X4),X7,X4) = X19 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__left__if2_1) ).

fof(c_0_996,axiom,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_minus(c_1,c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X12)),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__4_0) ).

fof(c_0_997,axiom,
    ! [X24,X22,X4] :
      ( c_List_Odrop(X22,X24,X4) != c_List_Olist_ONil
      | c_lessequals(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat) ),
    file('<stdin>',cls_List_Odrop__eq__Nil_0) ).

fof(c_0_998,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_0,c_HOL_Oinverse(X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__positive__iff__positive_1) ).

fof(c_0_999,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_lessequals(c_HOL_Oinverse(X19,X4),c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1) ).

fof(c_0_1000,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,X19,X4)
      | c_lessequals(c_0,c_HOL_Oinverse(X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1) ).

fof(c_0_1001,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_HOL_Oinverse(X19,X4),c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__negative__iff__negative_1) ).

fof(c_0_1002,axiom,
    ! [X103,X14] :
      ( ~ c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg) ),
    file('<stdin>',cls_Public_OSpy__spies__bad__shrK_0) ).

fof(c_0_1003,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_nat),tc_nat) = c_minus(X15,c_Suc(X27),tc_nat),
    file('<stdin>',cls_SetInterval_Ocard__greaterThanLessThan_0) ).

fof(c_0_1004,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X27,X15,tc_nat),tc_nat) = c_minus(c_Suc(X15),X27,tc_nat),
    file('<stdin>',cls_SetInterval_Ocard__atLeastAtMost_0) ).

fof(c_0_1005,axiom,
    ! [X2,X22,X4] :
      ( X22 = c_0
      | c_List_Oset(c_List_Oreplicate(X22,X2,X4),X4) = c_insert(X2,c_emptyset,X4) ),
    file('<stdin>',cls_List_Oset__replicate_0) ).

fof(c_0_1006,axiom,
    ! [X2,X22,X4] : c_List_Orev(c_List_Oreplicate(X22,X2,X4),X4) = c_List_Oreplicate(X22,X2,X4),
    file('<stdin>',cls_List_Orev__replicate_0) ).

fof(c_0_1007,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_uminus(X19,X4),c_uminus(X28,X4),X4) = c_divide(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ominus__divide__divide_0) ).

fof(c_0_1008,axiom,
    ! [X22] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X22)),tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onot__zle__0__negative_0) ).

fof(c_0_1009,axiom,
    ! [X89,X20] :
      ( ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(X20,c_Message_Osynth(X89),tc_set(tc_Message_Omsg)) ),
    file('<stdin>',cls_Message_Osynth__subset__iff_0) ).

fof(c_0_1010,axiom,
    ! [X89,X20] :
      ( ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(X20,c_Message_Oparts(X89),tc_set(tc_Message_Omsg)) ),
    file('<stdin>',cls_Message_Oparts__subset__iff_0) ).

fof(c_0_1011,axiom,
    ! [X89,X20] :
      ( ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(X20,c_Message_Oanalz(X89),tc_set(tc_Message_Omsg)) ),
    file('<stdin>',cls_Message_Oanalz__subset__iff_0) ).

fof(c_0_1012,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X44,X17,X4)
      | c_in(X44,c_SetInterval_OlessThan(X17,X4),X4) ),
    file('<stdin>',cls_SetInterval_OlessThan__iff_1) ).

fof(c_0_1013,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X17,X44,X4)
      | c_in(X44,c_SetInterval_OgreaterThan(X17,X4),X4) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__iff_1) ).

fof(c_0_1014,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_lessequals(X44,X17,X4)
      | c_in(X44,c_SetInterval_OatMost(X17,X4),X4) ),
    file('<stdin>',cls_SetInterval_OatMost__iff_1) ).

fof(c_0_1015,axiom,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_lessequals(X17,X44,X4)
      | c_in(X44,c_SetInterval_OatLeast(X17,X4),X4) ),
    file('<stdin>',cls_SetInterval_OatLeast__iff_1) ).

fof(c_0_1016,axiom,
    ! [X13,X14,X4] : c_inter(X14,c_minus(X13,X14,tc_set(X4)),X4) = c_emptyset,
    file('<stdin>',cls_Set_ODiff__disjoint_0) ).

fof(c_0_1017,axiom,
    ! [X60,X44] :
      ( ~ c_less(X44,X60,tc_nat)
      | c_List_Olast(c_List_Oupt(X44,X60),tc_nat) = c_minus(X60,c_1,tc_nat) ),
    file('<stdin>',cls_List_Olast__upt_0) ).

fof(c_0_1018,axiom,
    ! [X97,X98,X106,X104,X107,X105] :
      ( c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OSays(X107,X106,X97)
      | X98 = X97 ),
    file('<stdin>',cls_Event_Oevent_Oinject__1_2) ).

fof(c_0_1019,axiom,
    ! [X97,X98,X106,X104,X107,X105] :
      ( c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OSays(X107,X106,X97)
      | X104 = X106 ),
    file('<stdin>',cls_Event_Oevent_Oinject__1_1) ).

fof(c_0_1020,axiom,
    ! [X97,X98,X106,X104,X107,X105] :
      ( c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OSays(X107,X106,X97)
      | X105 = X107 ),
    file('<stdin>',cls_Event_Oevent_Oinject__1_0) ).

fof(c_0_1021,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Sum__Type_OInr(X2,X3,X4) != c_Sum__Type_OInr(X1,X3,X4)
      | X2 = X1 ),
    file('<stdin>',cls_Sum__Type_OInr__eq_0) ).

fof(c_0_1022,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Sum__Type_OInl(X2,X4,X3) != c_Sum__Type_OInl(X1,X4,X3)
      | X2 = X1 ),
    file('<stdin>',cls_Sum__Type_OInl__eq_0) ).

fof(c_0_1023,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_4) ).

fof(c_0_1024,axiom,
    ! [X52,X26,X24,X4] :
      ( c_append(X24,X26,X4) != c_append(X24,X52,X4)
      | X26 = X52 ),
    file('<stdin>',cls_List_Osame__append__eq_0) ).

fof(c_0_1025,axiom,
    ! [X64,X65,X43,X19,X4] :
      ( c_List_Olist_OCons(X19,X65,X4) != c_List_Olist_OCons(X43,X64,X4)
      | X65 = X64 ),
    file('<stdin>',cls_List_Olist_Oinject_1) ).

fof(c_0_1026,axiom,
    ! [X64,X65,X43,X19,X4] :
      ( c_List_Olist_OCons(X19,X65,X4) != c_List_Olist_OCons(X43,X64,X4)
      | X19 = X43 ),
    file('<stdin>',cls_List_Olist_Oinject_0) ).

fof(c_0_1027,axiom,
    ! [X52,X26,X24,X4] :
      ( c_append(X26,X24,X4) != c_append(X52,X24,X4)
      | X26 = X52 ),
    file('<stdin>',cls_List_Oappend__same__eq_0) ).

fof(c_0_1028,axiom,
    ! [X9,X11,X3,X4] :
      ( c_Datatype__Universe_OIn1(X11,X4,X3) != c_Datatype__Universe_OIn1(X9,X4,X3)
      | X11 = X9 ),
    file('<stdin>',cls_Datatype__Universe_OIn1__eq_0) ).

fof(c_0_1029,axiom,
    ! [X9,X11,X3,X4] :
      ( c_Datatype__Universe_OIn0(X11,X4,X3) != c_Datatype__Universe_OIn0(X9,X4,X3)
      | X11 = X9 ),
    file('<stdin>',cls_Datatype__Universe_OIn0__eq_0) ).

fof(c_0_1030,axiom,
    ! [X28,X19,X3,X4] :
      ( c_Datatype__Universe_OAtom(X19,X4,X3) != c_Datatype__Universe_OAtom(X28,X4,X3)
      | X19 = X28 ),
    file('<stdin>',cls_Datatype__Universe_OAtom__Atom__eq_0) ).

fof(c_0_1031,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Datatype__Universe_ONumb(X2,X4,X3) != c_Datatype__Universe_ONumb(X1,X4,X3)
      | X2 = X1 ),
    file('<stdin>',cls_Datatype__Universe_ONumb__inject__dest_0) ).

fof(c_0_1032,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Datatype__Universe_OLeaf(X2,X4,X3) != c_Datatype__Universe_OLeaf(X1,X4,X3)
      | X2 = X1 ),
    file('<stdin>',cls_Datatype__Universe_OLeaf__inject__dest_0) ).

fof(c_0_1033,axiom,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(c_uminus(X49,tc_IntDef_Oint),X12,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozminus__dvd__iff_0) ).

fof(c_0_1034,axiom,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(X49,c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odvd__zminus__iff_0) ).

fof(c_0_1035,axiom,
    ! [X89,X20] : c_Message_Oparts(c_union(X20,X89,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__Un_0) ).

fof(c_0_1036,axiom,
    ! [X94,X89] : c_Message_OkeysFor(c_union(X89,X94,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X89),c_Message_OkeysFor(X94),tc_nat),
    file('<stdin>',cls_Message_OkeysFor__Un_0) ).

fof(c_0_1037,axiom,
    ! [X22,X16] : c_Orderings_Omin(c_Suc(X16),c_Suc(X22),tc_nat) = c_Suc(c_Orderings_Omin(X16,X22,tc_nat)),
    file('<stdin>',cls_Nat_Omin__Suc__Suc_0) ).

fof(c_0_1038,axiom,
    ! [X22,X16] : c_Orderings_Omax(c_Suc(X16),c_Suc(X22),tc_nat) = c_Suc(c_Orderings_Omax(X16,X22,tc_nat)),
    file('<stdin>',cls_Nat_Omax__Suc__Suc_0) ).

fof(c_0_1039,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X48,X84),tc_nat) ),
    file('<stdin>',cls_NatBin_Omult__nat__number__of_1) ).

fof(c_0_1040,axiom,
    ! [X22,X16] : c_IntDef_Oint(c_plus(X16,X22,tc_nat)) = c_plus(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint),
    file('<stdin>',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).

fof(c_0_1041,axiom,
    ! [X28,X14] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X28,X14)),c_Message_OsymKeys,tc_nat),
    file('<stdin>',cls_Public_Onot__symKeys__priK_0) ).

fof(c_0_1042,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Osynth(c_Message_Osynth(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Osynth__synthD__dest_0) ).

fof(c_0_1043,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oparts(c_Message_Oparts(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oparts__partsD__dest_0) ).

fof(c_0_1044,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oanalz(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz__analzD__dest_0) ).

fof(c_0_1045,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_0,c_divide(X28,c_0,X4),X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Otimes__divide__self__right_0) ).

fof(c_0_1046,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_divide(X28,c_0,X4),c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Otimes__divide__self__left_0) ).

fof(c_0_1047,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(X19,c_0,X4),c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__right__if2_0) ).

fof(c_0_1048,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,c_times(X28,c_0,X4),X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__right__if1_0) ).

fof(c_0_1049,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(c_0,X19,X4),c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__left__if2_0) ).

fof(c_0_1050,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,c_times(c_0,X28,X4),X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__divide__cancel__left__if1_0) ).

fof(c_0_1051,axiom,
    ! [X28,X19,X3,X4] : c_Sum__Type_OInr(X28,X3,X4) != c_Sum__Type_OInl(X19,X4,X3),
    file('<stdin>',cls_Sum__Type_OInr__not__Inl_0) ).

fof(c_0_1052,axiom,
    ! [X28,X19,X3,X4] : c_Sum__Type_OInl(X19,X4,X3) != c_Sum__Type_OInr(X28,X3,X4),
    file('<stdin>',cls_Sum__Type_OInl__not__Inr_0) ).

fof(c_0_1053,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_ONumb(X17,X4,X3) != c_Datatype__Universe_OLeaf(X19,X4,X3),
    file('<stdin>',cls_Datatype__Universe_ONumb__not__Leaf_0) ).

fof(c_0_1054,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_OLeaf(X19,X4,X3) != c_Datatype__Universe_ONumb(X17,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OLeaf__not__Numb_0) ).

fof(c_0_1055,axiom,
    ! [X9,X11,X3,X4] : c_Datatype__Universe_OIn1(X9,X4,X3) != c_Datatype__Universe_OIn0(X11,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OIn1__not__In0_0) ).

fof(c_0_1056,axiom,
    ! [X9,X11,X3,X4] : c_Datatype__Universe_OIn0(X11,X4,X3) != c_Datatype__Universe_OIn1(X9,X4,X3),
    file('<stdin>',cls_Datatype__Universe_OIn0__not__In1_0) ).

fof(c_0_1057,axiom,
    ! [X25,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(X25),X89,tc_Message_Omsg)
      | c_in(c_Message_OinvKey(X25),c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat) ),
    file('<stdin>',cls_Event_OkeysFor__synth_H_3) ).

fof(c_0_1058,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X19,X14,X4) != c_insert(X28,c_emptyset,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_H_0) ).

fof(c_0_1059,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X28,c_emptyset,X4) != c_insert(X19,X14,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_0) ).

fof(c_0_1060,axiom,
    ! [X89,X20] :
      ( ~ c_lessequals(X20,c_Message_Osynth(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X89),tc_set(tc_Message_Omsg)) ),
    file('<stdin>',cls_Message_Osynth__subset__iff_1) ).

fof(c_0_1061,axiom,
    ! [X89,X20] :
      ( ~ c_lessequals(X20,c_Message_Oparts(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X89),tc_set(tc_Message_Omsg)) ),
    file('<stdin>',cls_Message_Oparts__subset__iff_1) ).

fof(c_0_1062,axiom,
    ! [X89,X20] :
      ( ~ c_lessequals(X20,c_Message_Oanalz(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X89),tc_set(tc_Message_Omsg)) ),
    file('<stdin>',cls_Message_Oanalz__subset__iff_1) ).

fof(c_0_1063,axiom,
    ! [X2,X4] : c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) = c_List_Orev(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4),
    file('<stdin>',cls_List_Osingleton__rev__conv_1) ).

fof(c_0_1064,axiom,
    ! [X2,X4] : c_List_Orev(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),
    file('<stdin>',cls_List_Orev__singleton__conv_1) ).

fof(c_0_1065,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_uminus(X19,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).

fof(c_0_1066,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_0,X19,X4)
      | c_lessequals(c_uminus(X19,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).

fof(c_0_1067,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_0,c_uminus(X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).

fof(c_0_1068,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_lessequals(c_0,c_uminus(X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).

fof(c_0_1069,axiom,
    ! [X22,X16,X17] :
      ( c_times(X16,X17,tc_nat) != c_times(X22,X17,tc_nat)
      | X16 = X22
      | X17 = c_0 ),
    file('<stdin>',cls_Nat_Omult__cancel2_0) ).

fof(c_0_1070,axiom,
    ! [X22,X16,X17] :
      ( c_times(X17,X16,tc_nat) != c_times(X17,X22,tc_nat)
      | X16 = X22
      | X17 = c_0 ),
    file('<stdin>',cls_Nat_Omult__cancel1_0) ).

fof(c_0_1071,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_uminus(X19,X4),c_IntDef_OInts,X4) ),
    file('<stdin>',cls_IntDef_OInts__minus_0) ).

fof(c_0_1072,axiom,
    ! [X2,X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X12,X2),X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__12_1) ).

fof(c_0_1073,axiom,
    ! [X2,X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_Parity_Oeven(X22,tc_nat)
      | c_Nat_Opower(c_uminus(X2,X4),X22,X4) = c_Nat_Opower(X2,X22,X4) ),
    file('<stdin>',cls_Parity_Opower__minus__even_0) ).

fof(c_0_1074,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_nat),tc_nat) = c_minus(X15,X27,tc_nat),
    file('<stdin>',cls_SetInterval_Ocard__greaterThanAtMost_0) ).

fof(c_0_1075,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X27,X15,tc_nat),tc_nat) = c_minus(X15,X27,tc_nat),
    file('<stdin>',cls_SetInterval_Ocard__atLeastLessThan_0) ).

fof(c_0_1076,axiom,
    ! [X22,X16,X17] :
      ( c_plus(X16,X17,tc_nat) != c_plus(X22,X17,tc_nat)
      | X16 = X22 ),
    file('<stdin>',cls_Nat_Onat__add__right__cancel_0) ).

fof(c_0_1077,axiom,
    ! [X22,X16,X17] :
      ( c_plus(X17,X16,tc_nat) != c_plus(X17,X22,tc_nat)
      | X16 = X22 ),
    file('<stdin>',cls_Nat_Onat__add__left__cancel_0) ).

fof(c_0_1078,axiom,
    ! [X28,X19,X4] :
      ( c_insert(X19,c_emptyset,X4) != c_insert(X28,c_emptyset,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Set_Osingleton__inject__dest_0) ).

fof(c_0_1079,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(X2,X4) != c_Numeral_Onumber__of(X1,X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__1_0) ).

fof(c_0_1080,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oring(X4)
      | c_times(c_uminus(X19,X4),c_uminus(X28,X4),X4) = c_times(X19,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ominus__mult__minus_0) ).

fof(c_0_1081,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_0,X22,tc_nat)
      | c_less(c_0,c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__0__less__iff_1) ).

fof(c_0_1082,axiom,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(X12,c_0,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X12,X4),c_0,X4) ),
    file('<stdin>',cls_IntDef_Oof__int__less__0__iff_1) ).

fof(c_0_1083,axiom,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(X12,c_0,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X12,X4),c_0,X4) ),
    file('<stdin>',cls_IntDef_Oof__int__le__0__iff_1) ).

fof(c_0_1084,axiom,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,X49,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__0__less__iff_1) ).

fof(c_0_1085,axiom,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,X49,tc_IntDef_Oint)
      | c_lessequals(c_0,c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__0__le__iff_1) ).

fof(c_0_1086,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oadd__nat__number__of_0) ).

fof(c_0_1087,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) != c_Numeral_Onumber__of(X84,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_1) ).

fof(c_0_1088,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) != c_Numeral_Onumber__of(X84,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_0) ).

fof(c_0_1089,axiom,
    ! [X1] :
      ( ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1 ),
    file('<stdin>',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).

fof(c_0_1090,axiom,
    ! [X22,X16] : c_plus(c_Suc(X16),X22,tc_nat) = c_Suc(c_plus(X16,X22,tc_nat)),
    file('<stdin>',cls_Nat_Oop_A_L_Oadd__Suc_0) ).

fof(c_0_1091,axiom,
    ! [X22,X16] : c_plus(X16,c_Suc(X22),tc_nat) = c_Suc(c_plus(X16,X22,tc_nat)),
    file('<stdin>',cls_Nat_Oadd__Suc__right_0) ).

fof(c_0_1092,axiom,
    ! [X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_minus(c_Numeral_Onumber__of(X48,X4),c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X12)),X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__5_0) ).

fof(c_0_1093,axiom,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_1,X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__3_0) ).

fof(c_0_1094,axiom,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_1,c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X12),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__2_0) ).

fof(c_0_1095,axiom,
    ! [X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X48),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oless__0__number__of_0) ).

fof(c_0_1096,axiom,
    ! [X93,X89] :
      ( ~ c_in(X93,c_Message_OkeysFor(X89),tc_nat)
      | c_in(X93,c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat) ),
    file('<stdin>',cls_Event_OkeysFor__synth_H_2) ).

fof(c_0_1097,axiom,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X4),X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__4_1) ).

fof(c_0_1098,axiom,
    ! [X87,X88,X89] : c_Message_OkeysFor(c_insert(c_Message_OHPair(X88,X87),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__HPair_0) ).

fof(c_0_1099,axiom,
    ! [X103,X88,X14] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X14,X88),X103,tc_Event_Oevent)) = c_Event_Oused(X103),
    file('<stdin>',cls_Event_Oused__Gets_0) ).

fof(c_0_1100,axiom,
    ! [X87,X88,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__MPair_0) ).

fof(c_0_1101,axiom,
    ! [X16,X18] :
      ( c_Divides_Oop_Amod(X16,X18,tc_IntDef_Oint) != c_0
      | X16 = c_times(X18,c_Main_Ozmod__eq__0D__dest__1(X18,X16),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

fof(c_0_1102,axiom,
    ! [X16,X18] :
      ( c_Divides_Oop_Amod(X16,X18,tc_nat) != c_0
      | X16 = c_times(X18,c_Main_Omod__eq__0D__dest__1(X18,X16),tc_nat) ),
    file('<stdin>',cls_Divides_Omod__eq__0D__dest_0) ).

fof(c_0_1103,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X103)),tc_Message_Omsg),
    file('<stdin>',cls_Public_Oanalz__spies__pubK_0) ).

fof(c_0_1104,axiom,
    ! [X9,X89] :
      ( ~ c_in(c_Message_Omsg_ONonce(X9),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_ONonce__synth__eq_0) ).

fof(c_0_1105,axiom,
    ! [X93,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(X93),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OKey__synth__eq_0) ).

fof(c_0_1106,axiom,
    ! [X1,X3,X4] : c_Relation_Oconverse(c_Relation_Oconverse(X1,X4,X3),X3,X4) = X1,
    file('<stdin>',cls_Relation_Oconverse__converse_0) ).

fof(c_0_1107,axiom,
    ! [X24,X2,X4] : c_List_Oremove1(X2,c_List_Olist_OCons(X2,X24,X4),X4) = X24,
    file('<stdin>',cls_List_Oremove1_Osimps__2_0) ).

fof(c_0_1108,axiom,
    ! [X2,X14,X4] : c_in(X2,c_insert(X2,X14,X4),X4),
    file('<stdin>',cls_Set_Oinsert__iff_1) ).

fof(c_0_1109,axiom,
    ! [X26,X2,X4] : c_List_Oop_Amem(X2,c_List_Olist_OCons(X2,X26,X4),X4),
    file('<stdin>',cls_List_Oop_Amem_Osimps__2_1) ).

fof(c_0_1110,axiom,
    ! [X1,X24,X4] : c_List_Onth(c_List_Olist_OCons(X1,X24,X4),c_0,X4) = X1,
    file('<stdin>',cls_List_Onth__Cons__0_0) ).

fof(c_0_1111,axiom,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X49,tc_IntDef_Oint),X12,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozminus__dvd__iff_1) ).

fof(c_0_1112,axiom,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X49,c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odvd__zminus__iff_1) ).

fof(c_0_1113,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

fof(c_0_1114,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

fof(c_0_1115,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

fof(c_0_1116,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

fof(c_0_1117,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastLessThan(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

fof(c_0_1118,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastLessThan(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

fof(c_0_1119,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastAtMost(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

fof(c_0_1120,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastAtMost(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

fof(c_0_1121,axiom,
    ! [X24,X2,X4] :
      ( c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) != c_List_Orev(X24,X4)
      | X24 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) ),
    file('<stdin>',cls_List_Osingleton__rev__conv_0) ).

fof(c_0_1122,axiom,
    ! [X24,X2,X4] :
      ( c_List_Orev(X24,X4) != c_List_Olist_OCons(X2,c_List_Olist_ONil,X4)
      | X24 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) ),
    file('<stdin>',cls_List_Orev__singleton__conv_0) ).

fof(c_0_1123,axiom,
    ! [X1,X28] :
      ( X28 = c_0
      | c_div(c_times(X28,X1,tc_IntDef_Oint),X28,tc_IntDef_Oint) = X1 ),
    file('<stdin>',cls_IntDiv_Ozdiv__zmult__self2_0) ).

fof(c_0_1124,axiom,
    ! [X1,X28] :
      ( X28 = c_0
      | c_div(c_times(X1,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = X1 ),
    file('<stdin>',cls_IntDiv_Ozdiv__zmult__self1_0) ).

fof(c_0_1125,axiom,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X14,X13,tc_set(X4))
      | c_less(X14,X13,tc_set(X4))
      | X14 = X13 ),
    file('<stdin>',cls_Set_OpsubsetI_0) ).

fof(c_0_1126,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X88),c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Osynth_OHash_0) ).

fof(c_0_1127,axiom,
    ! [X9,X89] :
      ( ~ c_in(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X9),c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_ONonce__synth__eq_1) ).

fof(c_0_1128,axiom,
    ! [X93,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_OKey__synth__eq_1) ).

fof(c_0_1129,axiom,
    ! [X19,X4] : c_in(X19,c_insert(X19,c_emptyset,X4),X4),
    file('<stdin>',cls_Set_OsingletonI_0) ).

fof(c_0_1130,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__sum_2) ).

fof(c_0_1131,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_nat)
      | ~ c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__sum_2) ).

fof(c_0_1132,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__difference_2) ).

fof(c_0_1133,axiom,
    ! [X22,X16] : c_lessequals(X22,c_plus(X16,X22,tc_nat),tc_nat),
    file('<stdin>',cls_Nat_Ole__add2_0) ).

fof(c_0_1134,axiom,
    ! [X22,X16] : c_lessequals(X22,c_plus(X22,X16,tc_nat),tc_nat),
    file('<stdin>',cls_Nat_Ole__add1_0) ).

fof(c_0_1135,axiom,
    ! [X2,X22] :
      ( c_less(c_0,c_Nat_Opower(X2,X22,tc_nat),tc_nat)
      | X2 = c_0 ),
    file('<stdin>',cls_Power_Onat__zero__less__power__iff_1) ).

fof(c_0_1136,axiom,
    ! [X22,X16] : c_lessequals(c_minus(X16,X22,tc_nat),X16,tc_nat),
    file('<stdin>',cls_Nat_Odiff__le__self_0) ).

fof(c_0_1137,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_times(X28,X19,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozmod__zmult__self2_0) ).

fof(c_0_1138,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_times(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozmod__zmult__self1_0) ).

fof(c_0_1139,axiom,
    ! [X28,X19] : c_div(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Omod__div__trivial_0) ).

fof(c_0_1140,axiom,
    ! [X22,X16] : c_div(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) = c_0,
    file('<stdin>',cls_Divides_Onat__mod__div__trivial_0) ).

fof(c_0_1141,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_times(X16,X22,tc_nat),X22,tc_nat) = c_0,
    file('<stdin>',cls_Divides_Omod__mult__self__is__0_0) ).

fof(c_0_1142,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_times(X22,X16,tc_nat),X22,tc_nat) = c_0,
    file('<stdin>',cls_Divides_Omod__mult__self1__is__0_0) ).

fof(c_0_1143,axiom,
    ! [X22,X16] : c_lessequals(c_div(X16,X22,tc_nat),X16,tc_nat),
    file('<stdin>',cls_Divides_Odiv__le__dividend_0) ).

fof(c_0_1144,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X16,X17,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__triv__right_0) ).

fof(c_0_1145,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X17,X16,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__triv__left_0) ).

fof(c_0_1146,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X16,X17,tc_nat),tc_nat),
    file('<stdin>',cls_Divides_Odvd__triv__right_0) ).

fof(c_0_1147,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X17,X16,tc_nat),tc_nat),
    file('<stdin>',cls_Divides_Odvd__triv__left_0) ).

fof(c_0_1148,axiom,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X14,X13,tc_set(X4))
      | c_minus(X14,X13,tc_set(X4)) = c_emptyset ),
    file('<stdin>',cls_Set_ODiff__eq__empty__iff_1) ).

fof(c_0_1149,axiom,
    ! [X13,X14,X4] :
      ( c_minus(X14,X13,tc_set(X4)) != c_emptyset
      | c_lessequals(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_ODiff__eq__empty__iff_0) ).

fof(c_0_1150,axiom,
    ! [X13,X14,X4] :
      ( ~ c_less(X14,X13,tc_set(X4))
      | c_lessequals(X14,X13,tc_set(X4)) ),
    file('<stdin>',cls_Set_OpsubsetE_1) ).

fof(c_0_1151,axiom,
    ! [X1,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),c_1,tc_nat)
      | c_List_Orotate1(X1,X4) = X1 ),
    file('<stdin>',cls_List_Orotate1__length01_0) ).

fof(c_0_1152,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_Suc(X16),c_Suc(X22),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__less__eq_0) ).

fof(c_0_1153,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(c_Suc(X22),c_Suc(X16),tc_nat)
      | c_lessequals(X22,X16,tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__le__mono_0) ).

fof(c_0_1154,axiom,
    ! [X49,X12] :
      ( ~ c_less(c_IntDef_Onat(X12),c_IntDef_Onat(X49),tc_nat)
      | c_less(X12,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Ozless__nat__conj_1) ).

fof(c_0_1155,axiom,
    ! [X22,X16] :
      ( ~ c_less(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint)
      | c_less(X16,X22,tc_nat) ),
    file('<stdin>',cls_IntDef_Ozless__int_0) ).

fof(c_0_1156,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint)
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_IntDef_Ozle__int_0) ).

fof(c_0_1157,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_0 ),
    file('<stdin>',cls_NatBin_Omult__nat__number__of_0) ).

fof(c_0_1158,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_0 ),
    file('<stdin>',cls_NatBin_Omod__nat__number__of_0) ).

fof(c_0_1159,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_0 ),
    file('<stdin>',cls_NatBin_Odiv__nat__number__of_0) ).

fof(c_0_1160,axiom,
    ! [X49,X12] :
      ( ~ c_less(c_IntDef_Onat(X12),c_IntDef_Onat(X49),tc_nat)
      | c_less(c_0,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Ozless__nat__conj_0) ).

fof(c_0_1161,axiom,
    ! [X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_Numeral_Onumber__of(X48,X4),c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X48,X12),X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__4_0) ).

fof(c_0_1162,axiom,
    ! [X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,X12),X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__1_0) ).

fof(c_0_1163,axiom,
    ! [X13,X14,X4] : c_minus(X14,c_uminus(X13,tc_set(X4)),tc_set(X4)) = c_inter(X14,X13,X4),
    file('<stdin>',cls_Set_ODiff__Compl_0) ).

fof(c_0_1164,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz__conj__parts_0) ).

fof(c_0_1165,axiom,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,X22,X4) != c_0
      | c_less(c_0,X22,tc_nat) ),
    file('<stdin>',cls_Power_Opower__eq__0__iff_1) ).

fof(c_0_1166,axiom,
    ! [X2] : c_less(c_0,c_Nat_Opower(X2,c_0,tc_nat),tc_nat),
    file('<stdin>',cls_Power_Onat__zero__less__power__iff_2) ).

fof(c_0_1167,axiom,
    ! [X28,X19] : c_div(c_uminus(X19,tc_IntDef_Oint),c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X19,X28,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdiv__zminus__zminus_0) ).

fof(c_0_1168,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X48),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,c_Numeral_Onumber__of(X48,tc_nat),tc_nat) ),
    file('<stdin>',cls_NatBin_Oless__0__number__of_1) ).

fof(c_0_1169,axiom,
    ! [X49] :
      ( ~ c_less(c_Suc(c_0),c_IntDef_Onat(X49),tc_nat)
      | c_less(c_1,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Oone__less__nat__eq_0) ).

fof(c_0_1170,axiom,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB1),X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__5_0) ).

fof(c_0_1171,axiom,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_Suc(X16),c_Suc(X22),tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__less__eq_1) ).

fof(c_0_1172,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(X22,X16,tc_nat)
      | c_lessequals(c_Suc(X22),c_Suc(X16),tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__le__mono_1) ).

fof(c_0_1173,axiom,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Ozless__int_1) ).

fof(c_0_1174,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Ozle__int_1) ).

fof(c_0_1175,axiom,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,X22,tc_nat)
      | c_Nat_Opower(c_0,X22,X4) = c_0 ),
    file('<stdin>',cls_Power_Opower__eq__0__iff_2) ).

fof(c_0_1176,axiom,
    ! [X22,X16] : ~ c_less(c_IntDef_Oint(X22),c_uminus(c_IntDef_Oint(X16),tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onot__int__zless__negative_0) ).

fof(c_0_1177,axiom,
    ! [X27,X17,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X27,X17,X4)
      | c_SetInterval_OgreaterThanAtMost(X17,X27,X4) = c_emptyset ),
    file('<stdin>',cls_SetInterval_OgreaterThanAtMost__empty_0) ).

fof(c_0_1178,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X22,X16,X4)
      | c_SetInterval_OatLeastLessThan(X16,X22,X4) = c_emptyset ),
    file('<stdin>',cls_SetInterval_OatLeastLessThan__empty_0) ).

fof(c_0_1179,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_less(X22,X16,X4)
      | c_SetInterval_OatLeastAtMost(X16,X22,X4) = c_emptyset ),
    file('<stdin>',cls_SetInterval_OatLeastAtMost__empty_0) ).

fof(c_0_1180,axiom,
    ! [X7,X14,X4] :
      ( c_in(X7,X14,X4)
      | c_in(X7,c_uminus(X14,tc_set(X4)),X4) ),
    file('<stdin>',cls_Set_OCompl__iff_1) ).

fof(c_0_1181,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X2,X4),X4) = c_Numeral_Onumber__of(X2,X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__6_1) ).

fof(c_0_1182,axiom,
    ! [X24,X22,X4] : c_Nat_Osize(c_List_Orotate(X22,X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olength__rotate_0) ).

fof(c_0_1183,axiom,
    ! [X28,X3,X4] : c_Nat_Osize(c_Sum__Type_OInr(X28,X3,X4),tc_sum(X4,X3)) = c_0,
    file('<stdin>',cls_Datatype_Osum_Osize__2_0) ).

fof(c_0_1184,axiom,
    ! [X19,X3,X4] : c_Nat_Osize(c_Sum__Type_OInl(X19,X4,X3),tc_sum(X4,X3)) = c_0,
    file('<stdin>',cls_Datatype_Osum_Osize__1_0) ).

fof(c_0_1185,axiom,
    ! [X22,X16] :
      ( ~ c_less(X16,c_Suc(X22),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Oless__Suc__eq__le_0) ).

fof(c_0_1186,axiom,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X6,X4)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X4,X4),X4) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).

fof(c_0_1187,axiom,
    ! [X24,X44,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Otake(X44,X24,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__take_0) ).

fof(c_0_1188,axiom,
    ! [X24,X59,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Osublist(X24,X59,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__sublistI_0) ).

fof(c_0_1189,axiom,
    ! [X24,X22,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Orotate(X22,X24,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__rotate_1) ).

fof(c_0_1190,axiom,
    ! [X24,X2,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Oremove1(X2,X24,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__remove1_0) ).

fof(c_0_1191,axiom,
    ! [X24,X44,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Odrop(X44,X24,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__drop_0) ).

fof(c_0_1192,axiom,
    ! [X49] :
      ( ~ c_less(c_1,X49,tc_IntDef_Oint)
      | c_less(c_Suc(c_0),c_IntDef_Onat(X49),tc_nat) ),
    file('<stdin>',cls_IntArith_Oone__less__nat__eq_1) ).

fof(c_0_1193,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_less(X16,c_Suc(X22),tc_nat) ),
    file('<stdin>',cls_Nat_Oless__Suc__eq__le_1) ).

fof(c_0_1194,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,X89,tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Osynth_OInj_0) ).

fof(c_0_1195,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,X89,tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oanalz_OInj_0) ).

fof(c_0_1196,axiom,
    ! [X88,X89] :
      ( ~ c_in(X88,X89,tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    file('<stdin>',cls_Message_Oparts_OInj_0) ).

fof(c_0_1197,axiom,
    ! [X22,X17] : c_Binomial_Obinomial(c_Suc(X22),c_Suc(X17)) = c_plus(c_Binomial_Obinomial(X22,X17),c_Binomial_Obinomial(X22,c_Suc(X17)),tc_nat),
    file('<stdin>',cls_Binomial_Obinomial__Suc__Suc_0) ).

fof(c_0_1198,axiom,
    ! [X93] :
      ( ~ c_in(c_Message_OinvKey(X93),c_Message_OsymKeys,tc_nat)
      | c_in(X93,c_Message_OsymKeys,tc_nat) ),
    file('<stdin>',cls_Public_OsymKeys__invKey__iff_0) ).

fof(c_0_1199,axiom,
    ! [X49] :
      ( ~ c_less(c_0,c_IntDef_Onat(X49),tc_nat)
      | c_less(c_0,X49,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Ozero__less__nat__eq_0) ).

fof(c_0_1200,axiom,
    ! [X22] :
      ( ~ c_less(c_0,c_IntDef_Oint(X22),tc_IntDef_Oint)
      | c_less(c_0,X22,tc_nat) ),
    file('<stdin>',cls_IntDef_Ozero__less__int__conv_0) ).

fof(c_0_1201,axiom,
    ! [X1,X2] :
      ( c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__sum_3) ).

fof(c_0_1202,axiom,
    ! [X1,X2] :
      ( c_Parity_Oeven(X1,tc_nat)
      | c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__sum_3) ).

fof(c_0_1203,axiom,
    ! [X1,X2] :
      ( c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__difference_3) ).

fof(c_0_1204,axiom,
    ! [X41,X2,X4] :
      ( ~ c_in(X2,c_Datatype_Oo2s(X41,X4),X4)
      | X41 = c_Datatype_Ooption_OSome(X2,X4) ),
    file('<stdin>',cls_Datatype_Oelem__o2s_0) ).

fof(c_0_1205,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X19,c_uminus(X28,X4),X4) = c_plus(X19,X28,X4) ),
    file('<stdin>',cls_OrderedGroup_Odiff__minus__eq__add_0) ).

fof(c_0_1206,axiom,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_0 != c_Numeral_Onumber__of(X1,X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__6_0) ).

fof(c_0_1207,axiom,
    ! [X51,X4] :
      ( c_in(c_Main_Oconcat__eq__Nil__conv__1(X51,X4),c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Oconcat(X51,X4) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oconcat__eq__Nil__conv_1) ).

fof(c_0_1208,axiom,
    ! [X51,X4] :
      ( c_in(c_Main_ONil__eq__concat__conv__1(X51,X4),c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Olist_ONil = c_List_Oconcat(X51,X4) ),
    file('<stdin>',cls_List_ONil__eq__concat__conv_1) ).

fof(c_0_1209,axiom,
    ! [X93] :
      ( ~ c_in(X93,c_Message_OsymKeys,tc_nat)
      | c_in(c_Message_OinvKey(X93),c_Message_OsymKeys,tc_nat) ),
    file('<stdin>',cls_Public_OsymKeys__invKey__iff_1) ).

fof(c_0_1210,axiom,
    ! [X49] :
      ( ~ c_less(c_0,X49,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Onat(X49),tc_nat) ),
    file('<stdin>',cls_IntDef_Ozero__less__nat__eq_1) ).

fof(c_0_1211,axiom,
    ! [X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_0,c_IntDef_Oint(X22),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDef_Ozero__less__int__conv_1) ).

fof(c_0_1212,axiom,
    ! [X12,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,c_Numeral_Onumber__of(X12,tc_nat),X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Parity_Opower__eq__0__iff__number__of_0) ).

fof(c_0_1213,axiom,
    ! [X1,X22] :
      ( ~ c_less(X1,X22,tc_nat)
      | c_Divides_Oop_Amod(X1,X22,tc_nat) = X1 ),
    file('<stdin>',cls_Divides_Omod__less_0) ).

fof(c_0_1214,axiom,
    ! [X84] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Suc(c_0) ),
    file('<stdin>',cls_NatBin_Oone__mod__nat__number__of_0) ).

fof(c_0_1215,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_6) ).

fof(c_0_1216,axiom,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__nat__number__of_10) ).

fof(c_0_1217,axiom,
    ! [X48] :
      ( ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)),tc_IntDef_Oint)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).

fof(c_0_1218,axiom,
    ! [X22,X16] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_minus(X16,X22,tc_nat) = c_0 ),
    file('<stdin>',cls_Nat_Odiff__is__0__eq_H_0) ).

fof(c_0_1219,axiom,
    ! [X22,X16] :
      ( c_minus(X16,X22,tc_nat) != c_0
      | c_lessequals(X16,X22,tc_nat) ),
    file('<stdin>',cls_Nat_Odiff__is__0__eq_0) ).

fof(c_0_1220,axiom,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_div(X16,X22,tc_nat) = c_0 ),
    file('<stdin>',cls_Divides_Odiv__less_0) ).

fof(c_0_1221,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__product_2) ).

fof(c_0_1222,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__product_1) ).

fof(c_0_1223,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_nat)
      | c_Parity_Oeven(c_times(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__product_2) ).

fof(c_0_1224,axiom,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_times(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__product_1) ).

fof(c_0_1225,axiom,
    ! [X4] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X4)),tc_nat),
    file('<stdin>',cls_List_Olength__greater__0__conv_0) ).

fof(c_0_1226,axiom,
    ! [X26,X24,X4] :
      ( X26 = c_List_Olist_ONil
      | c_List_Olast(c_append(X24,X26,X4),X4) = c_List_Olast(X26,X4) ),
    file('<stdin>',cls_List_Olast__appendR_0) ).

fof(c_0_1227,axiom,
    ! [X24,X2,X4] :
      ( X24 = c_List_Olist_ONil
      | c_List_Olast(c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olast(X24,X4) ),
    file('<stdin>',cls_List_Olast_Osimps_1) ).

fof(c_0_1228,axiom,
    ! [X26,X24,X4] :
      ( X24 = c_List_Olist_ONil
      | c_List_Ohd(c_append(X24,X26,X4),X4) = c_List_Ohd(X24,X4) ),
    file('<stdin>',cls_List_Ohd__append2_0) ).

fof(c_0_1229,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Omeet(X19,c_uminus(X19,X4),X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Omeet__0__eq__0_0) ).

fof(c_0_1230,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Ojoin(X19,c_uminus(X19,X4),X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Ojoin__0__eq__0_0) ).

fof(c_0_1231,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Otl(X24,X4),tc_List_Olist(X4)) = c_minus(c_Nat_Osize(X24,tc_List_Olist(X4)),c_1,tc_nat),
    file('<stdin>',cls_List_Olength__tl_0) ).

fof(c_0_1232,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Obutlast(X24,X4),tc_List_Olist(X4)) = c_minus(c_Nat_Osize(X24,tc_List_Olist(X4)),c_1,tc_nat),
    file('<stdin>',cls_List_Olength__butlast_0) ).

fof(c_0_1233,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_1,c_1,X4) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__1_0) ).

fof(c_0_1234,axiom,
    ! [X6,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X6,X4),X4,X4) = c_Relation_ORange(X6,X4,X4),
    file('<stdin>',cls_Transitive__Closure_Otrancl__range_0) ).

fof(c_0_1235,axiom,
    ! [X6,X4] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X6,X4),X4,X4) = c_Relation_ODomain(X6,X4,X4),
    file('<stdin>',cls_Transitive__Closure_Otrancl__domain_0) ).

fof(c_0_1236,axiom,
    ! [X24,X22,X4] : c_List_Oset(c_List_Orotate(X22,X24,X4),X4) = c_List_Oset(X24,X4),
    file('<stdin>',cls_List_Oset__rotate_0) ).

fof(c_0_1237,axiom,
    ! [X24,X2,X4] : c_List_Oitrev(X24,X2,X4) = c_append(c_List_Orev(X24,X4),X2,X4),
    file('<stdin>',cls_List_Oitrev_0) ).

fof(c_0_1238,axiom,
    ! [X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(X22,X22,tc_nat) = c_1 ),
    file('<stdin>',cls_Divides_Odiv__self_0) ).

fof(c_0_1239,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(X2,X4) != c_0
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4) ),
    file('<stdin>',cls_IntArith_Oarith__special__8_0) ).

fof(c_0_1240,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg),
    file('<stdin>',cls_Public_Ospies__pubK_0) ).

fof(c_0_1241,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_lessequals(c_HOL_Oabs(X19,X4),c_0,X4)
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oabs__le__zero__iff_0) ).

fof(c_0_1242,axiom,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_HOL_Oinverse(c_Numeral_Onumber__of(X12,X3),X3) = c_divide(c_1,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oinverse__eq__divide__number__of_0) ).

fof(c_0_1243,axiom,
    ! [X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_NatArith_Oof__nat(X16,X4),c_0,X4)
      | X16 = c_0 ),
    file('<stdin>',cls_NatArith_Oof__nat__le__0__iff_0) ).

fof(c_0_1244,axiom,
    ! [X2,X4] : c_in(X2,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X2,X4),X4),X4),
    file('<stdin>',cls_Datatype_Oelem__o2s_1) ).

fof(c_0_1245,axiom,
    ! [X22,X27,X4] : c_List_Osublist(X27,c_SetInterval_OlessThan(X22,tc_nat),X4) = c_List_Otake(X22,X27,X4),
    file('<stdin>',cls_List_Osublist__upt__eq__take_0) ).

fof(c_0_1246,axiom,
    ! [X24,X4] : c_List_Olast(c_append(X24,c_List_Olist_ONil,X4),X4) = c_List_Olast(X24,X4),
    file('<stdin>',cls_List_Olast__appendL_0) ).

fof(c_0_1247,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_less(c_HOL_Oabs(X19,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__not__less__zero_0) ).

fof(c_0_1248,axiom,
    ! [X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_NatArith_Oof__nat(X16,X4),c_0,X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__less__0__iff_0) ).

fof(c_0_1249,axiom,
    ! [X88,X93] : ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    file('<stdin>',cls_Public_OCrypt__notin__used__empty_0) ).

fof(c_0_1250,axiom,
    ! [X49,X12] : c_plus(X49,c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X49,X12,tc_IntDef_Oint),
    file('<stdin>',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).

fof(c_0_1251,axiom,
    ! [X1,X2,X4] : c_Nat_Osize(c_List_Oreplicate(X1,X2,X4),tc_List_Olist(X4)) = X1,
    file('<stdin>',cls_List_Olength__replicate_0) ).

fof(c_0_1252,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_less(c_0,c_HOL_Oabs(c_0,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Ozero__less__abs__iff_0) ).

fof(c_0_1253,axiom,
    ! [X1,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_Finite__Set_OMin(c_insert(X1,c_emptyset,X4),X4) = X1 ),
    file('<stdin>',cls_Finite__Set_OMin__singleton_0) ).

fof(c_0_1254,axiom,
    ! [X1,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_Finite__Set_OMax(c_insert(X1,c_emptyset,X4),X4) = X1 ),
    file('<stdin>',cls_Finite__Set_OMax__singleton_0) ).

fof(c_0_1255,axiom,
    ! [X12,X48] : c_Numeral_Obin__mult(c_Numeral_OBit(X48,c_Numeral_Obit_OB1),X12) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X48,X12),c_Numeral_Obit_OB0),X12),
    file('<stdin>',cls_Numeral_Obin__mult__1_0) ).

fof(c_0_1256,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) != c_0
      | c_0 = c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oeq__divide__eq__number__of_2) ).

fof(c_0_1257,axiom,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) != c_0
      | c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3) = c_0 ),
    file('<stdin>',cls_NatSimprocs_Odivide__eq__eq__number__of_1) ).

fof(c_0_1258,axiom,
    ! [X9,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X9),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__Number_0) ).

fof(c_0_1259,axiom,
    ! [X9,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__Nonce_0) ).

fof(c_0_1260,axiom,
    ! [X93,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__Key_0) ).

fof(c_0_1261,axiom,
    ! [X88,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__Hash_0) ).

fof(c_0_1262,axiom,
    ! [X89,X14] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X14),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    file('<stdin>',cls_Message_OkeysFor__insert__Agent_0) ).

fof(c_0_1263,axiom,
    ! [X1,X22,X4] :
      ( X22 = c_0
      | c_List_Olast(c_List_Oreplicate(X22,X1,X4),X4) = X1 ),
    file('<stdin>',cls_List_Olast__replicate_0) ).

fof(c_0_1264,axiom,
    ! [X1,X60] :
      ( ~ c_less(X1,X60,tc_nat)
      | c_List_Ohd(c_List_Oupt(X1,X60),tc_nat) = X1 ),
    file('<stdin>',cls_List_Ohd__upt_0) ).

fof(c_0_1265,axiom,
    ! [X1,X22,X4] :
      ( X22 = c_0
      | c_List_Ohd(c_List_Oreplicate(X22,X1,X4),X4) = X1 ),
    file('<stdin>',cls_List_Ohd__replicate_0) ).

fof(c_0_1266,axiom,
    ! [X28,X14] : ~ c_in(c_Public_OpublicKey(X28,X14),c_Message_OsymKeys,tc_nat),
    file('<stdin>',cls_Public_Onot__symKeys__pubK_0) ).

fof(c_0_1267,axiom,
    ! [X9,X13] : ~ c_in(c_Message_Omsg_ONonce(X9),c_Message_Oparts(c_Event_OinitState(X13)),tc_Message_Omsg),
    file('<stdin>',cls_Public_ONonce__notin__initState_0) ).

fof(c_0_1268,axiom,
    ! [X1,X2,X42] : c_List_Otl(c_List_Olist_OCons(X2,X1,X42),X42) = X1,
    file('<stdin>',cls_List_Otl_Osimps__2_0) ).

fof(c_0_1269,axiom,
    ! [X1,X24,X4] : c_List_Ohd(c_List_Olist_OCons(X1,X24,X4),X4) = X1,
    file('<stdin>',cls_List_Ohd_Osimps_0) ).

fof(c_0_1270,axiom,
    ! [X48] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_nat),tc_nat)
      | c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).

fof(c_0_1271,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_0,X4) = c_divide(X28,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__cancel__right_1) ).

fof(c_0_1272,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,X19,X4) = c_divide(c_0,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Odivide__cancel__left_1) ).

fof(c_0_1273,axiom,
    ! [X48,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) = c_Numeral_Onumber__of(X48,X3) ),
    file('<stdin>',cls_NatSimprocs_Ominus__equation__iff__number__of_1) ).

fof(c_0_1274,axiom,
    ! [X48,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_Numeral_Onumber__of(X48,X3) = c_uminus(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oequation__minus__iff__number__of_1) ).

fof(c_0_1275,axiom,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_emptyset != c_Union(X14,X4)
      | X25 = c_emptyset ),
    file('<stdin>',cls_Set_Oempty__Union__conv_0) ).

fof(c_0_1276,axiom,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_Union(X14,X4) != c_emptyset
      | X25 = c_emptyset ),
    file('<stdin>',cls_Set_OUnion__empty__conv_0) ).

fof(c_0_1277,axiom,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_UNIV != c_Inter(X14,X4)
      | X25 = c_UNIV ),
    file('<stdin>',cls_Set_OInter__UNIV__conv__2_0) ).

fof(c_0_1278,axiom,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_Inter(X14,X4) != c_UNIV
      | X25 = c_UNIV ),
    file('<stdin>',cls_Set_OInter__UNIV__conv__1_0) ).

fof(c_0_1279,axiom,
    ! [X98,X104,X105] : c_Nat_Osize(c_Event_Oevent_OSays(X105,X104,X98),tc_Event_Oevent) = c_0,
    file('<stdin>',cls_Event_Oevent_Osize__1_0) ).

fof(c_0_1280,axiom,
    ! [X24,X4] :
      ( c_Nat_Osize(c_List_Oremdups(X24,X4),tc_List_Olist(X4)) != c_Nat_Osize(X24,tc_List_Olist(X4))
      | c_List_Oremdups(X24,X4) = X24 ),
    file('<stdin>',cls_List_Olength__remdups__eq_0) ).

fof(c_0_1281,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_HOL_Oabs(X19,X4) = c_uminus(X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__of__nonpos_0) ).

fof(c_0_1282,axiom,
    ! [X6,X4] : c_union(c_Transitive__Closure_Otrancl(X6,X4),c_Relation_OId,tc_prod(X4,X4)) = c_Transitive__Closure_Ortrancl(X6,X4),
    file('<stdin>',cls_Transitive__Closure_Oreflcl__trancl_0) ).

fof(c_0_1283,axiom,
    ! [X1,X4] : c_Set_Ocontents(c_insert(X1,c_emptyset,X4),X4) = X1,
    file('<stdin>',cls_Set_Ocontents__eq_0) ).

fof(c_0_1284,axiom,
    ! [X2,X4] : c_List_Olast(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) = X2,
    file('<stdin>',cls_List_Olast_Osimps_0) ).

fof(c_0_1285,axiom,
    ! [X49] :
      ( ~ c_less(c_HOL_Oabs(X49,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
      | X49 = c_0 ),
    file('<stdin>',cls_IntArith_Ozabs__less__one__iff_0) ).

fof(c_0_1286,axiom,
    ! [X22,X16] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X22)),tc_IntDef_Oint),c_IntDef_Oint(X16),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onegative__zless_0) ).

fof(c_0_1287,axiom,
    ! [X22,X16] : c_minus(c_Suc(X16),c_Suc(X22),tc_nat) = c_minus(X16,X22,tc_nat),
    file('<stdin>',cls_Nat_Odiff__Suc__Suc_0) ).

fof(c_0_1288,axiom,
    ! [X2,X42] : c_List_Obutlast(c_List_Olist_OCons(X2,c_List_Olist_ONil,X42),X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Obutlast_Osimps__2_0) ).

fof(c_0_1289,axiom,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_Finite__Set_Ocard(X14,X4) != c_0
      | X14 = c_emptyset ),
    file('<stdin>',cls_Finite__Set_Ocard__0__eq_0) ).

fof(c_0_1290,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Event_Oused(X103),tc_Message_Omsg),
    file('<stdin>',cls_Public_OpublicKey__into__used_0) ).

fof(c_0_1291,axiom,
    ! [X28,X13,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Event_OinitState(X13),tc_Message_Omsg),
    file('<stdin>',cls_Public_OpublicKey__in__initState_0) ).

fof(c_0_1292,axiom,
    ! [X91,X98] : c_Nat_Osize(c_Message_Omsg_OCrypt(X91,X98),tc_Message_Omsg) = c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    file('<stdin>',cls_Message_Omsg_Osize__7_0) ).

fof(c_0_1293,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Power_Orecpower(X4)
      | c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X2,X4) = c_Numeral_Onumber__of(c_Numeral_OMin,X4) ),
    file('<stdin>',cls_Parity_Oneg__one__odd__power_0) ).

fof(c_0_1294,axiom,
    ! [X2,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_uminus(c_1,X4),X2,X4) = c_uminus(c_1,X4) ),
    file('<stdin>',cls_Parity_Ominus__one__odd__power_0) ).

fof(c_0_1295,axiom,
    ! [X19,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | c_SetInterval_OatLeastAtMost(X19,X19,X4) = c_insert(X19,c_emptyset,X4) ),
    file('<stdin>',cls_SetInterval_OatLeastAtMost__singleton_0) ).

fof(c_0_1296,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X19,c_0,X4) = c_times(X28,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).

fof(c_0_1297,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_0,X19,X4) = c_times(c_0,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).

fof(c_0_1298,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X2,c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) = c_uminus(X2,X4) ),
    file('<stdin>',cls_NatSimprocs_Odivide__minus1_0) ).

fof(c_0_1299,axiom,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Power_Orecpower(X4)
      | ~ c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X2,X4) = c_1 ),
    file('<stdin>',cls_Parity_Oneg__one__even__power_0) ).

fof(c_0_1300,axiom,
    ! [X2,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_uminus(c_1,X4),X2,X4) = c_1 ),
    file('<stdin>',cls_Parity_Ominus__one__even__power_0) ).

fof(c_0_1301,axiom,
    ! [X1,X4] : c_Nat_Opower(X1,c_1,tc_set(tc_prod(X4,X4))) = X1,
    file('<stdin>',cls_Relation__Power_Orel__pow__1_0) ).

fof(c_0_1302,axiom,
    ! [X86,X42] : c_Nat_Opower(X86,c_0,tc_set(tc_prod(X42,X42))) = c_Relation_OId,
    file('<stdin>',cls_Relation__Power_Orelpow_Osimps__1_0) ).

fof(c_0_1303,axiom,
    ! [X16] : c_SetInterval_OatLeastLessThan(X16,c_Suc(X16),tc_nat) = c_insert(X16,c_emptyset,tc_nat),
    file('<stdin>',cls_SetInterval_OatLeastLessThan__singleton_0) ).

fof(c_0_1304,axiom,
    ! [X12,X48] : c_Numeral_Obin__add(c_Numeral_OBit(X48,c_Numeral_Obit_OB1),c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X48,c_Numeral_Obin__succ(X12)),c_Numeral_Obit_OB0),
    file('<stdin>',cls_Numeral_Obin__add__BIT__11_0) ).

fof(c_0_1305,axiom,
    ! [X1,X4] :
      ( X1 = c_List_Olist_ONil
      | c_List_Olist_OCons(c_List_Ohd(X1,X4),c_List_Otl(X1,X4),X4) = X1 ),
    file('<stdin>',cls_List_Ohd__Cons__tl_0) ).

fof(c_0_1306,axiom,
    ! [X61,X4] :
      ( c_in(c_List_Olast(X61,X4),c_List_Oset(X61,X4),X4)
      | X61 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olast__in__set_0) ).

fof(c_0_1307,axiom,
    ! [X24,X4] :
      ( c_in(c_List_Ohd(X24,X4),c_List_Oset(X24,X4),X4)
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Ohd__in__set_0) ).

fof(c_0_1308,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OSays(X105,X104,X98),
    file('<stdin>',cls_Event_Oevent_Odistinct__4_0) ).

fof(c_0_1309,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_ONotes(X95,X97),
    file('<stdin>',cls_Event_Oevent_Odistinct__3_0) ).

fof(c_0_1310,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OSays(X105,X104,X98),
    file('<stdin>',cls_Event_Oevent_Odistinct__2_0) ).

fof(c_0_1311,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OGets(X95,X97),
    file('<stdin>',cls_Event_Oevent_Odistinct__1_0) ).

fof(c_0_1312,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,X1,X4)
      | c_OrderedGroup_Opprt(X1,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Opprt__eq__id_0) ).

fof(c_0_1313,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X1,c_0,X4)
      | c_OrderedGroup_Onprt(X1,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Onprt__eq__id_0) ).

fof(c_0_1314,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_lessequals(c_0,X1,X4)
      | c_HOL_Oabs(X1,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Oabs__of__nonneg_0) ).

fof(c_0_1315,axiom,
    ! [X16,X42] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X42)
      | c_NatArith_Oof__nat(c_Suc(X16),X42) = c_plus(c_NatArith_Oof__nat(X16,X42),c_1,X42) ),
    file('<stdin>',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).

fof(c_0_1316,axiom,
    ! [X2,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X2,c_0,X4)
      | c_OrderedGroup_Opprt(X2,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Opprt__eq__0_0) ).

fof(c_0_1317,axiom,
    ! [X2,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,X2,X4)
      | c_OrderedGroup_Onprt(X2,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Onprt__eq__0_0) ).

fof(c_0_1318,axiom,
    ! [X4] :
      ( ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X4))
      | c_Finite__Set_Ocard(c_emptyset,X4) = c_0 ),
    file('<stdin>',cls_Finite__Set_Ocard__0__eq_1) ).

fof(c_0_1319,axiom,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Numeral_Onumber__of(X12,tc_nat) != c_0
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4) = c_1 ),
    file('<stdin>',cls_Parity_Opower__0__left__number__of_0) ).

fof(c_0_1320,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,X28,X4) != c_0
      | X28 = c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__0__iff_0) ).

fof(c_0_1321,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_1 != c_divide(X19,X28,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Ring__and__Field_Oone__eq__divide__iff_1) ).

fof(c_0_1322,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_1 != c_divide(X28,X19,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Ring__and__Field_Oeq__divide__eq__1_1) ).

fof(c_0_1323,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(X28,X19,X4) != c_1
      | X19 = X28 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__eq__1_1) ).

fof(c_0_1324,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,X28,X4) != c_1
      | X19 = X28 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__1__iff_1) ).

fof(c_0_1325,axiom,
    ! [X1,X12,X48] : c_Numeral_Obin__add(c_Numeral_OBit(X48,c_Numeral_Obit_OB0),c_Numeral_OBit(X12,X1)) = c_Numeral_OBit(c_Numeral_Obin__add(X48,X12),X1),
    file('<stdin>',cls_Numeral_Obin__add__BIT__0_0) ).

fof(c_0_1326,axiom,
    ! [X22,X16] : c_times(X16,c_0,tc_nat) = c_times(X22,c_0,tc_nat),
    file('<stdin>',cls_Nat_Omult__cancel2_1) ).

fof(c_0_1327,axiom,
    ! [X22,X16] : c_times(c_0,X16,tc_nat) = c_times(c_0,X22,tc_nat),
    file('<stdin>',cls_Nat_Omult__cancel1_1) ).

fof(c_0_1328,axiom,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,X22,X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Power_Opower__eq__0__iff_0) ).

fof(c_0_1329,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_Oempty__Union__conv__1(X14,X4),X14,tc_set(X4))
      | c_emptyset = c_Union(X14,X4) ),
    file('<stdin>',cls_Set_Oempty__Union__conv_1) ).

fof(c_0_1330,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_OUnion__empty__conv__1(X14,X4),X14,tc_set(X4))
      | c_Union(X14,X4) = c_emptyset ),
    file('<stdin>',cls_Set_OUnion__empty__conv_1) ).

fof(c_0_1331,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_OInter__UNIV__conv__2__1(X14,X4),X14,tc_set(X4))
      | c_UNIV = c_Inter(X14,X4) ),
    file('<stdin>',cls_Set_OInter__UNIV__conv__2_1) ).

fof(c_0_1332,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_OInter__UNIV__conv__1__1(X14,X4),X14,tc_set(X4))
      | c_Inter(X14,X4) = c_UNIV ),
    file('<stdin>',cls_Set_OInter__UNIV__conv__1_1) ).

fof(c_0_1333,axiom,
    ! [X48,X16] :
      ( c_IntDef_Oint(X16) != c_Numeral_Onumber__of(X48,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntArith_Oint__eq__iff__number__of_1) ).

fof(c_0_1334,axiom,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X48,tc_nat),X4) = c_0 ),
    file('<stdin>',cls_NatBin_Oof__nat__number__of__eq_0) ).

fof(c_0_1335,axiom,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(X19,X3) != c_Numeral_Onumber__of(X48,X3)
      | c_uminus(c_Numeral_Onumber__of(X48,X3),X3) = X19 ),
    file('<stdin>',cls_NatSimprocs_Ominus__equation__iff__number__of_0) ).

fof(c_0_1336,axiom,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_Numeral_Onumber__of(X48,X3) != c_uminus(X28,X3)
      | X28 = c_uminus(c_Numeral_Onumber__of(X48,X3),X3) ),
    file('<stdin>',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).

fof(c_0_1337,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_0 != c_divide(c_1,X19,X4)
      | X19 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Ozero__eq__1__divide__iff_0) ).

fof(c_0_1338,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(c_1,X19,X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Oone__divide__eq__0__iff_0) ).

fof(c_0_1339,axiom,
    ! [X49,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(X49,c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) = c_uminus(X49,X4) ),
    file('<stdin>',cls_Numeral_Omult__minus1__right_0) ).

fof(c_0_1340,axiom,
    ! [X49,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X49,X4) = c_uminus(X49,X4) ),
    file('<stdin>',cls_Numeral_Omult__minus1_0) ).

fof(c_0_1341,axiom,
    ! [X12,X48] : c_Numeral_Obin__add(c_Numeral_OBit(X48,c_Numeral_Obit_OB1),c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X48,X12),c_Numeral_Obit_OB1),
    file('<stdin>',cls_Numeral_Obin__add__BIT__10_0) ).

fof(c_0_1342,axiom,
    ! [X60,X44] :
      ( ~ c_lessequals(X60,X44,tc_nat)
      | c_List_Oupt(X44,X60) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oupt__eq__Nil__conv_2) ).

fof(c_0_1343,axiom,
    ! [X9] : ~ c_in(c_Message_Omsg_ONonce(X9),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    file('<stdin>',cls_Public_ONonce__notin__used__empty_0) ).

fof(c_0_1344,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_1 != c_divide(X28,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oeq__divide__eq__1_0) ).

fof(c_0_1345,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(X28,c_0,X4) != c_1 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__eq__1_0) ).

fof(c_0_1346,axiom,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_times(X19,X7,X4) != X7
      | X7 = c_0
      | X19 = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__right2_0) ).

fof(c_0_1347,axiom,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 != c_times(X28,X7,X4)
      | X7 = c_0
      | X28 = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__right1_0) ).

fof(c_0_1348,axiom,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_times(X7,X19,X4) != X7
      | X7 = c_0
      | X19 = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__left2_0) ).

fof(c_0_1349,axiom,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 != c_times(X7,X28,X4)
      | X7 = c_0
      | X28 = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__left1_0) ).

fof(c_0_1350,axiom,
    ! [X103,X14] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_Oknows(X14,X103),tc_Message_Omsg),
    file('<stdin>',cls_Public_OshrK__in__knows_0) ).

fof(c_0_1351,axiom,
    ! [X98] : c_Nat_Osize(c_Message_Omsg_OHash(X98),tc_Message_Omsg) = c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    file('<stdin>',cls_Message_Omsg_Osize__5_0) ).

fof(c_0_1352,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | c_times(X19,X28,X4) != c_0
      | X28 = c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__eq__0__iff_0) ).

fof(c_0_1353,axiom,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4) = c_0
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    file('<stdin>',cls_Parity_Opower__0__left__number__of_1) ).

fof(c_0_1354,axiom,
    ! [X60,X44] : c_Nat_Osize(c_List_Oupt(X44,X60),tc_List_Olist(tc_nat)) = c_minus(X60,X44,tc_nat),
    file('<stdin>',cls_List_Olength__upt_0) ).

fof(c_0_1355,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X19,X28,X4) != c_0
      | X19 = X28 ),
    file('<stdin>',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).

fof(c_0_1356,axiom,
    ! [X14,X4] :
      ( ~ c_lessequals(X14,c_emptyset,tc_set(X4))
      | X14 = c_emptyset ),
    file('<stdin>',cls_Set_Osubset__empty_0) ).

fof(c_0_1357,axiom,
    ! [X14,X4] : c_Relation_Oconverse(c_Relation_Odiag(X14,X4),X4,X4) = c_Relation_Odiag(X14,X4),
    file('<stdin>',cls_Relation_Oconverse__diag_0) ).

fof(c_0_1358,axiom,
    ! [X22,X16] : c_lessequals(c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint),c_IntDef_Oint(X16),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onegative__zle_0) ).

fof(c_0_1359,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_uminus(X19,X4),X4) = c_uminus(c_HOL_Oinverse(X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__minus__eq_0) ).

fof(c_0_1360,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_HOL_Oabs(c_HOL_Oinverse(X19,X4),X4) = c_HOL_Oinverse(c_HOL_Oabs(X19,X4),X4) ),
    file('<stdin>',cls_Ring__and__Field_Oabs__inverse_0) ).

fof(c_0_1361,axiom,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X48,tc_nat),X4) = c_Numeral_Onumber__of(X48,X4) ),
    file('<stdin>',cls_NatBin_Oof__nat__number__of__eq_1) ).

fof(c_0_1362,axiom,
    ! [X14,X4] : ~ c_less(X14,c_emptyset,tc_set(X4)),
    file('<stdin>',cls_Set_Onot__psubset__empty_0) ).

fof(c_0_1363,axiom,
    ! [X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_less(X2,X2,X4) ),
    file('<stdin>',cls_Orderings_Oorder__less__irrefl_0) ).

fof(c_0_1364,axiom,
    ! [X14,X4] : c_inter(X14,c_uminus(X14,tc_set(X4)),X4) = c_emptyset,
    file('<stdin>',cls_Set_OCompl__disjoint_0) ).

fof(c_0_1365,axiom,
    ! [X14,X4] : c_inter(c_uminus(X14,tc_set(X4)),X14,X4) = c_emptyset,
    file('<stdin>',cls_Set_OCompl__disjoint2_0) ).

fof(c_0_1366,axiom,
    ! [X2,X42] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X2,X42),X42) = c_insert(X2,c_emptyset,X42),
    file('<stdin>',cls_Datatype_Oo2s_Osimps__2_0) ).

fof(c_0_1367,axiom,
    ! [X49] :
      ( ~ c_lessequals(c_0,X49,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X49)) = X49 ),
    file('<stdin>',cls_IntDef_Oint__nat__eq_0) ).

fof(c_0_1368,axiom,
    ! [X22] :
      ( ~ c_lessequals(c_IntDef_Oint(X22),c_0,tc_IntDef_Oint)
      | X22 = c_0 ),
    file('<stdin>',cls_IntDef_Oint__le__0__conv_0) ).

fof(c_0_1369,axiom,
    ! [X16] :
      ( ~ c_Divides_Oop_Advd(X16,c_Suc(c_0),tc_nat)
      | X16 = c_Suc(c_0) ),
    file('<stdin>',cls_Divides_Odvd__1__iff__1_0) ).

fof(c_0_1370,axiom,
    ! [X48] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oeq__number__of__0_0) ).

fof(c_0_1371,axiom,
    ! [X48] :
      ( c_0 != c_Numeral_Onumber__of(X48,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oeq__0__number__of_0) ).

fof(c_0_1372,axiom,
    ! [X24,X4] :
      ( c_less(c_0,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olength__greater__0__conv_1) ).

fof(c_0_1373,axiom,
    ! [X17] : ~ c_less(c_IntDef_Oint(X17),c_0,tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Oint__less__0__conv_0) ).

fof(c_0_1374,axiom,
    ! [X24,X4] :
      ( c_List_Oremdups(X24,X4) != X24
      | c_Nat_Osize(c_List_Oremdups(X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Olength__remdups__eq_1) ).

fof(c_0_1375,axiom,
    ! [X22] :
      ( ~ c_less(X22,c_Suc(c_0),tc_nat)
      | X22 = c_0 ),
    file('<stdin>',cls_Nat_Oless__Suc0_0) ).

fof(c_0_1376,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(X19,c_HOL_Oinverse(X19,X4),X4) = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Oright__inverse_0) ).

fof(c_0_1377,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(c_HOL_Oinverse(X19,X4),X19,X4) = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).

fof(c_0_1378,axiom,
    ! [X24,X22,X4] :
      ( c_List_Otake(X22,X24,X4) != c_List_Olist_ONil
      | X22 = c_0
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Otake__eq__Nil_0) ).

fof(c_0_1379,axiom,
    ! [X22,X16] :
      ( c_Suc(c_0) != c_times(X16,X22,tc_nat)
      | X22 = c_1 ),
    file('<stdin>',cls_Nat_Oone__eq__mult__iff_1) ).

fof(c_0_1380,axiom,
    ! [X22,X16] :
      ( c_Suc(c_0) != c_times(X16,X22,tc_nat)
      | X16 = c_1 ),
    file('<stdin>',cls_Nat_Oone__eq__mult__iff_0) ).

fof(c_0_1381,axiom,
    ! [X22,X16] :
      ( c_times(X16,X22,tc_nat) != c_Suc(c_0)
      | X22 = c_1 ),
    file('<stdin>',cls_Nat_Omult__eq__1__iff_1) ).

fof(c_0_1382,axiom,
    ! [X22,X16] :
      ( c_times(X16,X22,tc_nat) != c_Suc(c_0)
      | X16 = c_1 ),
    file('<stdin>',cls_Nat_Omult__eq__1__iff_0) ).

fof(c_0_1383,axiom,
    ! [X26,X24,X4] :
      ( X24 != c_append(X24,X26,X4)
      | X26 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oself__append__conv_0) ).

fof(c_0_1384,axiom,
    ! [X26,X24,X4] :
      ( X26 != c_append(X24,X26,X4)
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oself__append__conv2_0) ).

fof(c_0_1385,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != X24
      | X26 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__self__conv_0) ).

fof(c_0_1386,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != X26
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__self__conv2_0) ).

fof(c_0_1387,axiom,
    ! [X88] : ~ c_in(X88,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__emptyE_0) ).

fof(c_0_1388,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Onot__one__less__zero_0) ).

fof(c_0_1389,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_1,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Onot__one__le__zero_0) ).

fof(c_0_1390,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_less(c_0,c_HOL_Oabs(X19,X4),X4)
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Ozero__less__abs__iff_1) ).

fof(c_0_1391,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_plus(X19,c_uminus(X19,X4),X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oright__minus_0) ).

fof(c_0_1392,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_plus(c_uminus(X19,X4),X19,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).

fof(c_0_1393,axiom,
    ! [X13,X14,X4] :
      ( c_union(X14,X13,X4) != c_emptyset
      | X13 = c_emptyset ),
    file('<stdin>',cls_Set_OUn__empty_1) ).

fof(c_0_1394,axiom,
    ! [X13,X14,X4] :
      ( c_union(X14,X13,X4) != c_emptyset
      | X14 = c_emptyset ),
    file('<stdin>',cls_Set_OUn__empty_0) ).

fof(c_0_1395,axiom,
    ! [X13,X14,X4] :
      ( c_inter(X14,X13,X4) != c_UNIV
      | X13 = c_UNIV ),
    file('<stdin>',cls_Set_OInt__UNIV_1) ).

fof(c_0_1396,axiom,
    ! [X13,X14,X4] :
      ( c_inter(X14,X13,X4) != c_UNIV
      | X14 = c_UNIV ),
    file('<stdin>',cls_Set_OInt__UNIV_0) ).

fof(c_0_1397,axiom,
    ! [X24,X22,X4] :
      ( c_List_Orotate(X22,X24,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Orotate__is__Nil__conv_0) ).

fof(c_0_1398,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != c_List_Olist_ONil
      | X26 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__is__Nil__conv_1) ).

fof(c_0_1399,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__is__Nil__conv_0) ).

fof(c_0_1400,axiom,
    ! [X26,X24,X4] :
      ( c_List_Olist_ONil != c_append(X24,X26,X4)
      | X26 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__is__append__conv_1) ).

fof(c_0_1401,axiom,
    ! [X26,X24,X4] :
      ( c_List_Olist_ONil != c_append(X24,X26,X4)
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__is__append__conv_0) ).

fof(c_0_1402,axiom,
    ! [X6,X14,X4] :
      ( c_Equiv__Relations_Oquotient(X14,X6,X4) != c_emptyset
      | X14 = c_emptyset ),
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty_0) ).

fof(c_0_1403,axiom,
    ! [X6,X14,X4] :
      ( c_emptyset != c_Equiv__Relations_Oquotient(X14,X6,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty2_0) ).

fof(c_0_1404,axiom,
    ! [X2,X82,X4] : c_List_Olist_OCons(X2,X82,X4) != X82,
    file('<stdin>',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

fof(c_0_1405,axiom,
    ! [X24,X2,X4] : X24 != c_List_Olist_OCons(X2,X24,X4),
    file('<stdin>',cls_List_Onot__Cons__self_0) ).

fof(c_0_1406,axiom,
    ! [X22,X16] :
      ( c_times(X16,X22,tc_nat) != c_0
      | X22 = c_0
      | X16 = c_0 ),
    file('<stdin>',cls_Nat_Omult__is__0_0) ).

fof(c_0_1407,axiom,
    ! [X1] :
      ( ~ c_in(X1,c_Message_OsymKeys,tc_nat)
      | c_Message_OinvKey(X1) = X1 ),
    file('<stdin>',cls_Public_OinvKey__K_0) ).

fof(c_0_1408,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_lessequals(c_0,c_OrderedGroup_Opprt(X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Ozero__le__pprt_0) ).

fof(c_0_1409,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_lessequals(c_OrderedGroup_Onprt(X19,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Onprt__le__zero_0) ).

fof(c_0_1410,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_lessequals(c_0,c_HOL_Oabs(X19,X4),X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__ge__zero_0) ).

fof(c_0_1411,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_0,c_NatArith_Oof__nat(X22,X4),X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__0__le__iff_0) ).

fof(c_0_1412,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_in(c_NatArith_Oof__nat(X22,X4),c_IntDef_ONats,X4) ),
    file('<stdin>',cls_IntDef_Oof__nat__in__Nats_0) ).

fof(c_0_1413,axiom,
    ! [X19,X14,X4] : c_insert(X19,X14,X4) != c_emptyset,
    file('<stdin>',cls_Set_Oinsert__not__empty_0) ).

fof(c_0_1414,axiom,
    ! [X19,X14,X4] : c_emptyset != c_insert(X19,X14,X4),
    file('<stdin>',cls_Set_Oempty__not__insert_0) ).

fof(c_0_1415,axiom,
    ! [X64,X43,X4] : c_List_Olist_OCons(X43,X64,X4) != c_List_Olist_ONil,
    file('<stdin>',cls_List_Olist_Odistinct__2_0) ).

fof(c_0_1416,axiom,
    ! [X64,X43,X4] : c_List_Olist_ONil != c_List_Olist_OCons(X43,X64,X4),
    file('<stdin>',cls_List_Olist_Odistinct__1_0) ).

fof(c_0_1417,axiom,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_Infinite__Set_Onat__infinite_0) ).

fof(c_0_1418,axiom,
    ! [X2,X88] : c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X2)),X2) = c_Message_OHPair(X88,X2),
    file('<stdin>',cls_Message_OMPair__eq__HPair_2) ).

fof(c_0_1419,axiom,
    ! [X2,X88] : c_Message_OHPair(X88,X2) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X2)),X2),
    file('<stdin>',cls_Message_OHPair__eq__MPair_2) ).

fof(c_0_1420,axiom,
    ! [X49] :
      ( ~ c_lessequals(X49,c_0,tc_IntDef_Oint)
      | c_IntDef_Onat(X49) = c_0 ),
    file('<stdin>',cls_IntDef_Onat__le__0_0) ).

fof(c_0_1421,axiom,
    ! [X22,X16] :
      ( c_plus(X16,X22,tc_nat) != c_0
      | X22 = c_0 ),
    file('<stdin>',cls_Nat_Oadd__is__0_1) ).

fof(c_0_1422,axiom,
    ! [X22,X16] :
      ( c_plus(X16,X22,tc_nat) != c_0
      | X16 = c_0 ),
    file('<stdin>',cls_Nat_Oadd__is__0_0) ).

fof(c_0_1423,axiom,
    ! [X19] : c_div(X19,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X19,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdiv__minus1__right_0) ).

fof(c_0_1424,axiom,
    ! [X14,X4] : c_in(c_List_Olist_ONil,c_List_Olists(X14,X4),tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olists_ONil_0) ).

fof(c_0_1425,axiom,
    ! [X24,X4] : c_in(c_List_Oset(X24,X4),c_Finite__Set_OFinites,tc_set(X4)),
    file('<stdin>',cls_List_Ofinite__set_0) ).

fof(c_0_1426,axiom,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_uminus(X49,tc_IntDef_Oint),X4) = c_uminus(c_IntDef_Oof__int(X49,X4),X4) ),
    file('<stdin>',cls_IntDef_Oof__int__minus_0) ).

fof(c_0_1427,axiom,
    ! [X7,X4] : ~ c_in(X7,c_emptyset,X4),
    file('<stdin>',cls_Set_Oempty__iff_0) ).

fof(c_0_1428,axiom,
    ! [X2,X42] : ~ c_List_Oop_Amem(X2,c_List_Olist_ONil,X42),
    file('<stdin>',cls_List_Oop_Amem_Osimps__1_0) ).

fof(c_0_1429,axiom,
    ! [X22] : ~ c_less(X22,X22,tc_nat),
    file('<stdin>',cls_Nat_Oless__irrefl_0) ).

fof(c_0_1430,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)) = c_0 ),
    file('<stdin>',cls_NatBin_Oint__nat__number__of_0) ).

fof(c_0_1431,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X48,tc_nat)) = c_1 ),
    file('<stdin>',cls_NatBin_OSuc__nat__number__of_0) ).

fof(c_0_1432,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Omeet(c_0,c_uminus(c_0,X4),X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Omeet__0__eq__0_1) ).

fof(c_0_1433,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Ojoin(c_0,c_uminus(c_0,X4),X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Ojoin__0__eq__0_1) ).

fof(c_0_1434,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_lessequals(c_HOL_Oabs(c_0,X4),c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__le__zero__iff_1) ).

fof(c_0_1435,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_NatArith_Oof__nat(c_0,X4),c_0,X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__le__0__iff_1) ).

fof(c_0_1436,axiom,
    ! [X22] :
      ( ~ c_less(X22,c_1,tc_nat)
      | X22 = c_0 ),
    file('<stdin>',cls_Nat_Oless__one_0) ).

fof(c_0_1437,axiom,
    ! [X44] :
      ( ~ c_lessequals(X44,c_0,tc_nat)
      | X44 = c_0 ),
    file('<stdin>',cls_Nat_Ole__0__eq_0) ).

fof(c_0_1438,axiom,
    ! [X16] :
      ( ~ c_Divides_Oop_Advd(c_0,X16,tc_IntDef_Oint)
      | X16 = c_0 ),
    file('<stdin>',cls_IntDiv_Ozdvd__0__left_0) ).

fof(c_0_1439,axiom,
    ! [X16] :
      ( ~ c_Divides_Oop_Advd(c_0,X16,tc_nat)
      | X16 = c_0 ),
    file('<stdin>',cls_Divides_Odvd__0__left__iff_0) ).

fof(c_0_1440,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_Oall__not__in__conv__1(X14,X4),X14,X4)
      | X14 = c_emptyset ),
    file('<stdin>',cls_Set_Oall__not__in__conv_0) ).

fof(c_0_1441,axiom,
    ! [X1,X4] : c_Relation_ORange(c_Relation_Odiag(X1,X4),X4,X4) = X1,
    file('<stdin>',cls_Relation_ORange__diag_0) ).

fof(c_0_1442,axiom,
    ! [X1,X4] : c_Relation_ODomain(c_Relation_Odiag(X1,X4),X4,X4) = X1,
    file('<stdin>',cls_Relation_ODomain__diag_0) ).

fof(c_0_1443,axiom,
    ! [X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X48,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X48),tc_nat) ),
    file('<stdin>',cls_NatBin_OSuc__nat__number__of_1) ).

fof(c_0_1444,axiom,
    ! [X22] : ~ c_less(X22,c_0,tc_nat),
    file('<stdin>',cls_Nat_Onot__less0_0) ).

fof(c_0_1445,axiom,
    ! [X86,X4] : c_Relation_ORange(c_Transitive__Closure_Ortrancl(X86,X4),X4,X4) = c_UNIV,
    file('<stdin>',cls_Transitive__Closure_ORange__rtrancl_0) ).

fof(c_0_1446,axiom,
    ! [X86,X4] : c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X86,X4),X4,X4) = c_UNIV,
    file('<stdin>',cls_Transitive__Closure_ODomain__rtrancl_0) ).

fof(c_0_1447,axiom,
    ! [X17] : c_in(c_SetInterval_OlessThan(X17,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__lessThan_0) ).

fof(c_0_1448,axiom,
    ! [X17] : c_in(c_SetInterval_OatMost(X17,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__atMost_0) ).

fof(c_0_1449,axiom,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    file('<stdin>',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).

fof(c_0_1450,axiom,
    ~ c_less(c_0,c_0,tc_nat),
    file('<stdin>',cls_Nat_Onot__gr0_1) ).

fof(c_0_1451,axiom,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(c_List_Orev(X24,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    file('<stdin>',cls_List_Odistinct__rev_0) ).

fof(c_0_1452,axiom,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(c_List_Orotate1(X24,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    file('<stdin>',cls_List_Odistinct1__rotate_0) ).

fof(c_0_1453,axiom,
    ! [X103,X14] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_Oused(X103),tc_Message_Omsg),
    file('<stdin>',cls_Public_OshrK__in__used_0) ).

fof(c_0_1454,axiom,
    ! [X14] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_OinitState(X14),tc_Message_Omsg),
    file('<stdin>',cls_Public_OshrK__in__initState_0) ).

fof(c_0_1455,axiom,
    ! [X60,X44] :
      ( c_List_Oupt(X44,X60) != c_List_Olist_ONil
      | c_lessequals(X60,X44,tc_nat)
      | X60 = c_0 ),
    file('<stdin>',cls_List_Oupt__eq__Nil__conv_0) ).

fof(c_0_1456,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_Omsg_OMPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X109 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)) ),
    file('<stdin>',cls_Message_OMPair__eq__HPair_0) ).

fof(c_0_1457,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X88,X87) != c_Message_Omsg_OMPair(X109,X108)
      | X109 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)) ),
    file('<stdin>',cls_Message_OHPair__eq__MPair_0) ).

fof(c_0_1458,axiom,
    ! [X89] : c_Message_Oparts(c_Message_Osynth(X89)) = c_union(c_Message_Oparts(X89),c_Message_Osynth(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oparts__synth_0) ).

fof(c_0_1459,axiom,
    ! [X89] : c_Message_Oanalz(c_Message_Osynth(X89)) = c_union(c_Message_Oanalz(X89),c_Message_Osynth(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_Oanalz__synth_0) ).

fof(c_0_1460,axiom,
    ! [X12,X48] : c_Numeral_Obin__mult(c_Numeral_OBit(X48,c_Numeral_Obit_OB0),X12) = c_Numeral_OBit(c_Numeral_Obin__mult(X48,X12),c_Numeral_Obit_OB0),
    file('<stdin>',cls_Numeral_Obin__mult__0_0) ).

fof(c_0_1461,axiom,
    ! [X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)) = c_Numeral_Onumber__of(X48,tc_IntDef_Oint) ),
    file('<stdin>',cls_NatBin_Oint__nat__number__of_1) ).

fof(c_0_1462,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(c_0,X19,X4) = c_uminus(X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Odiff__0_0) ).

fof(c_0_1463,axiom,
    ! [X60,X44] :
      ( c_lessequals(X44,X60,tc_nat)
      | c_List_Oupt(X44,c_Suc(X60)) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oupt_Oupt__Suc_1) ).

fof(c_0_1464,axiom,
    ! [X14,X4] :
      ( c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_Finite__Set_Ocard(X14,X4) = c_0 ),
    file('<stdin>',cls_Finite__Set_Ocard__infinite_0) ).

fof(c_0_1465,axiom,
    ! [X19] : c_Divides_Oop_Amod(X19,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozmod__minus1__right_0) ).

fof(c_0_1466,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__7_0) ).

fof(c_0_1467,axiom,
    ! [X22] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X22)),tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Oneg__zminus__int_0) ).

fof(c_0_1468,axiom,
    c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
    file('<stdin>',cls_IntArith_Ozabs__less__one__iff_1) ).

fof(c_0_1469,axiom,
    ! [X2,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | X2 = c_0
      | c_1 = c_divide(X2,X2,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oeq__divide__eq__1_2) ).

fof(c_0_1470,axiom,
    ! [X2,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | X2 = c_0
      | c_divide(X2,X2,X4) = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__eq__1_2) ).

fof(c_0_1471,axiom,
    ! [X4] : c_Pow(c_emptyset,X4) = c_insert(c_emptyset,c_emptyset,tc_set(X4)),
    file('<stdin>',cls_Set_OPow__empty_0) ).

fof(c_0_1472,axiom,
    ! [X42] : c_List_Olistset(c_List_Olist_ONil,X42) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X42)),
    file('<stdin>',cls_List_Olistset_Osimps__1_0) ).

fof(c_0_1473,axiom,
    ! [X7,X28,X112,X14] : c_Public_OpublicKey(X7,X112) != c_Message_OinvKey(c_Public_OpublicKey(X28,X14)),
    file('<stdin>',cls_Public_OpublicKey__neq__privateKey_0) ).

fof(c_0_1474,axiom,
    ! [X7,X28,X112,X14] : c_Message_OinvKey(c_Public_OpublicKey(X28,X14)) != c_Public_OpublicKey(X7,X112),
    file('<stdin>',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).

fof(c_0_1475,axiom,
    ! [X2] :
      ( ~ c_Parity_Oeven(c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__neg_0) ).

fof(c_0_1476,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    file('<stdin>',cls_NatBin_Oeq__number__of__0_2) ).

fof(c_0_1477,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    file('<stdin>',cls_NatBin_Oeq__number__of__0_1) ).

fof(c_0_1478,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X48,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__0__number__of_2) ).

fof(c_0_1479,axiom,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X48,tc_nat) ),
    file('<stdin>',cls_NatBin_Oeq__0__number__of_1) ).

fof(c_0_1480,axiom,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X6,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Owf__lex_0) ).

fof(c_0_1481,axiom,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X6,X4),tc_List_Olist(X4)) ),
    file('<stdin>',cls_List_Owf__lenlex_0) ).

fof(c_0_1482,axiom,
    ! [X16] : c_IntDef_Oint(c_Suc(X16)) = c_plus(c_1,c_IntDef_Oint(X16),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Oint__Suc_0) ).

fof(c_0_1483,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__0__iff_2) ).

fof(c_0_1484,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,X28,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__eq__0__iff_1) ).

fof(c_0_1485,axiom,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OlessThan(X17,X4),tc_set(X4)) = c_SetInterval_OatLeast(X17,X4) ),
    file('<stdin>',cls_SetInterval_OCompl__lessThan_0) ).

fof(c_0_1486,axiom,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OgreaterThan(X17,X4),tc_set(X4)) = c_SetInterval_OatMost(X17,X4) ),
    file('<stdin>',cls_SetInterval_OCompl__greaterThan_0) ).

fof(c_0_1487,axiom,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OatMost(X17,X4),tc_set(X4)) = c_SetInterval_OgreaterThan(X17,X4) ),
    file('<stdin>',cls_SetInterval_OCompl__atMost_0) ).

fof(c_0_1488,axiom,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OatLeast(X17,X4),tc_set(X4)) = c_SetInterval_OlessThan(X17,X4) ),
    file('<stdin>',cls_SetInterval_OCompl__atLeast_0) ).

fof(c_0_1489,axiom,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_uminus(c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X12),X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__2_0) ).

fof(c_0_1490,axiom,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_0,c_Suc(X22),X4) = c_0 ),
    file('<stdin>',cls_Power_Opower__0__Suc_0) ).

fof(c_0_1491,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Orotate1(X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olength__rotate1_0) ).

fof(c_0_1492,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Orev(X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    file('<stdin>',cls_List_Olength__rev_0) ).

fof(c_0_1493,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_0 = c_divide(c_1,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ozero__eq__1__divide__iff_1) ).

fof(c_0_1494,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(c_1,c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Oone__divide__eq__0__iff_1) ).

fof(c_0_1495,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__self__if_0) ).

fof(c_0_1496,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__3_0) ).

fof(c_0_1497,axiom,
    ! [X13,X14,X4] :
      ( c_uminus(X14,tc_set(X4)) != c_uminus(X13,tc_set(X4))
      | X14 = X13 ),
    file('<stdin>',cls_Set_OCompl__eq__Compl__iff_0) ).

fof(c_0_1498,axiom,
    ! [X22,X89] : c_in(c_Message_Omsg_ONumber(X22),c_Message_Osynth(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_ONumber__synth_0) ).

fof(c_0_1499,axiom,
    ! [X89,X14] : c_in(c_Message_Omsg_OAgent(X14),c_Message_Osynth(X89),tc_Message_Omsg),
    file('<stdin>',cls_Message_OAgent__synth_0) ).

fof(c_0_1500,axiom,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Orev(X24,X4),X4) ),
    file('<stdin>',cls_List_Odistinct__rev_1) ).

fof(c_0_1501,axiom,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Orotate1(X24,X4),X4) ),
    file('<stdin>',cls_List_Odistinct1__rotate_1) ).

fof(c_0_1502,axiom,
    ! [X1,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omax(X1,X1,X3) = X1 ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).

fof(c_0_1503,axiom,
    ! [X1,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omin(X1,X1,X3) = X1 ),
    file('<stdin>',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).

fof(c_0_1504,axiom,
    ! [X1,X4] :
      ( ~ class_LOrder_Omeet__semilorder(X4)
      | c_LOrder_Omeet(X1,X1,X4) = X1 ),
    file('<stdin>',cls_LOrder_Omeet__idempotent_0) ).

fof(c_0_1505,axiom,
    ! [X1,X4] :
      ( ~ class_LOrder_Ojoin__semilorder(X4)
      | c_LOrder_Ojoin(X1,X1,X4) = X1 ),
    file('<stdin>',cls_LOrder_Ojoin__idempotent_0) ).

fof(c_0_1506,axiom,
    ! [X49] :
      ( c_lessequals(c_0,X49,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X49)) = c_0 ),
    file('<stdin>',cls_IntDef_Oint__nat__eq_1) ).

fof(c_0_1507,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X19,X19,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Odiff__self_0) ).

fof(c_0_1508,axiom,
    ! [X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | c_lessequals(X2,X2,X4) ),
    file('<stdin>',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

fof(c_0_1509,axiom,
    ! [X7,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 = c_times(c_1,X7,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__right1_2) ).

fof(c_0_1510,axiom,
    ! [X7,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 = c_times(X7,c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__left1_2) ).

fof(c_0_1511,axiom,
    ! [X1,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X1,c_1,X4) = X1 ),
    file('<stdin>',cls_Ring__and__Field_Odivide__1_0) ).

fof(c_0_1512,axiom,
    ! [X1,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(X1,c_1,X4) = X1 ),
    file('<stdin>',cls_Power_Opower__one__right_0) ).

fof(c_0_1513,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X4)
      | c_times(X1,c_1,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).

fof(c_0_1514,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X4)
      | c_times(c_1,X1,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).

fof(c_0_1515,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X1,c_0,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Odiff__0__right_0) ).

fof(c_0_1516,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
      | c_plus(c_0,X1,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).

fof(c_0_1517,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
      | c_plus(X1,c_0,X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Oadd__0__right_0) ).

fof(c_0_1518,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_uminus(X19,X4),X4) = c_HOL_Oabs(X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__minus__cancel_0) ).

fof(c_0_1519,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_HOL_Oabs(X19,X4),X4) = c_HOL_Oabs(X19,X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__idempotent_0) ).

fof(c_0_1520,axiom,
    ! [X14,X4] : c_minus(X14,X14,tc_set(X4)) = c_emptyset,
    file('<stdin>',cls_Set_ODiff__cancel_0) ).

fof(c_0_1521,axiom,
    c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
    file('<stdin>',cls_SetInterval_OatMost__0_0) ).

fof(c_0_1522,axiom,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(X19,X4) != c_HOL_Oinverse(X28,X4)
      | X19 = X28 ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__eq__iff__eq_0) ).

fof(c_0_1523,axiom,
    ! [X14,X4] : c_lessequals(X14,X14,tc_set(X4)),
    file('<stdin>',cls_Set_Osubset__refl_0) ).

fof(c_0_1524,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X4)
      | c_times(X19,c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__zero__right_0) ).

fof(c_0_1525,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X4)
      | c_times(c_0,X19,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Omult__zero__left_0) ).

fof(c_0_1526,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 = c_times(X28,c_0,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__right1_1) ).

fof(c_0_1527,axiom,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 = c_times(c_0,X28,X4) ),
    file('<stdin>',cls_Ring__and__Field_Omult__cancel__left1_1) ).

fof(c_0_1528,axiom,
    ! [X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(X19,c_0,X4) = c_1 ),
    file('<stdin>',cls_Power_Orecpower__class_Oaxioms__1_0) ).

fof(c_0_1529,axiom,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_1,X22,X4) = c_1 ),
    file('<stdin>',cls_Power_Opower__one_0) ).

fof(c_0_1530,axiom,
    ! [X1,X4] : c_minus(X1,c_emptyset,tc_set(X4)) = X1,
    file('<stdin>',cls_Set_ODiff__empty_0) ).

fof(c_0_1531,axiom,
    ! [X14,X4] : c_lessequals(X14,c_UNIV,tc_set(X4)),
    file('<stdin>',cls_Set_Osubset__UNIV_0) ).

fof(c_0_1532,axiom,
    ! [X14,X4] : c_minus(c_emptyset,X14,tc_set(X4)) = c_emptyset,
    file('<stdin>',cls_Set_Oempty__Diff_0) ).

fof(c_0_1533,axiom,
    ! [X1,X4] : c_uminus(c_uminus(X1,tc_set(X4)),tc_set(X4)) = X1,
    file('<stdin>',cls_Set_Odouble__complement_0) ).

fof(c_0_1534,axiom,
    ! [X14,X4] : c_minus(X14,c_UNIV,tc_set(X4)) = c_emptyset,
    file('<stdin>',cls_Set_ODiff__UNIV_0) ).

fof(c_0_1535,axiom,
    c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
    file('<stdin>',cls_Divides_Odvd__1__iff__1_1) ).

fof(c_0_1536,axiom,
    ! [X14,X4] : c_lessequals(c_emptyset,X14,tc_set(X4)),
    file('<stdin>',cls_Set_Oempty__subsetI_0) ).

fof(c_0_1537,axiom,
    ! [X22] : c_less(X22,c_Suc(X22),tc_nat),
    file('<stdin>',cls_Nat_OlessI_0) ).

fof(c_0_1538,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_0,c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Ozero__le__one_0) ).

fof(c_0_1539,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_less(c_0,c_1,X4) ),
    file('<stdin>',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).

fof(c_0_1540,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_in(c_1,c_IntDef_ONats,X4) ),
    file('<stdin>',cls_IntDef_ONats__1_0) ).

fof(c_0_1541,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_in(c_0,c_IntDef_ONats,X4) ),
    file('<stdin>',cls_IntDef_ONats__0_0) ).

fof(c_0_1542,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_in(c_1,c_IntDef_OInts,X4) ),
    file('<stdin>',cls_IntDef_OInts__1_0) ).

fof(c_0_1543,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_in(c_0,c_IntDef_OInts,X4) ),
    file('<stdin>',cls_IntDef_OInts__0_0) ).

fof(c_0_1544,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_NatArith_Oof__nat(X22,tc_IntDef_Oint),X4) = c_NatArith_Oof__nat(X22,X4) ),
    file('<stdin>',cls_IntDef_Oof__int__of__nat__eq_0) ).

fof(c_0_1545,axiom,
    ! [X88] : c_in(c_Public_OshrK(X88),c_Message_OsymKeys,tc_nat),
    file('<stdin>',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).

fof(c_0_1546,axiom,
    ! [X4] : c_lessequals(c_emptyset,c_emptyset,tc_set(X4)),
    file('<stdin>',cls_Set_Osubset__empty_1) ).

fof(c_0_1547,axiom,
    ! [X12] : c_Numeral_Obin__minus(c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X12)),c_Numeral_Obit_OB1),
    file('<stdin>',cls_Numeral_Obin__minus__1_0) ).

fof(c_0_1548,axiom,
    ! [X22] : c_lessequals(c_0,c_IntDef_Oint(X22),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Ozero__zle__int_0) ).

fof(c_0_1549,axiom,
    ! [X22] : c_less(c_0,c_Suc(X22),tc_nat),
    file('<stdin>',cls_Nat_Ozero__less__Suc_0) ).

fof(c_0_1550,axiom,
    ! [X4] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X4)),
    file('<stdin>',cls_Finite__Set_OFinites_OemptyI_0) ).

fof(c_0_1551,axiom,
    ! [X1] : c_div(X1,c_Suc(c_0),tc_nat) = X1,
    file('<stdin>',cls_Divides_Odiv__1_0) ).

fof(c_0_1552,axiom,
    ! [X16] : c_Divides_Oop_Amod(X16,c_Suc(c_0),tc_nat) = c_0,
    file('<stdin>',cls_Divides_Omod__1_0) ).

fof(c_0_1553,axiom,
    ! [X17] : c_Divides_Oop_Advd(c_Suc(c_0),X17,tc_nat),
    file('<stdin>',cls_Divides_Odvd__1__left_0) ).

fof(c_0_1554,axiom,
    ! [X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_Parity_Oeven__neg_1) ).

fof(c_0_1555,axiom,
    ! [X1,X4] : c_union(X1,X1,X4) = X1,
    file('<stdin>',cls_Set_OUn__absorb_0) ).

fof(c_0_1556,axiom,
    ! [X1,X4] : c_inter(X1,X1,X4) = X1,
    file('<stdin>',cls_Set_OInt__absorb_0) ).

fof(c_0_1557,axiom,
    ! [X1,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_HOL_Oinverse(X1,X4),X4) = X1 ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__inverse__eq_0) ).

fof(c_0_1558,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    file('<stdin>',cls_Nat_Oless__Suc0_1) ).

fof(c_0_1559,axiom,
    ! [X19] :
      ( X19 = c_0
      | c_div(X19,X19,tc_IntDef_Oint) = c_1 ),
    file('<stdin>',cls_IntDiv_Ozdiv__self_0) ).

fof(c_0_1560,axiom,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Oint__le__0__conv_1) ).

fof(c_0_1561,axiom,
    ! [X48,X16] :
      ( c_IntDef_Oint(X16) != c_Numeral_Onumber__of(X48,tc_IntDef_Oint)
      | X16 = c_IntDef_Onat(c_Numeral_Onumber__of(X48,tc_IntDef_Oint)) ),
    file('<stdin>',cls_IntArith_Oint__eq__iff__number__of_0) ).

fof(c_0_1562,axiom,
    ! [X6,X4] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X6,X4),X4) = c_Transitive__Closure_Ortrancl(X6,X4),
    file('<stdin>',cls_Transitive__Closure_Ortrancl__idemp_0) ).

fof(c_0_1563,axiom,
    ! [X1,X4] : c_union(X1,c_emptyset,X4) = X1,
    file('<stdin>',cls_Set_OUn__empty__right_0) ).

fof(c_0_1564,axiom,
    ! [X1,X4] : c_union(c_emptyset,X1,X4) = X1,
    file('<stdin>',cls_Set_OUn__empty__left_0) ).

fof(c_0_1565,axiom,
    ! [X1,X4] : c_inter(X1,c_UNIV,X4) = X1,
    file('<stdin>',cls_Set_OInt__UNIV__right_0) ).

fof(c_0_1566,axiom,
    ! [X1,X4] : c_inter(c_UNIV,X1,X4) = X1,
    file('<stdin>',cls_Set_OInt__UNIV__left_0) ).

fof(c_0_1567,axiom,
    ! [X24,X4] : c_List_Oset(c_List_Orotate1(X24,X4),X4) = c_List_Oset(X24,X4),
    file('<stdin>',cls_List_Oset__rotate1_0) ).

fof(c_0_1568,axiom,
    ! [X24,X4] : c_List_Oset(c_List_Orev(X24,X4),X4) = c_List_Oset(X24,X4),
    file('<stdin>',cls_List_Oset__rev_0) ).

fof(c_0_1569,axiom,
    ! [X24,X4] : c_List_Oset(c_List_Oremdups(X24,X4),X4) = c_List_Oset(X24,X4),
    file('<stdin>',cls_List_Oset__remdups_0) ).

fof(c_0_1570,axiom,
    ! [X24,X4] : X24 = c_append(X24,c_List_Olist_ONil,X4),
    file('<stdin>',cls_List_Oself__append__conv_1) ).

fof(c_0_1571,axiom,
    ! [X26,X4] : X26 = c_append(c_List_Olist_ONil,X26,X4),
    file('<stdin>',cls_List_Oself__append__conv2_1) ).

fof(c_0_1572,axiom,
    ! [X1,X42] : c_List_Oitrev(c_List_Olist_ONil,X1,X42) = X1,
    file('<stdin>',cls_List_Oitrev_Osimps__1_0) ).

fof(c_0_1573,axiom,
    ! [X1,X4] : c_List_Odrop(c_0,X1,X4) = X1,
    file('<stdin>',cls_List_Odrop__0_0) ).

fof(c_0_1574,axiom,
    ! [X24,X4] : c_append(X24,c_List_Olist_ONil,X4) = X24,
    file('<stdin>',cls_List_Oappend__self__conv_1) ).

fof(c_0_1575,axiom,
    ! [X26,X4] : c_append(c_List_Olist_ONil,X26,X4) = X26,
    file('<stdin>',cls_List_Oappend__self__conv2_1) ).

fof(c_0_1576,axiom,
    ! [X1,X4] : c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X4) = X1,
    file('<stdin>',cls_Datatype_Ounit_Orecs_0) ).

fof(c_0_1577,axiom,
    ! [X1,X4] : c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X4) = X1,
    file('<stdin>',cls_Datatype_Ounit_Ocases_0) ).

fof(c_0_1578,axiom,
    ! [X28,X33,X14] : c_Message_OinvKey(c_Public_OpublicKey(X28,X33)) != c_Public_OshrK(X14),
    file('<stdin>',cls_Public_OshrK__neq__priK_0) ).

fof(c_0_1579,axiom,
    ! [X28,X33,X14] : c_Public_OshrK(X14) != c_Message_OinvKey(c_Public_OpublicKey(X28,X33)),
    file('<stdin>',cls_Public_OpriK__neq__shrK_0) ).

fof(c_0_1580,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OlessThan(X2,X4) != c_SetInterval_OlessThan(X1,X4)
      | X2 = X1 ),
    file('<stdin>',cls_SetInterval_OlessThan__eq__iff_0) ).

fof(c_0_1581,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OgreaterThan(X2,X4) != c_SetInterval_OgreaterThan(X1,X4)
      | X2 = X1 ),
    file('<stdin>',cls_SetInterval_OgreaterThan__eq__iff_0) ).

fof(c_0_1582,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OatMost(X2,X4) != c_SetInterval_OatMost(X1,X4)
      | X2 = X1 ),
    file('<stdin>',cls_SetInterval_OatMost__eq__iff_0) ).

fof(c_0_1583,axiom,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OatLeast(X2,X4) != c_SetInterval_OatLeast(X1,X4)
      | X2 = X1 ),
    file('<stdin>',cls_SetInterval_OatLeast__eq__iff_0) ).

fof(c_0_1584,axiom,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(X19,X4) != c_uminus(X28,X4)
      | X19 = X28 ),
    file('<stdin>',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).

fof(c_0_1585,axiom,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_NatArith_Oof__nat(X16,X4) != c_NatArith_Oof__nat(X22,X4)
      | X16 = X22 ),
    file('<stdin>',cls_NatArith_Oof__nat__eq__iff_0) ).

fof(c_0_1586,axiom,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oof__int(X12,X4) != c_IntDef_Oof__int(X49,X4)
      | X12 = X49 ),
    file('<stdin>',cls_IntDef_Oof__int__eq__iff_0) ).

fof(c_0_1587,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X4) = c_Numeral_Onumber__of(c_Numeral_OMin,X4) ),
    file('<stdin>',cls_IntArith_Oof__int__m1_0) ).

fof(c_0_1588,axiom,
    ! [X14,X4] : c_union(X14,c_UNIV,X4) = c_UNIV,
    file('<stdin>',cls_Set_OUn__UNIV__right_0) ).

fof(c_0_1589,axiom,
    ! [X13,X4] : c_union(c_UNIV,X13,X4) = c_UNIV,
    file('<stdin>',cls_Set_OUn__UNIV__left_0) ).

fof(c_0_1590,axiom,
    ! [X14,X4] : c_inter(X14,c_emptyset,X4) = c_emptyset,
    file('<stdin>',cls_Set_OInt__empty__right_0) ).

fof(c_0_1591,axiom,
    ! [X13,X4] : c_inter(c_emptyset,X13,X4) = c_emptyset,
    file('<stdin>',cls_Set_OInt__empty__left_0) ).

fof(c_0_1592,axiom,
    ! [X4] : c_Relation_Oconverse(c_Relation_OId,X4,X4) = c_Relation_OId,
    file('<stdin>',cls_Relation_Oconverse__Id_0) ).

fof(c_0_1593,axiom,
    ! [X3,X4] : c_Relation_ORange(c_emptyset,X3,X4) = c_emptyset,
    file('<stdin>',cls_Relation_ORange__empty_0) ).

fof(c_0_1594,axiom,
    ! [X4] : c_Relation_ORange(c_Relation_OId,X4,X4) = c_UNIV,
    file('<stdin>',cls_Relation_ORange__Id_0) ).

fof(c_0_1595,axiom,
    ! [X3,X4] : c_Relation_ODomain(c_emptyset,X4,X3) = c_emptyset,
    file('<stdin>',cls_Relation_ODomain__empty_0) ).

fof(c_0_1596,axiom,
    ! [X4] : c_Relation_ODomain(c_Relation_OId,X4,X4) = c_UNIV,
    file('<stdin>',cls_Relation_ODomain__Id_0) ).

fof(c_0_1597,axiom,
    ! [X22] :
      ( c_less(c_0,X22,tc_nat)
      | X22 = c_0 ),
    file('<stdin>',cls_Nat_Onot__gr0_0) ).

fof(c_0_1598,axiom,
    ! [X16] : c_minus(X16,X16,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Odiff__self__eq__0_0) ).

fof(c_0_1599,axiom,
    ! [X22,X4] : c_List_Otake(X22,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Otake__eq__Nil_2) ).

fof(c_0_1600,axiom,
    ! [X24,X4] : c_List_Otake(c_0,X24,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Otake__eq__Nil_1) ).

fof(c_0_1601,axiom,
    ! [X14,X4] : c_List_Osublist(c_List_Olist_ONil,X14,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Osublist__nil_0) ).

fof(c_0_1602,axiom,
    ! [X24,X4] : c_List_Osublist(X24,c_emptyset,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Osublist__empty_0) ).

fof(c_0_1603,axiom,
    ! [X22,X4] : c_List_Orotate(X22,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Orotate__is__Nil__conv_1) ).

fof(c_0_1604,axiom,
    ! [X2,X42] : c_List_Oreplicate(c_0,X2,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oreplicate_Oreplicate__0_0) ).

fof(c_0_1605,axiom,
    ! [X2,X42] : c_List_Oremove1(X2,c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oremove1_Osimps__1_0) ).

fof(c_0_1606,axiom,
    ! [X66,X42] : c_List_Olist__inter(c_List_Olist_ONil,X66,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Olist__inter_Osimps__1_0) ).

fof(c_0_1607,axiom,
    ! [X6,X42] : c_List_Olexn(X6,c_0,X42) = c_emptyset,
    file('<stdin>',cls_List_Olexn_Osimps__1_0) ).

fof(c_0_1608,axiom,
    ! [X22,X42] : c_List_Odrop(X22,c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Odrop_Odrop__Nil_0) ).

fof(c_0_1609,axiom,
    ! [X19] : c_Divides_Oop_Amod(X19,X19,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozmod__self_0) ).

fof(c_0_1610,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,X16,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__refl_0) ).

fof(c_0_1611,axiom,
    ! [X6,X4] : c_Equiv__Relations_Oquotient(c_emptyset,X6,X4) = c_emptyset,
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty_1) ).

fof(c_0_1612,axiom,
    ! [X6,X4] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X6,X4),
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty2_1) ).

fof(c_0_1613,axiom,
    ! [X22] : c_Divides_Oop_Amod(X22,X22,tc_nat) = c_0,
    file('<stdin>',cls_Divides_Omod__self_0) ).

fof(c_0_1614,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,X16,tc_nat),
    file('<stdin>',cls_Divides_Odvd__refl_0) ).

fof(c_0_1615,axiom,
    ! [X2,X4] : c_in(X2,c_UNIV,X4),
    file('<stdin>',cls_Set_OUNIV__I_0) ).

fof(c_0_1616,axiom,
    ! [X1] : c_minus(X1,c_0,tc_nat) = X1,
    file('<stdin>',cls_Nat_Oop_A_N_Odiff__0_0) ).

fof(c_0_1617,axiom,
    ! [X1] : c_plus(c_0,X1,tc_nat) = X1,
    file('<stdin>',cls_Nat_Oop_A_L_Oadd__0_0) ).

fof(c_0_1618,axiom,
    c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
    file('<stdin>',cls_Nat_Oone__eq__mult__iff_2) ).

fof(c_0_1619,axiom,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    file('<stdin>',cls_Nat_Omult__eq__1__iff_2) ).

fof(c_0_1620,axiom,
    ! [X1] : c_Orderings_Omax(X1,c_0,tc_nat) = X1,
    file('<stdin>',cls_Nat_Omax__0R_0) ).

fof(c_0_1621,axiom,
    ! [X1] : c_Orderings_Omax(c_0,X1,tc_nat) = X1,
    file('<stdin>',cls_Nat_Omax__0L_0) ).

fof(c_0_1622,axiom,
    ! [X1] : c_plus(X1,c_0,tc_nat) = X1,
    file('<stdin>',cls_Nat_Oadd__0__right_0) ).

fof(c_0_1623,axiom,
    ! [X1] : c_div(X1,c_1,tc_IntDef_Oint) = X1,
    file('<stdin>',cls_IntDiv_Ozdiv__1_0) ).

fof(c_0_1624,axiom,
    ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
    file('<stdin>',cls_IntDiv_ODIVISION__BY__ZERO_0) ).

fof(c_0_1625,axiom,
    ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1,
    file('<stdin>',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).

fof(c_0_1626,axiom,
    ! [X4] : c_union(c_emptyset,c_emptyset,X4) = c_emptyset,
    file('<stdin>',cls_Set_OUn__empty_2) ).

fof(c_0_1627,axiom,
    ! [X4] : c_inter(c_UNIV,c_UNIV,X4) = c_UNIV,
    file('<stdin>',cls_Set_OInt__UNIV_2) ).

fof(c_0_1628,axiom,
    ! [X29] : c_Nat_Opower(X29,c_0,tc_nat) = c_1,
    file('<stdin>',cls_Power_Opower_Osimps__1_0) ).

fof(c_0_1629,axiom,
    ! [X22] : c_times(c_0,X22,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Oop_A_K_Omult__0_0) ).

fof(c_0_1630,axiom,
    ! [X16] : c_times(X16,c_0,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Omult__0__right_0) ).

fof(c_0_1631,axiom,
    ! [X22] : c_Orderings_Omin(X22,c_0,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Omin__0R_0) ).

fof(c_0_1632,axiom,
    ! [X22] : c_Orderings_Omin(c_0,X22,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Omin__0L_0) ).

fof(c_0_1633,axiom,
    ! [X22] : c_minus(c_0,X22,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Odiff__0__eq__0_0) ).

fof(c_0_1634,axiom,
    ! [X4] : c_append(c_List_Olist_ONil,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oappend__is__Nil__conv_2) ).

fof(c_0_1635,axiom,
    ! [X4] : c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X4),
    file('<stdin>',cls_List_ONil__is__append__conv_2) ).

fof(c_0_1636,axiom,
    ! [X28] : c_Divides_Oop_Amod(c_0,X28,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozmod__zero_0) ).

fof(c_0_1637,axiom,
    ! [X19] : c_Divides_Oop_Amod(X19,c_1,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozmod__1_0) ).

fof(c_0_1638,axiom,
    ! [X28] : c_div(c_0,X28,tc_IntDef_Oint) = c_0,
    file('<stdin>',cls_IntDiv_Ozdiv__zero_0) ).

fof(c_0_1639,axiom,
    ! [X29] : c_Nat_Opower(X29,c_0,tc_IntDef_Oint) = c_1,
    file('<stdin>',cls_IntDiv_Opower_Osimps__1_0) ).

fof(c_0_1640,axiom,
    ! [X16] : c_Divides_Oop_Amod(c_0,X16,tc_nat) = c_0,
    file('<stdin>',cls_Divides_Omod__0_0) ).

fof(c_0_1641,axiom,
    ! [X16] : c_div(c_0,X16,tc_nat) = c_0,
    file('<stdin>',cls_Divides_Odiv__0_0) ).

fof(c_0_1642,axiom,
    ! [X19] : c_div(X19,c_0,tc_nat) = c_0,
    file('<stdin>',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).

fof(c_0_1643,axiom,
    ! [X22] : c_lessequals(c_0,X22,tc_nat),
    file('<stdin>',cls_Nat_Ole0_0) ).

fof(c_0_1644,axiom,
    ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__1__left_0) ).

fof(c_0_1645,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,c_0,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__0__right_0) ).

fof(c_0_1646,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,c_0,tc_nat),
    file('<stdin>',cls_Divides_Odvd__0__right_0) ).

fof(c_0_1647,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__11_0) ).

fof(c_0_1648,axiom,
    ! [X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(c_uminus(c_1,X3),X3) = c_1 ),
    file('<stdin>',cls_NatSimprocs_Oequation__minus__iff__1_1) ).

fof(c_0_1649,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) = c_1 ),
    file('<stdin>',cls_IntArith_Oabs__minus__one_0) ).

fof(c_0_1650,axiom,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(X28,X3) != c_1
      | X28 = c_uminus(c_1,X3) ),
    file('<stdin>',cls_NatSimprocs_Oequation__minus__iff__1_0) ).

fof(c_0_1651,axiom,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    file('<stdin>',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).

fof(c_0_1652,axiom,
    ! [X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | ~ c_Parity_Oeven(c_Suc(X2),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__Suc_0) ).

fof(c_0_1653,axiom,
    c_less(c_0,c_1,tc_nat),
    file('<stdin>',cls_Nat_Oless__one_1) ).

fof(c_0_1654,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    file('<stdin>',cls_Nat_Ole__0__eq_1) ).

fof(c_0_1655,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Oadd__is__0_2) ).

fof(c_0_1656,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__0__left_1) ).

fof(c_0_1657,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    file('<stdin>',cls_Divides_Odvd__0__left__iff_1) ).

fof(c_0_1658,axiom,
    ! [X13,X14] : c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,X14)) != c_Public_OshrK(X13),
    file('<stdin>',cls_Public_OpriEK__noteq__shrK_0) ).

fof(c_0_1659,axiom,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_uminus(X1,X4),X4) = X1 ),
    file('<stdin>',cls_OrderedGroup_Ominus__minus_0) ).

fof(c_0_1660,axiom,
    ! [X7,X28,X112,X14] :
      ( c_Public_OpublicKey(X28,X14) != c_Public_OpublicKey(X7,X112)
      | X14 = X112 ),
    file('<stdin>',cls_Public_OpublicKey__inject_1) ).

fof(c_0_1661,axiom,
    ! [X7,X28,X112,X14] :
      ( c_Public_OpublicKey(X28,X14) != c_Public_OpublicKey(X7,X112)
      | X28 = X7 ),
    file('<stdin>',cls_Public_OpublicKey__inject_0) ).

fof(c_0_1662,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_Omsg_OMPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X108 = X87 ),
    file('<stdin>',cls_Message_OMPair__eq__HPair_1) ).

fof(c_0_1663,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X88,X87) != c_Message_Omsg_OMPair(X109,X108)
      | X108 = X87 ),
    file('<stdin>',cls_Message_OHPair__eq__MPair_1) ).

fof(c_0_1664,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X108 = X87 ),
    file('<stdin>',cls_Message_OHPair__eq_1) ).

fof(c_0_1665,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X109 = X88 ),
    file('<stdin>',cls_Message_OHPair__eq_0) ).

fof(c_0_1666,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_ONotes(X96,X98) != c_Event_Oevent_ONotes(X95,X97)
      | X98 = X97 ),
    file('<stdin>',cls_Event_Oevent_Oinject__3_1) ).

fof(c_0_1667,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_ONotes(X96,X98) != c_Event_Oevent_ONotes(X95,X97)
      | X96 = X95 ),
    file('<stdin>',cls_Event_Oevent_Oinject__3_0) ).

fof(c_0_1668,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_OGets(X96,X98) != c_Event_Oevent_OGets(X95,X97)
      | X98 = X97 ),
    file('<stdin>',cls_Event_Oevent_Oinject__2_1) ).

fof(c_0_1669,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_OGets(X96,X98) != c_Event_Oevent_OGets(X95,X97)
      | X96 = X95 ),
    file('<stdin>',cls_Event_Oevent_Oinject__2_0) ).

fof(c_0_1670,axiom,
    ! [X90,X91,X97,X98] :
      ( c_Message_Omsg_OCrypt(X91,X98) != c_Message_Omsg_OCrypt(X90,X97)
      | X98 = X97 ),
    file('<stdin>',cls_Message_Omsg_Oinject__7_1) ).

fof(c_0_1671,axiom,
    ! [X90,X91,X97,X98] :
      ( c_Message_Omsg_OCrypt(X91,X98) != c_Message_Omsg_OCrypt(X90,X97)
      | X91 = X90 ),
    file('<stdin>',cls_Message_Omsg_Oinject__7_0) ).

fof(c_0_1672,axiom,
    ! [X99,X100,X101,X102] :
      ( c_Message_Omsg_OMPair(X102,X100) != c_Message_Omsg_OMPair(X101,X99)
      | X100 = X99 ),
    file('<stdin>',cls_Message_Omsg_Oinject__6_1) ).

fof(c_0_1673,axiom,
    ! [X99,X100,X101,X102] :
      ( c_Message_Omsg_OMPair(X102,X100) != c_Message_Omsg_OMPair(X101,X99)
      | X102 = X101 ),
    file('<stdin>',cls_Message_Omsg_Oinject__6_0) ).

fof(c_0_1674,axiom,
    ! [X26,X24,X4] :
      ( c_List_Orev(X24,X4) != c_List_Orev(X26,X4)
      | X24 = X26 ),
    file('<stdin>',cls_List_Orev__is__rev__conv_0) ).

fof(c_0_1675,axiom,
    ! [X55,X56,X57,X58] :
      ( c_List_Ochar_OChar(X58,X56) != c_List_Ochar_OChar(X57,X55)
      | X56 = X55 ),
    file('<stdin>',cls_List_Ochar_Oinject_1) ).

fof(c_0_1676,axiom,
    ! [X55,X56,X57,X58] :
      ( c_List_Ochar_OChar(X58,X56) != c_List_Ochar_OChar(X57,X55)
      | X58 = X57 ),
    file('<stdin>',cls_List_Ochar_Oinject_0) ).

fof(c_0_1677,axiom,
    ! [X43,X19,X4] :
      ( c_Datatype_Ooption_OSome(X19,X4) != c_Datatype_Ooption_OSome(X43,X4)
      | X19 = X43 ),
    file('<stdin>',cls_Datatype_Ooption_Oinject_0) ).

fof(c_0_1678,axiom,
    ! [X19,X4] : c_Nat_Osize(c_Datatype_Ooption_OSome(X19,X4),tc_Datatype_Ooption(X4)) = c_0,
    file('<stdin>',cls_Datatype_Ooption_Osize__2_0) ).

fof(c_0_1679,axiom,
    ! [X12] : c_Numeral_Obin__succ(c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X12),c_Numeral_Obit_OB0),
    file('<stdin>',cls_Numeral_Obin__succ__1_0) ).

fof(c_0_1680,axiom,
    ! [X12] : c_Numeral_Obin__pred(c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X12),c_Numeral_Obit_OB1),
    file('<stdin>',cls_Numeral_Obin__pred__0_0) ).

fof(c_0_1681,axiom,
    ! [X12] : c_Numeral_Obin__minus(c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X12),c_Numeral_Obit_OB0),
    file('<stdin>',cls_Numeral_Obin__minus__0_0) ).

fof(c_0_1682,axiom,
    ! [X39,X38] :
      ( class_Finite__Set_Ofinite(tc_sum(X39,X38))
      | ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X39) ),
    file('<stdin>',clsarity_sum_0) ).

fof(c_0_1683,axiom,
    ! [X39,X38] :
      ( class_Finite__Set_Ofinite(tc_prod(X39,X38))
      | ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X39) ),
    file('<stdin>',clsarity_prod_0) ).

fof(c_0_1684,axiom,
    ! [X39,X38] :
      ( class_Finite__Set_Ofinite(tc_fun(X39,X38))
      | ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X39) ),
    file('<stdin>',clsarity_fun_0) ).

fof(c_0_1685,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X4),X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__2_0) ).

fof(c_0_1686,axiom,
    ! [X87,X109,X88,X93] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OCrypt(X93,X109),
    file('<stdin>',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).

fof(c_0_1687,axiom,
    ! [X87,X109,X88,X93] : c_Message_Omsg_OCrypt(X93,X109) != c_Message_OHPair(X88,X87),
    file('<stdin>',cls_Message_OHPair__neqs__6_0) ).

fof(c_0_1688,axiom,
    ! [X97,X98,X95,X96] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X96,X98),
    file('<stdin>',cls_Event_Oevent_Odistinct__6_0) ).

fof(c_0_1689,axiom,
    ! [X97,X98,X95,X96] : c_Event_Oevent_OGets(X96,X98) != c_Event_Oevent_ONotes(X95,X97),
    file('<stdin>',cls_Event_Oevent_Odistinct__5_0) ).

fof(c_0_1690,axiom,
    ! [X2,X4] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X2,X4),X4) ),
    file('<stdin>',cls_Datatype_Onot__Some__eq_0) ).

fof(c_0_1691,axiom,
    ! [X2,X4] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X2,X4),X4) ),
    file('<stdin>',cls_Datatype_Onot__None__eq_0) ).

fof(c_0_1692,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X4) = c_1 ),
    file('<stdin>',cls_Numeral_Onumeral__1__eq__1_0) ).

fof(c_0_1693,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_IntDef_Oint(X22),X4) = c_NatArith_Oof__nat(X22,X4) ),
    file('<stdin>',cls_IntDef_Oof__int__int__eq_0) ).

fof(c_0_1694,axiom,
    ! [X1,X4] : c_Union(c_Pow(X1,X4),X4) = X1,
    file('<stdin>',cls_Set_OUnion__Pow__eq_0) ).

fof(c_0_1695,axiom,
    ! [X1,X4] : c_List_Orev(c_List_Orev(X1,X4),X4) = X1,
    file('<stdin>',cls_List_Orev__rev__ident_0) ).

fof(c_0_1696,axiom,
    ! [X1,X4] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X4),X4) = X1,
    file('<stdin>',cls_Datatype_Othe_Osimps_0) ).

fof(c_0_1697,axiom,
    ! [X24,X4] : c_List_Odistinct(c_List_Oremdups(X24,X4),X4),
    file('<stdin>',cls_List_Odistinct__remdups_0) ).

fof(c_0_1698,axiom,
    ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) = c_Suc(X15),
    file('<stdin>',cls_SetInterval_Ocard__atMost_0) ).

fof(c_0_1699,axiom,
    ! [X12] : c_Numeral_Obin__succ(c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(X12,c_Numeral_Obit_OB1),
    file('<stdin>',cls_Numeral_Obin__succ__0_0) ).

fof(c_0_1700,axiom,
    ! [X12] : c_Numeral_Obin__pred(c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(X12,c_Numeral_Obit_OB0),
    file('<stdin>',cls_Numeral_Obin__pred__1_0) ).

fof(c_0_1701,axiom,
    ! [X12] : c_IntDef_Onat(c_Numeral_Onumber__of(X12,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X12,tc_nat),
    file('<stdin>',cls_NatBin_Onat__number__of_0) ).

fof(c_0_1702,axiom,
    ! [X22] : c_IntDef_Onat(c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint)) = c_0,
    file('<stdin>',cls_IntDef_Onat__zminus__int_0) ).

fof(c_0_1703,axiom,
    ! [X98,X96] : c_Nat_Osize(c_Event_Oevent_ONotes(X96,X98),tc_Event_Oevent) = c_0,
    file('<stdin>',cls_Event_Oevent_Osize__3_0) ).

fof(c_0_1704,axiom,
    ! [X98,X96] : c_Nat_Osize(c_Event_Oevent_OGets(X96,X98),tc_Event_Oevent) = c_0,
    file('<stdin>',cls_Event_Oevent_Osize__2_0) ).

fof(c_0_1705,axiom,
    ! [X60,X44] : c_List_Odistinct(c_List_Oupt(X44,X60),tc_nat),
    file('<stdin>',cls_List_Odistinct__upt_0) ).

fof(c_0_1706,axiom,
    ! [X56,X58] : c_Nat_Osize(c_List_Ochar_OChar(X58,X56),tc_List_Ochar) = c_0,
    file('<stdin>',cls_List_Ochar_Osize_0) ).

fof(c_0_1707,axiom,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(X19,X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0) ).

fof(c_0_1708,axiom,
    ! [X2,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(X2,X4) != c_1
      | X2 = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__eq__1__iff_0) ).

fof(c_0_1709,axiom,
    ! [X22,X16] :
      ( c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint) != c_IntDef_Oint(X16)
      | X16 = c_0 ),
    file('<stdin>',cls_IntDef_Onegative__eq__positive_1) ).

fof(c_0_1710,axiom,
    ! [X22,X16] :
      ( c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint) != c_IntDef_Oint(X16)
      | X22 = c_0 ),
    file('<stdin>',cls_IntDef_Onegative__eq__positive_0) ).

fof(c_0_1711,axiom,
    ! [X14,X4] :
      ( c_Main_Oempty__Union__conv__1(X14,X4) != c_emptyset
      | c_emptyset = c_Union(X14,X4) ),
    file('<stdin>',cls_Set_Oempty__Union__conv_2) ).

fof(c_0_1712,axiom,
    ! [X14,X4] :
      ( c_Main_OUnion__empty__conv__1(X14,X4) != c_emptyset
      | c_Union(X14,X4) = c_emptyset ),
    file('<stdin>',cls_Set_OUnion__empty__conv_2) ).

fof(c_0_1713,axiom,
    ! [X14,X4] :
      ( c_Main_OInter__UNIV__conv__2__1(X14,X4) != c_UNIV
      | c_UNIV = c_Inter(X14,X4) ),
    file('<stdin>',cls_Set_OInter__UNIV__conv__2_2) ).

fof(c_0_1714,axiom,
    ! [X14,X4] :
      ( c_Main_OInter__UNIV__conv__1__1(X14,X4) != c_UNIV
      | c_Inter(X14,X4) = c_UNIV ),
    file('<stdin>',cls_Set_OInter__UNIV__conv__1_2) ).

fof(c_0_1715,axiom,
    ! [X51,X4] :
      ( c_Main_Oconcat__eq__Nil__conv__1(X51,X4) != c_List_Olist_ONil
      | c_List_Oconcat(X51,X4) = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oconcat__eq__Nil__conv_2) ).

fof(c_0_1716,axiom,
    ! [X51,X4] :
      ( c_Main_ONil__eq__concat__conv__1(X51,X4) != c_List_Olist_ONil
      | c_List_Olist_ONil = c_List_Oconcat(X51,X4) ),
    file('<stdin>',cls_List_ONil__eq__concat__conv_2) ).

fof(c_0_1717,axiom,
    ! [X1] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
    file('<stdin>',cls_SetInterval_Ocard__lessThan_0) ).

fof(c_0_1718,axiom,
    ! [X24,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_0
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olength__0__conv_0) ).

fof(c_0_1719,axiom,
    c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1,
    file('<stdin>',cls_NatBin_Onat__numeral__1__eq__1_0) ).

fof(c_0_1720,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_uminus(c_1,X4) = c_Numeral_Onumber__of(c_Numeral_OMin,X4) ),
    file('<stdin>',cls_Numeral_Obin__arith__extra__simps__3_0) ).

fof(c_0_1721,axiom,
    ! [X2] :
      ( c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_Suc(X2),tc_nat) ),
    file('<stdin>',cls_Parity_Oeven__nat__Suc_1) ).

fof(c_0_1722,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(X19,X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).

fof(c_0_1723,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_0 != c_uminus(X19,X4)
      | c_0 = X19 ),
    file('<stdin>',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).

fof(c_0_1724,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(X19,X4) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oabs__eq__0_0) ).

fof(c_0_1725,axiom,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_0 != c_HOL_Oabs(X19,X4)
      | X19 = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oabs__0__eq_0) ).

fof(c_0_1726,axiom,
    ! [X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_NatArith_Oof__nat(X16,X4) != c_0
      | X16 = c_0 ),
    file('<stdin>',cls_NatArith_Oof__nat__eq__0__iff_0) ).

fof(c_0_1727,axiom,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_0 != c_NatArith_Oof__nat(X22,X4)
      | c_0 = X22 ),
    file('<stdin>',cls_NatArith_Oof__nat__0__eq__iff_0) ).

fof(c_0_1728,axiom,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oof__int(X12,X4) != c_0
      | X12 = c_0 ),
    file('<stdin>',cls_IntDef_Oof__int__eq__0__iff_0) ).

fof(c_0_1729,axiom,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 != c_IntDef_Oof__int(X49,X4)
      | c_0 = X49 ),
    file('<stdin>',cls_IntDef_Oof__int__0__eq__iff_0) ).

fof(c_0_1730,axiom,
    ! [X39,X38] : class_Nat_Opower(tc_fun(X39,X38)),
    file('<stdin>',clsarity_fun_1) ).

fof(c_0_1731,axiom,
    ! [X22] : ~ c_IntDef_Oneg(c_IntDef_Oint(X22),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onot__neg__int_0) ).

fof(c_0_1732,axiom,
    ! [X28,X33,X14] : c_Public_OpublicKey(X28,X33) != c_Public_OshrK(X14),
    file('<stdin>',cls_Public_OshrK__neq__pubK_0) ).

fof(c_0_1733,axiom,
    ! [X28,X33,X14] : c_Public_OshrK(X14) != c_Public_OpublicKey(X28,X33),
    file('<stdin>',cls_Public_OpubK__neq__shrK_0) ).

fof(c_0_1734,axiom,
    ! [X87,X88,X9] : c_Message_OHPair(X88,X87) != c_Message_Omsg_ONumber(X9),
    file('<stdin>',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).

fof(c_0_1735,axiom,
    ! [X87,X88,X9] : c_Message_OHPair(X88,X87) != c_Message_Omsg_ONonce(X9),
    file('<stdin>',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).

fof(c_0_1736,axiom,
    ! [X87,X88,X93] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OKey(X93),
    file('<stdin>',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).

fof(c_0_1737,axiom,
    ! [X110,X87,X88] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OHash(X110),
    file('<stdin>',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).

fof(c_0_1738,axiom,
    ! [X87,X88,X14] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OAgent(X14),
    file('<stdin>',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).

fof(c_0_1739,axiom,
    ! [X110,X87,X88] : c_Message_Omsg_OHash(X110) != c_Message_OHPair(X88,X87),
    file('<stdin>',cls_Message_OHPair__neqs__5_0) ).

fof(c_0_1740,axiom,
    ! [X87,X88,X93] : c_Message_Omsg_OKey(X93) != c_Message_OHPair(X88,X87),
    file('<stdin>',cls_Message_OHPair__neqs__4_0) ).

fof(c_0_1741,axiom,
    ! [X87,X88,X9] : c_Message_Omsg_ONumber(X9) != c_Message_OHPair(X88,X87),
    file('<stdin>',cls_Message_OHPair__neqs__3_0) ).

fof(c_0_1742,axiom,
    ! [X87,X88,X9] : c_Message_Omsg_ONonce(X9) != c_Message_OHPair(X88,X87),
    file('<stdin>',cls_Message_OHPair__neqs__2_0) ).

fof(c_0_1743,axiom,
    ! [X87,X88,X14] : c_Message_Omsg_OAgent(X14) != c_Message_OHPair(X88,X87),
    file('<stdin>',cls_Message_OHPair__neqs__1_0) ).

fof(c_0_1744,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_1,X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__9_0) ).

fof(c_0_1745,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_0,X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__8_0) ).

fof(c_0_1746,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | ~ c_IntDef_Oiszero(c_1,X4) ),
    file('<stdin>',cls_Numeral_Obin__rel__simps__10_0) ).

fof(c_0_1747,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_0,X4) = c_0 ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1) ).

fof(c_0_1748,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_1,X4) = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Oinverse__eq__1__iff_1) ).

fof(c_0_1749,axiom,
    ! [X22] : c_Binomial_Obinomial(c_Suc(X22),X22) = c_Suc(X22),
    file('<stdin>',cls_Binomial_Obinomial__Suc__n_0) ).

fof(c_0_1750,axiom,
    ! [X24,X4] :
      ( c_List_Oset(X24,X4) != c_emptyset
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oset__empty_0) ).

fof(c_0_1751,axiom,
    ! [X24,X4] :
      ( c_emptyset != c_List_Oset(X24,X4)
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oset__empty2_0) ).

fof(c_0_1752,axiom,
    ! [X24,X4] :
      ( c_List_Orotate1(X24,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Orotate1__is__Nil__conv_0) ).

fof(c_0_1753,axiom,
    ! [X24,X4] :
      ( c_List_Orev(X24,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Orev__is__Nil__conv_0) ).

fof(c_0_1754,axiom,
    ! [X2,X4] :
      ( c_List_Olist_ONil != c_List_Oremdups(X2,X4)
      | X2 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oremdups__eq__nil__right__iff_0) ).

fof(c_0_1755,axiom,
    ! [X2,X4] :
      ( c_List_Oremdups(X2,X4) != c_List_Olist_ONil
      | X2 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oremdups__eq__nil__iff_0) ).

fof(c_0_1756,axiom,
    ! [X24,X4] :
      ( c_List_Olist_ONil != c_List_Orev(X24,X4)
      | X24 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__is__rev__conv_0) ).

fof(c_0_1757,axiom,
    ! [X41,X4] :
      ( c_Datatype_Oo2s(X41,X4) != c_emptyset
      | X41 = c_Datatype_Ooption_ONone ),
    file('<stdin>',cls_Datatype_Oo2s__empty__eq_0) ).

fof(c_0_1758,axiom,
    ! [X33] : c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X33))) = c_emptyset,
    file('<stdin>',cls_Public_OkeysFor__parts__initState_0) ).

fof(c_0_1759,axiom,
    ! [X16] : c_HOL_Oabs(c_IntDef_Oint(X16),tc_IntDef_Oint) = c_IntDef_Oint(X16),
    file('<stdin>',cls_IntDef_Oabs__int__eq_0) ).

fof(c_0_1760,axiom,
    ! [X43,X4] : c_Datatype_Ooption_OSome(X43,X4) != c_Datatype_Ooption_ONone,
    file('<stdin>',cls_Datatype_Ooption_Odistinct__2_0) ).

fof(c_0_1761,axiom,
    ! [X43,X4] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X43,X4),
    file('<stdin>',cls_Datatype_Ooption_Odistinct__1_0) ).

fof(c_0_1762,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_HOL_Oabs(c_1,X4) = c_1 ),
    file('<stdin>',cls_Ring__and__Field_Oabs__one_0) ).

fof(c_0_1763,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_OrderedGroup_Opprt(c_0,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Opprt__0_0) ).

fof(c_0_1764,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_OrderedGroup_Onprt(c_0,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Onprt__0_0) ).

fof(c_0_1765,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_0,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).

fof(c_0_1766,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_0 = c_uminus(c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).

fof(c_0_1767,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_0,X4) = c_0 ),
    file('<stdin>',cls_OrderedGroup_Oabs__eq__0_1) ).

fof(c_0_1768,axiom,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_0 = c_HOL_Oabs(c_0,X4) ),
    file('<stdin>',cls_OrderedGroup_Oabs__0__eq_1) ).

fof(c_0_1769,axiom,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(c_Numeral_OPls,X4) = c_0 ),
    file('<stdin>',cls_Numeral_Onumeral__0__eq__0_0) ).

fof(c_0_1770,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_NatArith_Oof__nat(c_0,X4) = c_0 ),
    file('<stdin>',cls_NatArith_Oof__nat__eq__0__iff_1) ).

fof(c_0_1771,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_NatArith_Oof__nat(c_1,X4) = c_1 ),
    file('<stdin>',cls_NatArith_Oof__nat__1_0) ).

fof(c_0_1772,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_0 = c_NatArith_Oof__nat(c_0,X4) ),
    file('<stdin>',cls_NatArith_Oof__nat__0__eq__iff_1) ).

fof(c_0_1773,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oof__int(c_0,X4) = c_0 ),
    file('<stdin>',cls_IntDef_Oof__int__eq__0__iff_1) ).

fof(c_0_1774,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_1,X4) = c_1 ),
    file('<stdin>',cls_IntDef_Oof__int__1_0) ).

fof(c_0_1775,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 = c_IntDef_Oof__int(c_0,X4) ),
    file('<stdin>',cls_IntDef_Oof__int__0__eq__iff_1) ).

fof(c_0_1776,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Omsg_OKey(X91),tc_Message_Omsg) = c_0,
    file('<stdin>',cls_Message_Omsg_Osize__4_0) ).

fof(c_0_1777,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Omsg_ONonce(X91),tc_Message_Omsg) = c_0,
    file('<stdin>',cls_Message_Omsg_Osize__3_0) ).

fof(c_0_1778,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Omsg_ONumber(X91),tc_Message_Omsg) = c_0,
    file('<stdin>',cls_Message_Omsg_Osize__2_0) ).

fof(c_0_1779,axiom,
    ! [X96] : c_Nat_Osize(c_Message_Omsg_OAgent(X96),tc_Message_Omsg) = c_0,
    file('<stdin>',cls_Message_Omsg_Osize__1_0) ).

fof(c_0_1780,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Oagent_OFriend(X91),tc_Message_Oagent) = c_0,
    file('<stdin>',cls_Message_Oagent_Osize__2_0) ).

fof(c_0_1781,axiom,
    ! [X4] : c_uminus(c_emptyset,tc_set(X4)) = c_UNIV,
    file('<stdin>',cls_Set_OCompl__empty__eq_0) ).

fof(c_0_1782,axiom,
    ! [X4] : c_uminus(c_UNIV,tc_set(X4)) = c_emptyset,
    file('<stdin>',cls_Set_OCompl__UNIV__eq_0) ).

fof(c_0_1783,axiom,
    ! [X4] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X4)) = c_0,
    file('<stdin>',cls_List_Olength__0__conv_1) ).

fof(c_0_1784,axiom,
    ! [X4] : c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X4)) = c_0,
    file('<stdin>',cls_Datatype_Ooption_Osize__1_0) ).

fof(c_0_1785,axiom,
    ! [X17] : c_Binomial_Obinomial(c_0,c_Suc(X17)) = c_0,
    file('<stdin>',cls_Binomial_Obinomial__0__Suc_0) ).

fof(c_0_1786,axiom,
    c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
    file('<stdin>',cls_IntDef_Onegative__eq__positive_2) ).

fof(c_0_1787,axiom,
    ! [X1] : c_Binomial_Obinomial(X1,c_Suc(c_0)) = X1,
    file('<stdin>',cls_Binomial_Obinomial__1_0) ).

fof(c_0_1788,axiom,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    file('<stdin>',cls_Parity_Oodd__one_0) ).

fof(c_0_1789,axiom,
    ! [X38] :
      ( class_Finite__Set_Ofinite(tc_set(X38))
      | ~ class_Finite__Set_Ofinite(X38) ),
    file('<stdin>',clsarity_set_3) ).

fof(c_0_1790,axiom,
    ! [X38] :
      ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X38))
      | ~ class_Finite__Set_Ofinite(X38) ),
    file('<stdin>',clsarity_Datatype__Ooption_0) ).

fof(c_0_1791,axiom,
    ! [X14] : c_Event_Oknows(X14,c_List_Olist_ONil) = c_Event_OinitState(X14),
    file('<stdin>',cls_Event_Oknows_Oknows__Nil_0) ).

fof(c_0_1792,axiom,
    ! [X12] : c_Numeral_Obin__mult(c_Numeral_OMin,X12) = c_Numeral_Obin__minus(X12),
    file('<stdin>',cls_Numeral_Obin__mult__Min_0) ).

fof(c_0_1793,axiom,
    ! [X12] : c_Numeral_Obin__add(X12,c_Numeral_OMin) = c_Numeral_Obin__pred(X12),
    file('<stdin>',cls_Numeral_Obin__add__Min__right_0) ).

fof(c_0_1794,axiom,
    ! [X12] : c_Numeral_Obin__add(c_Numeral_OMin,X12) = c_Numeral_Obin__pred(X12),
    file('<stdin>',cls_Numeral_Obin__add__Min_0) ).

fof(c_0_1795,axiom,
    ! [X1,X2] :
      ( c_Public_OshrK(X2) != c_Public_OshrK(X1)
      | X2 = X1 ),
    file('<stdin>',cls_Public_OshrK__injective_0) ).

fof(c_0_1796,axiom,
    ! [X97,X98] :
      ( c_Message_Omsg_OHash(X98) != c_Message_Omsg_OHash(X97)
      | X98 = X97 ),
    file('<stdin>',cls_Message_Omsg_Oinject__5_0) ).

fof(c_0_1797,axiom,
    ! [X90,X91] :
      ( c_Message_Omsg_OKey(X91) != c_Message_Omsg_OKey(X90)
      | X91 = X90 ),
    file('<stdin>',cls_Message_Omsg_Oinject__4_0) ).

fof(c_0_1798,axiom,
    ! [X90,X91] :
      ( c_Message_Omsg_ONonce(X91) != c_Message_Omsg_ONonce(X90)
      | X91 = X90 ),
    file('<stdin>',cls_Message_Omsg_Oinject__3_0) ).

fof(c_0_1799,axiom,
    ! [X90,X91] :
      ( c_Message_Omsg_ONumber(X91) != c_Message_Omsg_ONumber(X90)
      | X91 = X90 ),
    file('<stdin>',cls_Message_Omsg_Oinject__2_0) ).

fof(c_0_1800,axiom,
    ! [X95,X96] :
      ( c_Message_Omsg_OAgent(X96) != c_Message_Omsg_OAgent(X95)
      | X96 = X95 ),
    file('<stdin>',cls_Message_Omsg_Oinject__1_0) ).

fof(c_0_1801,axiom,
    ! [X92,X93] :
      ( c_Message_OinvKey(X93) != c_Message_OinvKey(X92)
      | X93 = X92 ),
    file('<stdin>',cls_Message_OinvKey__eq_0) ).

fof(c_0_1802,axiom,
    ! [X90,X91] :
      ( c_Message_Oagent_OFriend(X91) != c_Message_Oagent_OFriend(X90)
      | X91 = X90 ),
    file('<stdin>',cls_Message_Oagent_Oinject_0) ).

fof(c_0_1803,axiom,
    ! [X22,X16] :
      ( c_Suc(X16) != c_Suc(X22)
      | X16 = X22 ),
    file('<stdin>',cls_Nat_OSuc__Suc__eq_0) ).

fof(c_0_1804,axiom,
    ! [X22,X16] :
      ( c_IntDef_Oint(X16) != c_IntDef_Oint(X22)
      | X16 = X22 ),
    file('<stdin>',cls_IntDef_Oint__int__eq_0) ).

fof(c_0_1805,axiom,
    ! [X1,X4] : c_Fun_Oid(X1,X4) = X1,
    file('<stdin>',cls_Fun_Oid__apply_0) ).

fof(c_0_1806,axiom,
    ! [X14] : c_Message_OinvKey(c_Public_OshrK(X14)) = c_Public_OshrK(X14),
    file('<stdin>',cls_Public_OinvKey__shrK_0) ).

fof(c_0_1807,axiom,
    ! [X89] : c_Message_Oparts(c_Message_Oparts(X89)) = c_Message_Oparts(X89),
    file('<stdin>',cls_Message_Oparts__idem_0) ).

fof(c_0_1808,axiom,
    ! [X89] : c_Message_Oparts(c_Message_Oanalz(X89)) = c_Message_Oparts(X89),
    file('<stdin>',cls_Message_Oparts__analz_0) ).

fof(c_0_1809,axiom,
    ! [X89] : c_Message_Oanalz(c_Message_Oparts(X89)) = c_Message_Oparts(X89),
    file('<stdin>',cls_Message_Oanalz__parts_0) ).

fof(c_0_1810,axiom,
    ! [X89] : c_Message_Oanalz(c_Message_Oanalz(X89)) = c_Message_Oanalz(X89),
    file('<stdin>',cls_Message_Oanalz__idem_0) ).

fof(c_0_1811,axiom,
    ! [X22] : c_Binomial_Obinomial(X22,X22) = c_1,
    file('<stdin>',cls_Binomial_Obinomial__n__n_0) ).

fof(c_0_1812,axiom,
    c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    file('<stdin>',cls_Numeral_Obin__succ__Pls_0) ).

fof(c_0_1813,axiom,
    c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
    file('<stdin>',cls_Numeral_Obin__pred__Min_0) ).

fof(c_0_1814,axiom,
    c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    file('<stdin>',cls_Numeral_Obin__minus__Min_0) ).

fof(c_0_1815,axiom,
    ! [X1] : c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1,
    file('<stdin>',cls_Numeral_Obin__add__Pls__right_0) ).

fof(c_0_1816,axiom,
    ! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1,
    file('<stdin>',cls_Numeral_Obin__add__Pls_0) ).

fof(c_0_1817,axiom,
    ! [X1] : c_NatArith_Oof__nat(X1,tc_nat) = X1,
    file('<stdin>',cls_Finite__Set_Oof__nat__id_0) ).

fof(c_0_1818,axiom,
    ! [X4] : c_Transitive__Closure_Otrancl(c_emptyset,X4) = c_emptyset,
    file('<stdin>',cls_Transitive__Closure_Otrancl__empty_0) ).

fof(c_0_1819,axiom,
    ! [X4] : c_Transitive__Closure_Ortrancl(c_emptyset,X4) = c_Relation_OId,
    file('<stdin>',cls_Transitive__Closure_Ortrancl__empty_0) ).

fof(c_0_1820,axiom,
    ! [X4] : c_Union(c_emptyset,X4) = c_emptyset,
    file('<stdin>',cls_Set_OUnion__empty_0) ).

fof(c_0_1821,axiom,
    ! [X4] : c_Union(c_UNIV,X4) = c_UNIV,
    file('<stdin>',cls_Set_OUnion__UNIV_0) ).

fof(c_0_1822,axiom,
    ! [X4] : c_Pow(c_UNIV,X4) = c_UNIV,
    file('<stdin>',cls_Set_OPow__UNIV_0) ).

fof(c_0_1823,axiom,
    ! [X4] : c_Inter(c_emptyset,X4) = c_UNIV,
    file('<stdin>',cls_Set_OInter__empty_0) ).

fof(c_0_1824,axiom,
    ! [X4] : c_Inter(c_UNIV,X4) = c_emptyset,
    file('<stdin>',cls_Set_OInter__UNIV_0) ).

fof(c_0_1825,axiom,
    ! [X4] : c_Relation_Odiag(c_emptyset,X4) = c_emptyset,
    file('<stdin>',cls_Relation_Odiag__empty_0) ).

fof(c_0_1826,axiom,
    ! [X12] : c_Numeral_Obin__mult(c_Numeral_OPls,X12) = c_Numeral_OPls,
    file('<stdin>',cls_Numeral_Obin__mult__Pls_0) ).

fof(c_0_1827,axiom,
    ! [X44] : c_List_Oupt(X44,c_0) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oupt__eq__Nil__conv_1) ).

fof(c_0_1828,axiom,
    ! [X42] : c_List_Otl(c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Otl_Osimps__1_0) ).

fof(c_0_1829,axiom,
    ! [X4] : c_List_Oset(c_List_Olist_ONil,X4) = c_emptyset,
    file('<stdin>',cls_List_Oset__empty_1) ).

fof(c_0_1830,axiom,
    ! [X4] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X4),
    file('<stdin>',cls_List_Oset__empty2_1) ).

fof(c_0_1831,axiom,
    ! [X4] : c_List_Orotate1(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Orotate1__is__Nil__conv_1) ).

fof(c_0_1832,axiom,
    ! [X4] : c_List_Orev(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Orev__is__Nil__conv_1) ).

fof(c_0_1833,axiom,
    ! [X4] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X4),
    file('<stdin>',cls_List_Oremdups__eq__nil__right__iff_1) ).

fof(c_0_1834,axiom,
    ! [X4] : c_List_Oremdups(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oremdups__eq__nil__iff_1) ).

fof(c_0_1835,axiom,
    ! [X42] : c_List_Onull(c_List_Olist_ONil,X42),
    file('<stdin>',cls_List_Onull_Osimps__1_0) ).

fof(c_0_1836,axiom,
    ! [X4] : c_List_Olists(c_UNIV,X4) = c_UNIV,
    file('<stdin>',cls_List_Olists__UNIV_0) ).

fof(c_0_1837,axiom,
    ! [X42] : c_List_Odistinct(c_List_Olist_ONil,X42),
    file('<stdin>',cls_List_Odistinct_Osimps__1_0) ).

fof(c_0_1838,axiom,
    ! [X42] : c_List_Oconcat(c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oconcat_Osimps__1_0) ).

fof(c_0_1839,axiom,
    ! [X42] : c_List_Obutlast(c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Obutlast_Osimps__1_0) ).

fof(c_0_1840,axiom,
    ! [X4] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X4),
    file('<stdin>',cls_List_ONil__is__rev__conv_1) ).

fof(c_0_1841,axiom,
    ! [X4] : c_Finite__Set_Ocard(c_emptyset,X4) = c_0,
    file('<stdin>',cls_Finite__Set_Ocard__empty_0) ).

fof(c_0_1842,axiom,
    ! [X4] : c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X4) = c_emptyset,
    file('<stdin>',cls_Datatype_Oo2s__empty__eq_1) ).

fof(c_0_1843,axiom,
    ! [X22] : c_Binomial_Obinomial(X22,c_0) = c_1,
    file('<stdin>',cls_Binomial_Obinomial__n__0_0) ).

fof(c_0_1844,axiom,
    ! [X4] : c_Wellfounded__Recursion_Owf(c_emptyset,X4),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__empty_0) ).

fof(c_0_1845,axiom,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_5) ).

fof(c_0_1846,axiom,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_4) ).

fof(c_0_1847,axiom,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_3) ).

fof(c_0_1848,axiom,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_2) ).

fof(c_0_1849,axiom,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_1) ).

fof(c_0_1850,axiom,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_0) ).

fof(c_0_1851,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

fof(c_0_1852,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

fof(c_0_1853,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

fof(c_0_1854,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

fof(c_0_1855,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

fof(c_0_1856,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

fof(c_0_1857,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

fof(c_0_1858,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

fof(c_0_1859,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

fof(c_0_1860,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

fof(c_0_1861,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

fof(c_0_1862,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

fof(c_0_1863,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

fof(c_0_1864,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

fof(c_0_1865,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

fof(c_0_1866,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

fof(c_0_1867,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_9) ).

fof(c_0_1868,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_8) ).

fof(c_0_1869,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_7) ).

fof(c_0_1870,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_6) ).

fof(c_0_1871,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_5) ).

fof(c_0_1872,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_4) ).

fof(c_0_1873,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_3) ).

fof(c_0_1874,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_2) ).

fof(c_0_1875,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_11) ).

fof(c_0_1876,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_10) ).

fof(c_0_1877,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_1) ).

fof(c_0_1878,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_0) ).

fof(c_0_1879,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

fof(c_0_1880,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

fof(c_0_1881,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

fof(c_0_1882,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

fof(c_0_1883,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

fof(c_0_1884,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

fof(c_0_1885,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

fof(c_0_1886,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

fof(c_0_1887,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

fof(c_0_1888,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

fof(c_0_1889,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

fof(c_0_1890,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_7) ).

fof(c_0_1891,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_6) ).

fof(c_0_1892,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_5) ).

fof(c_0_1893,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_4) ).

fof(c_0_1894,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_3) ).

fof(c_0_1895,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_2) ).

fof(c_0_1896,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_1) ).

fof(c_0_1897,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_0) ).

fof(c_0_1898,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_4) ).

fof(c_0_1899,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_3) ).

fof(c_0_1900,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_2) ).

fof(c_0_1901,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_1) ).

fof(c_0_1902,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_0) ).

fof(c_0_1903,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_9) ).

fof(c_0_1904,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_8) ).

fof(c_0_1905,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_7) ).

fof(c_0_1906,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_6) ).

fof(c_0_1907,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_5) ).

fof(c_0_1908,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_4) ).

fof(c_0_1909,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_3) ).

fof(c_0_1910,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_2) ).

fof(c_0_1911,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_19) ).

fof(c_0_1912,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_18) ).

fof(c_0_1913,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_17) ).

fof(c_0_1914,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_16) ).

fof(c_0_1915,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_15) ).

fof(c_0_1916,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_14) ).

fof(c_0_1917,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_13) ).

fof(c_0_1918,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_12) ).

fof(c_0_1919,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_11) ).

fof(c_0_1920,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_10) ).

fof(c_0_1921,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_1) ).

fof(c_0_1922,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_0) ).

fof(c_0_1923,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_9) ).

fof(c_0_1924,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_8) ).

fof(c_0_1925,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_7) ).

fof(c_0_1926,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_6) ).

fof(c_0_1927,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_5) ).

fof(c_0_1928,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_4) ).

fof(c_0_1929,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_3) ).

fof(c_0_1930,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_2) ).

fof(c_0_1931,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_13) ).

fof(c_0_1932,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_12) ).

fof(c_0_1933,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_11) ).

fof(c_0_1934,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_10) ).

fof(c_0_1935,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_1) ).

fof(c_0_1936,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_0) ).

fof(c_0_1937,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_9) ).

fof(c_0_1938,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_8) ).

fof(c_0_1939,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_7) ).

fof(c_0_1940,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_6) ).

fof(c_0_1941,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_5) ).

fof(c_0_1942,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_4) ).

fof(c_0_1943,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_3) ).

fof(c_0_1944,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_2) ).

fof(c_0_1945,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_11) ).

fof(c_0_1946,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_10) ).

fof(c_0_1947,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_1) ).

fof(c_0_1948,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_0) ).

fof(c_0_1949,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_9) ).

fof(c_0_1950,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_8) ).

fof(c_0_1951,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_7) ).

fof(c_0_1952,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_6) ).

fof(c_0_1953,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_5) ).

fof(c_0_1954,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_4) ).

fof(c_0_1955,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_3) ).

fof(c_0_1956,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_22) ).

fof(c_0_1957,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_21) ).

fof(c_0_1958,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_20) ).

fof(c_0_1959,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_2) ).

fof(c_0_1960,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_19) ).

fof(c_0_1961,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_18) ).

fof(c_0_1962,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_17) ).

fof(c_0_1963,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_16) ).

fof(c_0_1964,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_15) ).

fof(c_0_1965,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_14) ).

fof(c_0_1966,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_13) ).

fof(c_0_1967,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_12) ).

fof(c_0_1968,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_11) ).

fof(c_0_1969,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_10) ).

fof(c_0_1970,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_1) ).

fof(c_0_1971,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_0) ).

fof(c_0_1972,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

fof(c_0_1973,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

fof(c_0_1974,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

fof(c_0_1975,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

fof(c_0_1976,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

fof(c_0_1977,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

fof(c_0_1978,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

fof(c_0_1979,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

fof(c_0_1980,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

fof(c_0_1981,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

fof(c_0_1982,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

fof(c_0_1983,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

fof(c_0_1984,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

fof(c_0_1985,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

fof(c_0_1986,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

fof(c_0_1987,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

fof(c_0_1988,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_9) ).

fof(c_0_1989,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_8) ).

fof(c_0_1990,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_7) ).

fof(c_0_1991,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_6) ).

fof(c_0_1992,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_5) ).

fof(c_0_1993,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_4) ).

fof(c_0_1994,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_3) ).

fof(c_0_1995,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_24) ).

fof(c_0_1996,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_23) ).

fof(c_0_1997,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_22) ).

fof(c_0_1998,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_21) ).

fof(c_0_1999,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_20) ).

fof(c_0_2000,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_2) ).

fof(c_0_2001,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_19) ).

fof(c_0_2002,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_18) ).

fof(c_0_2003,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_17) ).

fof(c_0_2004,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_16) ).

fof(c_0_2005,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_15) ).

fof(c_0_2006,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_14) ).

fof(c_0_2007,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_13) ).

fof(c_0_2008,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_12) ).

fof(c_0_2009,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_11) ).

fof(c_0_2010,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_10) ).

fof(c_0_2011,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_1) ).

fof(c_0_2012,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_0) ).

fof(c_0_2013,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

fof(c_0_2014,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

fof(c_0_2015,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

fof(c_0_2016,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

fof(c_0_2017,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

fof(c_0_2018,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

fof(c_0_2019,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

fof(c_0_2020,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

fof(c_0_2021,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

fof(c_0_2022,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

fof(c_0_2023,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

fof(c_0_2024,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

fof(c_0_2025,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

fof(c_0_2026,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

fof(c_0_2027,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

fof(c_0_2028,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

fof(c_0_2029,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

fof(c_0_2030,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

fof(c_0_2031,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

fof(c_0_2032,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

fof(c_0_2033,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

fof(c_0_2034,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

fof(c_0_2035,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

fof(c_0_2036,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

fof(c_0_2037,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

fof(c_0_2038,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

fof(c_0_2039,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

fof(c_0_2040,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

fof(c_0_2041,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

fof(c_0_2042,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

fof(c_0_2043,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

fof(c_0_2044,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

fof(c_0_2045,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

fof(c_0_2046,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

fof(c_0_2047,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

fof(c_0_2048,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

fof(c_0_2049,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

fof(c_0_2050,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

fof(c_0_2051,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

fof(c_0_2052,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

fof(c_0_2053,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

fof(c_0_2054,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

fof(c_0_2055,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

fof(c_0_2056,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

fof(c_0_2057,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

fof(c_0_2058,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

fof(c_0_2059,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

fof(c_0_2060,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

fof(c_0_2061,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

fof(c_0_2062,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

fof(c_0_2063,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

fof(c_0_2064,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

fof(c_0_2065,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

fof(c_0_2066,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

fof(c_0_2067,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

fof(c_0_2068,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

fof(c_0_2069,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

fof(c_0_2070,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

fof(c_0_2071,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

fof(c_0_2072,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

fof(c_0_2073,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

fof(c_0_2074,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_9) ).

fof(c_0_2075,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_8) ).

fof(c_0_2076,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_7) ).

fof(c_0_2077,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_6) ).

fof(c_0_2078,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_5) ).

fof(c_0_2079,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_4) ).

fof(c_0_2080,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_39) ).

fof(c_0_2081,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_38) ).

fof(c_0_2082,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_37) ).

fof(c_0_2083,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_36) ).

fof(c_0_2084,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_35) ).

fof(c_0_2085,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_34) ).

fof(c_0_2086,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_33) ).

fof(c_0_2087,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_32) ).

fof(c_0_2088,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_31) ).

fof(c_0_2089,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_30) ).

fof(c_0_2090,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_3) ).

fof(c_0_2091,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_29) ).

fof(c_0_2092,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_28) ).

fof(c_0_2093,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_27) ).

fof(c_0_2094,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_26) ).

fof(c_0_2095,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_25) ).

fof(c_0_2096,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_24) ).

fof(c_0_2097,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_23) ).

fof(c_0_2098,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_22) ).

fof(c_0_2099,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_21) ).

fof(c_0_2100,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_20) ).

fof(c_0_2101,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_2) ).

fof(c_0_2102,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_19) ).

fof(c_0_2103,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_18) ).

fof(c_0_2104,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_17) ).

fof(c_0_2105,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_16) ).

fof(c_0_2106,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_15) ).

fof(c_0_2107,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_14) ).

fof(c_0_2108,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_13) ).

fof(c_0_2109,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_12) ).

fof(c_0_2110,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_11) ).

fof(c_0_2111,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_10) ).

fof(c_0_2112,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_1) ).

fof(c_0_2113,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_0) ).

fof(c_0_2114,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).

fof(c_0_2115,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).

fof(c_0_2116,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).

fof(c_0_2117,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

fof(c_0_2118,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

fof(c_0_2119,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

fof(c_0_2120,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

fof(c_0_2121,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

fof(c_0_2122,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

fof(c_0_2123,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

fof(c_0_2124,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

fof(c_0_2125,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Olordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

fof(c_0_2126,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

fof(c_0_2127,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

fof(c_0_2128,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

fof(c_0_2129,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oaxclass__abs__if(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

fof(c_0_2130,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

fof(c_0_2131,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

fof(c_0_2132,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

fof(c_0_2133,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

fof(c_0_2134,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

fof(c_0_2135,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

fof(c_0_2136,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

fof(c_0_2137,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

fof(c_0_2138,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

fof(c_0_2139,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

fof(c_0_2140,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

fof(c_0_2141,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

fof(c_0_2142,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

fof(c_0_2143,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

fof(c_0_2144,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).

fof(c_0_2145,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).

fof(c_0_2146,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).

fof(c_0_2147,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).

fof(c_0_2148,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

fof(c_0_2149,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

fof(c_0_2150,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

fof(c_0_2151,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_9) ).

fof(c_0_2152,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_8) ).

fof(c_0_2153,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_7) ).

fof(c_0_2154,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_6) ).

fof(c_0_2155,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oidom(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_57) ).

fof(c_0_2156,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_56) ).

fof(c_0_2157,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__semidom(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_55) ).

fof(c_0_2158,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_54) ).

fof(c_0_2159,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_53) ).

fof(c_0_2160,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_52) ).

fof(c_0_2161,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_51) ).

fof(c_0_2162,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(c_0_2163,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_5) ).

fof(c_0_2164,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_49) ).

fof(c_0_2165,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Olordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_48) ).

fof(c_0_2166,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__ring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_47) ).

fof(c_0_2167,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oaxclass__abs__if(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_46) ).

fof(c_0_2168,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_45) ).

fof(c_0_2169,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_44) ).

fof(c_0_2170,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_43) ).

fof(c_0_2171,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_42) ).

fof(c_0_2172,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_41) ).

fof(c_0_2173,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_40) ).

fof(c_0_2174,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_4) ).

fof(c_0_2175,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_39) ).

fof(c_0_2176,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_38) ).

fof(c_0_2177,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_37) ).

fof(c_0_2178,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_36) ).

fof(c_0_2179,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_35) ).

fof(c_0_2180,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_34) ).

fof(c_0_2181,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_33) ).

fof(c_0_2182,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_32) ).

fof(c_0_2183,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_31) ).

fof(c_0_2184,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_30) ).

fof(c_0_2185,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_3) ).

fof(c_0_2186,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_29) ).

fof(c_0_2187,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_28) ).

fof(c_0_2188,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_27) ).

fof(c_0_2189,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_26) ).

fof(c_0_2190,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_25) ).

fof(c_0_2191,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_24) ).

fof(c_0_2192,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_23) ).

fof(c_0_2193,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_22) ).

fof(c_0_2194,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_21) ).

fof(c_0_2195,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_20) ).

fof(c_0_2196,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_2) ).

fof(c_0_2197,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_19) ).

fof(c_0_2198,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_18) ).

fof(c_0_2199,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_17) ).

fof(c_0_2200,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_16) ).

fof(c_0_2201,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_15) ).

fof(c_0_2202,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_14) ).

fof(c_0_2203,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_13) ).

fof(c_0_2204,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_12) ).

fof(c_0_2205,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_11) ).

fof(c_0_2206,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_10) ).

fof(c_0_2207,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_1) ).

fof(c_0_2208,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_0) ).

fof(c_0_2209,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_9) ).

fof(c_0_2210,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_8) ).

fof(c_0_2211,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_7) ).

fof(c_0_2212,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__semidom(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_60) ).

fof(c_0_2213,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_6) ).

fof(c_0_2214,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_59) ).

fof(c_0_2215,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_58) ).

fof(c_0_2216,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_57) ).

fof(c_0_2217,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_56) ).

fof(c_0_2218,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_55) ).

fof(c_0_2219,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_54) ).

fof(c_0_2220,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_53) ).

fof(c_0_2221,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_52) ).

fof(c_0_2222,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_51) ).

fof(c_0_2223,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_50) ).

fof(c_0_2224,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_5) ).

fof(c_0_2225,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_49) ).

fof(c_0_2226,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_48) ).

fof(c_0_2227,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_47) ).

fof(c_0_2228,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_46) ).

fof(c_0_2229,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_45) ).

fof(c_0_2230,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_44) ).

fof(c_0_2231,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Olordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_43) ).

fof(c_0_2232,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oaxclass__abs__if(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_42) ).

fof(c_0_2233,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_41) ).

fof(c_0_2234,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_40) ).

fof(c_0_2235,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_4) ).

fof(c_0_2236,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_39) ).

fof(c_0_2237,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__ring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_38) ).

fof(c_0_2238,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_37) ).

fof(c_0_2239,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_36) ).

fof(c_0_2240,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_35) ).

fof(c_0_2241,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__idom(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_34) ).

fof(c_0_2242,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_33) ).

fof(c_0_2243,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_32) ).

fof(c_0_2244,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_31) ).

fof(c_0_2245,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_30) ).

fof(c_0_2246,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_3) ).

fof(c_0_2247,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_29) ).

fof(c_0_2248,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_28) ).

fof(c_0_2249,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_27) ).

fof(c_0_2250,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_26) ).

fof(c_0_2251,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_25) ).

fof(c_0_2252,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_24) ).

fof(c_0_2253,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_23) ).

fof(c_0_2254,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_22) ).

fof(c_0_2255,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_21) ).

fof(c_0_2256,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_20) ).

fof(c_0_2257,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oidom(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_2) ).

fof(c_0_2258,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_19) ).

fof(c_0_2259,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_18) ).

fof(c_0_2260,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_17) ).

fof(c_0_2261,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_16) ).

fof(c_0_2262,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_15) ).

fof(c_0_2263,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_14) ).

fof(c_0_2264,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_13) ).

fof(c_0_2265,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_12) ).

fof(c_0_2266,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_11) ).

fof(c_0_2267,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_10) ).

fof(c_0_2268,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Oinverse(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_1) ).

fof(c_0_2269,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ofield(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_0) ).

fof(c_0_2270,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

fof(c_0_2271,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

fof(c_0_2272,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

fof(c_0_2273,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

fof(c_0_2274,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

fof(c_0_2275,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

fof(c_0_2276,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

fof(c_0_2277,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

fof(c_0_2278,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

fof(c_0_2279,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

fof(c_0_2280,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

fof(c_0_2281,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

fof(c_0_2282,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

fof(c_0_2283,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

fof(c_0_2284,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

fof(c_0_2285,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

fof(c_0_2286,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

fof(c_0_2287,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

fof(c_0_2288,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

fof(c_0_2289,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

fof(c_0_2290,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

fof(c_0_2291,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

fof(c_0_2292,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

fof(c_0_2293,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

fof(c_0_2294,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

fof(c_0_2295,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

fof(c_0_2296,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

fof(c_0_2297,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

fof(c_0_2298,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

fof(c_0_2299,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

fof(c_0_2300,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_9) ).

fof(c_0_2301,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_8) ).

fof(c_0_2302,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_7) ).

fof(c_0_2303,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_6) ).

fof(c_0_2304,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_5) ).

fof(c_0_2305,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_4) ).

fof(c_0_2306,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_30) ).

fof(c_0_2307,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_3) ).

fof(c_0_2308,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_29) ).

fof(c_0_2309,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_28) ).

fof(c_0_2310,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_27) ).

fof(c_0_2311,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_26) ).

fof(c_0_2312,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_25) ).

fof(c_0_2313,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_24) ).

fof(c_0_2314,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_23) ).

fof(c_0_2315,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_22) ).

fof(c_0_2316,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_21) ).

fof(c_0_2317,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_20) ).

fof(c_0_2318,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_2) ).

fof(c_0_2319,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_19) ).

fof(c_0_2320,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_18) ).

fof(c_0_2321,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_17) ).

fof(c_0_2322,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_16) ).

fof(c_0_2323,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_15) ).

fof(c_0_2324,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_14) ).

fof(c_0_2325,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_13) ).

fof(c_0_2326,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_12) ).

fof(c_0_2327,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_11) ).

fof(c_0_2328,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_10) ).

fof(c_0_2329,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_1) ).

fof(c_0_2330,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_0) ).

fof(c_0_2331,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_9) ).

fof(c_0_2332,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_8) ).

fof(c_0_2333,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_7) ).

fof(c_0_2334,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_6) ).

fof(c_0_2335,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_5) ).

fof(c_0_2336,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_4) ).

fof(c_0_2337,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_30) ).

fof(c_0_2338,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_3) ).

fof(c_0_2339,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_29) ).

fof(c_0_2340,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_28) ).

fof(c_0_2341,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_27) ).

fof(c_0_2342,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_26) ).

fof(c_0_2343,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_25) ).

fof(c_0_2344,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_24) ).

fof(c_0_2345,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_23) ).

fof(c_0_2346,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_22) ).

fof(c_0_2347,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_21) ).

fof(c_0_2348,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_20) ).

fof(c_0_2349,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_2) ).

fof(c_0_2350,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_19) ).

fof(c_0_2351,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_18) ).

fof(c_0_2352,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_17) ).

fof(c_0_2353,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_16) ).

fof(c_0_2354,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_15) ).

fof(c_0_2355,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_14) ).

fof(c_0_2356,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_13) ).

fof(c_0_2357,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_12) ).

fof(c_0_2358,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_11) ).

fof(c_0_2359,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_10) ).

fof(c_0_2360,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_1) ).

fof(c_0_2361,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_0) ).

fof(c_0_2362,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_9) ).

fof(c_0_2363,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_8) ).

fof(c_0_2364,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_7) ).

fof(c_0_2365,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_6) ).

fof(c_0_2366,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_5) ).

fof(c_0_2367,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_4) ).

fof(c_0_2368,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_32) ).

fof(c_0_2369,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oidom(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_31) ).

fof(c_0_2370,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Oinverse(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_30) ).

fof(c_0_2371,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_3) ).

fof(c_0_2372,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_29) ).

fof(c_0_2373,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_28) ).

fof(c_0_2374,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_27) ).

fof(c_0_2375,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_26) ).

fof(c_0_2376,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_25) ).

fof(c_0_2377,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_24) ).

fof(c_0_2378,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_23) ).

fof(c_0_2379,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_22) ).

fof(c_0_2380,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_21) ).

fof(c_0_2381,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_20) ).

fof(c_0_2382,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_2) ).

fof(c_0_2383,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_19) ).

fof(c_0_2384,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_18) ).

fof(c_0_2385,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_17) ).

fof(c_0_2386,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_16) ).

fof(c_0_2387,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_15) ).

fof(c_0_2388,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_14) ).

fof(c_0_2389,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_13) ).

fof(c_0_2390,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_12) ).

fof(c_0_2391,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_11) ).

fof(c_0_2392,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_10) ).

fof(c_0_2393,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_1) ).

fof(c_0_2394,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_0) ).

fof(c_0_2395,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X40)
      | class_HOL_Oinverse(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Odivision__by__zero_1) ).

fof(c_0_2396,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Odivision__by__zero_0) ).

fof(c_0_2397,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

fof(c_0_2398,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

fof(c_0_2399,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

fof(c_0_2400,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

fof(c_0_2401,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

fof(c_0_2402,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

fof(c_0_2403,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

fof(c_0_2404,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

fof(c_0_2405,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

fof(c_0_2406,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

fof(c_0_2407,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

fof(c_0_2408,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

fof(c_0_2409,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

fof(c_0_2410,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

fof(c_0_2411,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

fof(c_0_2412,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

fof(c_0_2413,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

fof(c_0_2414,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

fof(c_0_2415,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

fof(c_0_2416,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

fof(c_0_2417,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

fof(c_0_2418,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

fof(c_0_2419,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

fof(c_0_2420,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

fof(c_0_2421,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

fof(c_0_2422,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

fof(c_0_2423,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

fof(c_0_2424,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

fof(c_0_2425,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

fof(c_0_2426,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

fof(c_0_2427,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

fof(c_0_2428,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

fof(c_0_2429,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

fof(c_0_2430,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

fof(c_0_2431,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

fof(c_0_2432,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

fof(c_0_2433,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

fof(c_0_2434,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

fof(c_0_2435,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

fof(c_0_2436,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

fof(c_0_2437,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

fof(c_0_2438,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

fof(c_0_2439,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

fof(c_0_2440,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

fof(c_0_2441,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

fof(c_0_2442,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

fof(c_0_2443,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

fof(c_0_2444,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

fof(c_0_2445,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

fof(c_0_2446,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

fof(c_0_2447,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

fof(c_0_2448,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

fof(c_0_2449,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

fof(c_0_2450,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

fof(c_0_2451,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

fof(c_0_2452,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

fof(c_0_2453,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

fof(c_0_2454,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

fof(c_0_2455,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

fof(c_0_2456,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

fof(c_0_2457,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

fof(c_0_2458,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

fof(c_0_2459,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

fof(c_0_2460,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

fof(c_0_2461,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

fof(c_0_2462,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

fof(c_0_2463,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

fof(c_0_2464,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

fof(c_0_2465,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

fof(c_0_2466,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

fof(c_0_2467,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

fof(c_0_2468,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

fof(c_0_2469,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

fof(c_0_2470,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

fof(c_0_2471,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

fof(c_0_2472,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).

fof(c_0_2473,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

fof(c_0_2474,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

fof(c_0_2475,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

fof(c_0_2476,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).

fof(c_0_2477,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

fof(c_0_2478,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

fof(c_0_2479,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

fof(c_0_2480,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

fof(c_0_2481,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

fof(c_0_2482,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

fof(c_0_2483,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

fof(c_0_2484,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

fof(c_0_2485,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

fof(c_0_2486,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

fof(c_0_2487,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).

fof(c_0_2488,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).

fof(c_0_2489,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

fof(c_0_2490,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).

fof(c_0_2491,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).

fof(c_0_2492,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).

fof(c_0_2493,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

fof(c_0_2494,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).

fof(c_0_2495,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).

fof(c_0_2496,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

fof(c_0_2497,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

fof(c_0_2498,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

fof(c_0_2499,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_9) ).

fof(c_0_2500,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_8) ).

fof(c_0_2501,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_7) ).

fof(c_0_2502,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_6) ).

fof(c_0_2503,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_5) ).

fof(c_0_2504,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_4) ).

fof(c_0_2505,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_3) ).

fof(c_0_2506,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_2) ).

fof(c_0_2507,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_18) ).

fof(c_0_2508,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_17) ).

fof(c_0_2509,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_16) ).

fof(c_0_2510,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_15) ).

fof(c_0_2511,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_14) ).

fof(c_0_2512,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_13) ).

fof(c_0_2513,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_12) ).

fof(c_0_2514,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_11) ).

fof(c_0_2515,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_10) ).

fof(c_0_2516,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_1) ).

fof(c_0_2517,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_0) ).

fof(c_0_2518,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).

fof(c_0_2519,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).

fof(c_0_2520,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).

fof(c_0_2521,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

fof(c_0_2522,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

fof(c_0_2523,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

fof(c_0_2524,axiom,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

fof(c_0_2525,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_9) ).

fof(c_0_2526,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_8) ).

fof(c_0_2527,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_7) ).

fof(c_0_2528,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_6) ).

fof(c_0_2529,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_5) ).

fof(c_0_2530,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_4) ).

fof(c_0_2531,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_3) ).

fof(c_0_2532,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_24) ).

fof(c_0_2533,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_23) ).

fof(c_0_2534,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_22) ).

fof(c_0_2535,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_21) ).

fof(c_0_2536,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_20) ).

fof(c_0_2537,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_2) ).

fof(c_0_2538,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_19) ).

fof(c_0_2539,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_18) ).

fof(c_0_2540,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_17) ).

fof(c_0_2541,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_16) ).

fof(c_0_2542,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_15) ).

fof(c_0_2543,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_14) ).

fof(c_0_2544,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_13) ).

fof(c_0_2545,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_12) ).

fof(c_0_2546,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_11) ).

fof(c_0_2547,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_10) ).

fof(c_0_2548,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_1) ).

fof(c_0_2549,axiom,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Nat_Opower(X40) ),
    file('<stdin>',clsrel_Power_Orecpower_0) ).

fof(c_0_2550,axiom,
    ! [X40] :
      ( ~ class_Orderings_Oorder(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Orderings_Oorder_0) ).

fof(c_0_2551,axiom,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_Orderings_Olinorder_4) ).

fof(c_0_2552,axiom,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_Orderings_Olinorder_3) ).

fof(c_0_2553,axiom,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_Orderings_Olinorder_2) ).

fof(c_0_2554,axiom,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_Orderings_Olinorder_1) ).

fof(c_0_2555,axiom,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_Orderings_Olinorder_0) ).

fof(c_0_2556,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Osemigroup__mult_0) ).

fof(c_0_2557,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Osemigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Osemigroup__add_0) ).

fof(c_0_2558,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

fof(c_0_2559,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

fof(c_0_2560,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

fof(c_0_2561,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

fof(c_0_2562,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

fof(c_0_2563,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

fof(c_0_2564,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

fof(c_0_2565,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

fof(c_0_2566,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

fof(c_0_2567,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

fof(c_0_2568,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

fof(c_0_2569,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

fof(c_0_2570,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

fof(c_0_2571,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

fof(c_0_2572,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

fof(c_0_2573,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

fof(c_0_2574,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

fof(c_0_2575,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

fof(c_0_2576,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

fof(c_0_2577,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

fof(c_0_2578,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

fof(c_0_2579,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

fof(c_0_2580,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

fof(c_0_2581,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).

fof(c_0_2582,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).

fof(c_0_2583,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

fof(c_0_2584,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).

fof(c_0_2585,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

fof(c_0_2586,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).

fof(c_0_2587,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

fof(c_0_2588,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

fof(c_0_2589,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

fof(c_0_2590,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

fof(c_0_2591,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

fof(c_0_2592,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

fof(c_0_2593,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

fof(c_0_2594,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Olinorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

fof(c_0_2595,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

fof(c_0_2596,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

fof(c_0_2597,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

fof(c_0_2598,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

fof(c_0_2599,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

fof(c_0_2600,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

fof(c_0_2601,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

fof(c_0_2602,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

fof(c_0_2603,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

fof(c_0_2604,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

fof(c_0_2605,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

fof(c_0_2606,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

fof(c_0_2607,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

fof(c_0_2608,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Omonoid__mult(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Omonoid__mult_2) ).

fof(c_0_2609,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Omonoid__mult(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Omonoid__mult_1) ).

fof(c_0_2610,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Omonoid__mult(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Omonoid__mult_0) ).

fof(c_0_2611,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

fof(c_0_2612,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

fof(c_0_2613,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

fof(c_0_2614,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

fof(c_0_2615,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

fof(c_0_2616,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).

fof(c_0_2617,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

fof(c_0_2618,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

fof(c_0_2619,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

fof(c_0_2620,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

fof(c_0_2621,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

fof(c_0_2622,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

fof(c_0_2623,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).

fof(c_0_2624,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).

fof(c_0_2625,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

fof(c_0_2626,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).

fof(c_0_2627,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

fof(c_0_2628,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

fof(c_0_2629,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

fof(c_0_2630,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

fof(c_0_2631,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

fof(c_0_2632,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

fof(c_0_2633,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

fof(c_0_2634,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

fof(c_0_2635,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).

fof(c_0_2636,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

fof(c_0_2637,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

fof(c_0_2638,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

fof(c_0_2639,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

fof(c_0_2640,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

fof(c_0_2641,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

fof(c_0_2642,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).

fof(c_0_2643,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).

fof(c_0_2644,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

fof(c_0_2645,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).

fof(c_0_2646,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

fof(c_0_2647,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).

fof(c_0_2648,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

fof(c_0_2649,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

fof(c_0_2650,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

fof(c_0_2651,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

fof(c_0_2652,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

fof(c_0_2653,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).

fof(c_0_2654,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

fof(c_0_2655,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

fof(c_0_2656,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

fof(c_0_2657,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

fof(c_0_2658,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

fof(c_0_2659,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

fof(c_0_2660,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

fof(c_0_2661,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

fof(c_0_2662,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).

fof(c_0_2663,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).

fof(c_0_2664,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

fof(c_0_2665,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).

fof(c_0_2666,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

fof(c_0_2667,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

fof(c_0_2668,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_9) ).

fof(c_0_2669,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_8) ).

fof(c_0_2670,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_7) ).

fof(c_0_2671,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_6) ).

fof(c_0_2672,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_5) ).

fof(c_0_2673,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_4) ).

fof(c_0_2674,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_3) ).

fof(c_0_2675,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_2) ).

fof(c_0_2676,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_17) ).

fof(c_0_2677,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_16) ).

fof(c_0_2678,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_LOrder_Olorder(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_15) ).

fof(c_0_2679,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_14) ).

fof(c_0_2680,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_13) ).

fof(c_0_2681,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_12) ).

fof(c_0_2682,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_11) ).

fof(c_0_2683,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_10) ).

fof(c_0_2684,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_1) ).

fof(c_0_2685,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_0) ).

fof(c_0_2686,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

fof(c_0_2687,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

fof(c_0_2688,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

fof(c_0_2689,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

fof(c_0_2690,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

fof(c_0_2691,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

fof(c_0_2692,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

fof(c_0_2693,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

fof(c_0_2694,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

fof(c_0_2695,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

fof(c_0_2696,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).

fof(c_0_2697,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

fof(c_0_2698,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

fof(c_0_2699,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

fof(c_0_2700,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

fof(c_0_2701,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

fof(c_0_2702,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

fof(c_0_2703,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

fof(c_0_2704,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

fof(c_0_2705,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_7) ).

fof(c_0_2706,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_6) ).

fof(c_0_2707,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_5) ).

fof(c_0_2708,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_4) ).

fof(c_0_2709,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_3) ).

fof(c_0_2710,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_2) ).

fof(c_0_2711,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_1) ).

fof(c_0_2712,axiom,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_0) ).

fof(c_0_2713,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_9) ).

fof(c_0_2714,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Ozero(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_8) ).

fof(c_0_2715,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_7) ).

fof(c_0_2716,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_6) ).

fof(c_0_2717,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_5) ).

fof(c_0_2718,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_4) ).

fof(c_0_2719,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Numeral_Onumber(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_30) ).

fof(c_0_2720,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Otimes(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_3) ).

fof(c_0_2721,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_29) ).

fof(c_0_2722,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_28) ).

fof(c_0_2723,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_27) ).

fof(c_0_2724,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_26) ).

fof(c_0_2725,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_25) ).

fof(c_0_2726,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_24) ).

fof(c_0_2727,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_23) ).

fof(c_0_2728,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_22) ).

fof(c_0_2729,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_21) ).

fof(c_0_2730,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Oone(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_20) ).

fof(c_0_2731,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_2) ).

fof(c_0_2732,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_19) ).

fof(c_0_2733,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_18) ).

fof(c_0_2734,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_17) ).

fof(c_0_2735,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_16) ).

fof(c_0_2736,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_15) ).

fof(c_0_2737,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_14) ).

fof(c_0_2738,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_13) ).

fof(c_0_2739,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Ominus(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_12) ).

fof(c_0_2740,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_11) ).

fof(c_0_2741,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_10) ).

fof(c_0_2742,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_1) ).

fof(c_0_2743,axiom,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Oplus(X40) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_0) ).

fof(c_0_2744,axiom,
    ! [X40] :
      ( ~ class_LOrder_Omeet__semilorder(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_LOrder_Omeet__semilorder_1) ).

fof(c_0_2745,axiom,
    ! [X40] :
      ( ~ class_LOrder_Omeet__semilorder(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_LOrder_Omeet__semilorder_0) ).

fof(c_0_2746,axiom,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    file('<stdin>',clsrel_LOrder_Olorder_3) ).

fof(c_0_2747,axiom,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_LOrder_Olorder_2) ).

fof(c_0_2748,axiom,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_LOrder_Olorder_1) ).

fof(c_0_2749,axiom,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    file('<stdin>',clsrel_LOrder_Olorder_0) ).

fof(c_0_2750,axiom,
    ! [X40] :
      ( ~ class_LOrder_Ojoin__semilorder(X40)
      | class_Orderings_Oorder(X40) ),
    file('<stdin>',clsrel_LOrder_Ojoin__semilorder_1) ).

fof(c_0_2751,axiom,
    ! [X40] :
      ( ~ class_LOrder_Ojoin__semilorder(X40)
      | class_Orderings_Oord(X40) ),
    file('<stdin>',clsrel_LOrder_Ojoin__semilorder_0) ).

fof(c_0_2752,axiom,
    c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
    file('<stdin>',cls_Public_Okeymode_Osize__2_0) ).

fof(c_0_2753,axiom,
    c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
    file('<stdin>',cls_Public_Okeymode_Osize__1_0) ).

fof(c_0_2754,axiom,
    ! [X1] : c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
    file('<stdin>',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).

fof(c_0_2755,axiom,
    c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
    file('<stdin>',cls_Message_Oagent_Osize__3_0) ).

fof(c_0_2756,axiom,
    c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
    file('<stdin>',cls_Message_Oagent_Osize__1_0) ).

fof(c_0_2757,axiom,
    c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
    file('<stdin>',cls_SetInterval_OlessThan__0_0) ).

fof(c_0_2758,axiom,
    c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
    file('<stdin>',cls_SetInterval_OatLeast__0_0) ).

fof(c_0_2759,axiom,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    file('<stdin>',cls_Parity_Oeven__zero_0) ).

fof(c_0_2760,axiom,
    c_Parity_Oeven(c_0,tc_nat),
    file('<stdin>',cls_Parity_Oeven__nat__zero_0) ).

fof(c_0_2761,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
    file('<stdin>',cls_Numeral_Obit_Osize__2_0) ).

fof(c_0_2762,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
    file('<stdin>',cls_Numeral_Obit_Osize__1_0) ).

fof(c_0_2763,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
    file('<stdin>',cls_Numeral_OPls__0__eq_0) ).

fof(c_0_2764,axiom,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
    file('<stdin>',cls_Numeral_OMin__1__eq_0) ).

fof(c_0_2765,axiom,
    c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
    file('<stdin>',cls_NatBin_Onat__numeral__0__eq__0_0) ).

fof(c_0_2766,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__9_0) ).

fof(c_0_2767,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__8_0) ).

fof(c_0_2768,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__7_0) ).

fof(c_0_2769,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__6_0) ).

fof(c_0_2770,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__5_0) ).

fof(c_0_2771,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__4_0) ).

fof(c_0_2772,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__3_0) ).

fof(c_0_2773,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__2_0) ).

fof(c_0_2774,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__1_0) ).

fof(c_0_2775,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__16_0) ).

fof(c_0_2776,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__15_0) ).

fof(c_0_2777,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__14_0) ).

fof(c_0_2778,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__13_0) ).

fof(c_0_2779,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__12_0) ).

fof(c_0_2780,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__11_0) ).

fof(c_0_2781,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
    file('<stdin>',cls_List_Onibble_Osize__10_0) ).

fof(c_0_2782,axiom,
    ! [X1] : c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
    file('<stdin>',cls_IntDef_Onat__int_0) ).

fof(c_0_2783,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
    file('<stdin>',cls_Extraction_Osumbool_Osize__2_0) ).

fof(c_0_2784,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
    file('<stdin>',cls_Extraction_Osumbool_Osize__1_0) ).

fof(c_0_2785,axiom,
    c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
    file('<stdin>',cls_Datatype_Ounit_Osize_0) ).

fof(c_0_2786,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    file('<stdin>',cls_Wellfounded__Relations_Owf__less__than_0) ).

fof(c_0_2787,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    file('<stdin>',cls_Wellfounded__Relations_Otrans__less__than_0) ).

fof(c_0_2788,axiom,
    ! [X38] : class_Nat_Opower(tc_set(X38)),
    file('<stdin>',clsarity_set_4) ).

fof(c_0_2789,axiom,
    ! [X38] : class_Orderings_Oorder(tc_set(X38)),
    file('<stdin>',clsarity_set_2) ).

fof(c_0_2790,axiom,
    ! [X38] : class_Orderings_Oord(tc_set(X38)),
    file('<stdin>',clsarity_set_1) ).

fof(c_0_2791,axiom,
    ! [X38] : class_HOL_Ominus(tc_set(X38)),
    file('<stdin>',clsarity_set_0) ).

fof(c_0_2792,axiom,
    ! [X22] :
      ( c_IntDef_Oint(X22) != c_0
      | X22 = c_0 ),
    file('<stdin>',cls_IntDef_Oint__eq__0__conv_0) ).

fof(c_0_2793,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X4)
      | c_1 != c_0 ),
    file('<stdin>',cls_Ring__and__Field_Oone__neq__zero_0) ).

fof(c_0_2794,axiom,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X4)
      | c_0 != c_1 ),
    file('<stdin>',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).

fof(c_0_2795,axiom,
    ! [X91] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X91),
    file('<stdin>',cls_Message_Oagent_Odistinct__6_0) ).

fof(c_0_2796,axiom,
    ! [X91] : c_Message_Oagent_OFriend(X91) != c_Message_Oagent_OSpy,
    file('<stdin>',cls_Message_Oagent_Odistinct__5_0) ).

fof(c_0_2797,axiom,
    ! [X90] : c_Message_Oagent_OFriend(X90) != c_Message_Oagent_OServer,
    file('<stdin>',cls_Message_Oagent_Odistinct__2_0) ).

fof(c_0_2798,axiom,
    ! [X90] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X90),
    file('<stdin>',cls_Message_Oagent_Odistinct__1_0) ).

fof(c_0_2799,axiom,
    ! [X16] : c_0 != c_Suc(X16),
    file('<stdin>',cls_Nat_OZero__not__Suc_0) ).

fof(c_0_2800,axiom,
    ! [X16] : c_Suc(X16) != c_0,
    file('<stdin>',cls_Nat_OSuc__not__Zero_0) ).

fof(c_0_2801,axiom,
    c_IntDef_Onat(c_1) = c_Suc(c_0),
    file('<stdin>',cls_IntArith_Onat__1_0) ).

fof(c_0_2802,axiom,
    c_Message_Oanalz(c_emptyset) = c_emptyset,
    file('<stdin>',cls_Message_Oanalz__empty_0) ).

fof(c_0_2803,axiom,
    c_Message_Oparts(c_emptyset) = c_emptyset,
    file('<stdin>',cls_Message_Oparts__empty_0) ).

fof(c_0_2804,axiom,
    c_Message_OkeysFor(c_emptyset) = c_emptyset,
    file('<stdin>',cls_Message_OkeysFor__empty_0) ).

fof(c_0_2805,axiom,
    c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
    file('<stdin>',cls_Numeral_Obin__succ__Min_0) ).

fof(c_0_2806,axiom,
    c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
    file('<stdin>',cls_Numeral_Obin__pred__Pls_0) ).

fof(c_0_2807,axiom,
    c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
    file('<stdin>',cls_Numeral_Obin__minus__Pls_0) ).

fof(c_0_2808,axiom,
    c_1 = c_Suc(c_0),
    file('<stdin>',cls_Nat_OOne__nat__def_0) ).

fof(c_0_2809,axiom,
    c_IntDef_Onat(c_0) = c_0,
    file('<stdin>',cls_IntDef_Onat__zero_0) ).

fof(c_0_2810,axiom,
    c_IntDef_Oint(c_0) = c_0,
    file('<stdin>',cls_IntDef_Oint__eq__0__conv_1) ).

fof(c_0_2811,axiom,
    c_IntDef_Oint(c_1) = c_1,
    file('<stdin>',cls_IntDef_Oint__1_0) ).

fof(c_0_2812,axiom,
    class_HOL_Ominus(tc_nat),
    file('<stdin>',clsarity_nat_9) ).

fof(c_0_2813,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    file('<stdin>',clsarity_nat_8) ).

fof(c_0_2814,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('<stdin>',clsarity_nat_7) ).

fof(c_0_2815,axiom,
    class_LOrder_Olorder(tc_nat),
    file('<stdin>',clsarity_nat_6) ).

fof(c_0_2816,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    file('<stdin>',clsarity_nat_5) ).

fof(c_0_2817,axiom,
    class_Parity_Oeven__odd(tc_nat),
    file('<stdin>',clsarity_nat_47) ).

fof(c_0_2818,axiom,
    class_Numeral_Onumber(tc_nat),
    file('<stdin>',clsarity_nat_46) ).

fof(c_0_2819,axiom,
    class_Power_Orecpower(tc_nat),
    file('<stdin>',clsarity_nat_45) ).

fof(c_0_2820,axiom,
    class_Divides_Odiv(tc_nat),
    file('<stdin>',clsarity_nat_44) ).

fof(c_0_2821,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('<stdin>',clsarity_nat_43) ).

fof(c_0_2822,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('<stdin>',clsarity_nat_42) ).

fof(c_0_2823,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    file('<stdin>',clsarity_nat_41) ).

fof(c_0_2824,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    file('<stdin>',clsarity_nat_40) ).

fof(c_0_2825,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    file('<stdin>',clsarity_nat_4) ).

fof(c_0_2826,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('<stdin>',clsarity_nat_39) ).

fof(c_0_2827,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('<stdin>',clsarity_nat_38) ).

fof(c_0_2828,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('<stdin>',clsarity_nat_37) ).

fof(c_0_2829,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_36) ).

fof(c_0_2830,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('<stdin>',clsarity_nat_35) ).

fof(c_0_2831,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_34) ).

fof(c_0_2832,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_33) ).

fof(c_0_2833,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    file('<stdin>',clsarity_nat_32) ).

fof(c_0_2834,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    file('<stdin>',clsarity_nat_31) ).

fof(c_0_2835,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    file('<stdin>',clsarity_nat_30) ).

fof(c_0_2836,axiom,
    class_Orderings_Oorder(tc_nat),
    file('<stdin>',clsarity_nat_3) ).

fof(c_0_2837,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    file('<stdin>',clsarity_nat_29) ).

fof(c_0_2838,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_28) ).

fof(c_0_2839,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_27) ).

fof(c_0_2840,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('<stdin>',clsarity_nat_26) ).

fof(c_0_2841,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('<stdin>',clsarity_nat_25) ).

fof(c_0_2842,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('<stdin>',clsarity_nat_24) ).

fof(c_0_2843,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('<stdin>',clsarity_nat_23) ).

fof(c_0_2844,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    file('<stdin>',clsarity_nat_22) ).

fof(c_0_2845,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('<stdin>',clsarity_nat_21) ).

fof(c_0_2846,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('<stdin>',clsarity_nat_20) ).

fof(c_0_2847,axiom,
    class_Orderings_Oord(tc_nat),
    file('<stdin>',clsarity_nat_2) ).

fof(c_0_2848,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('<stdin>',clsarity_nat_19) ).

fof(c_0_2849,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('<stdin>',clsarity_nat_18) ).

fof(c_0_2850,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('<stdin>',clsarity_nat_17) ).

fof(c_0_2851,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    file('<stdin>',clsarity_nat_16) ).

fof(c_0_2852,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_15) ).

fof(c_0_2853,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_14) ).

fof(c_0_2854,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    file('<stdin>',clsarity_nat_13) ).

fof(c_0_2855,axiom,
    class_Nat_Opower(tc_nat),
    file('<stdin>',clsarity_nat_12) ).

fof(c_0_2856,axiom,
    class_HOL_Otimes(tc_nat),
    file('<stdin>',clsarity_nat_11) ).

fof(c_0_2857,axiom,
    class_HOL_Oplus(tc_nat),
    file('<stdin>',clsarity_nat_10) ).

fof(c_0_2858,axiom,
    class_HOL_Ozero(tc_nat),
    file('<stdin>',clsarity_nat_1) ).

fof(c_0_2859,axiom,
    class_HOL_Oone(tc_nat),
    file('<stdin>',clsarity_nat_0) ).

fof(c_0_2860,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    file('<stdin>',clsarity_bool_0) ).

fof(c_0_2861,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('<stdin>',clsarity_Product____Type__Ounit_0) ).

fof(c_0_2862,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_9) ).

fof(c_0_2863,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_8) ).

fof(c_0_2864,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_7) ).

fof(c_0_2865,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_64) ).

fof(c_0_2866,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_63) ).

fof(c_0_2867,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_62) ).

fof(c_0_2868,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_61) ).

fof(c_0_2869,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_60) ).

fof(c_0_2870,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_6) ).

fof(c_0_2871,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_59) ).

fof(c_0_2872,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_58) ).

fof(c_0_2873,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_57) ).

fof(c_0_2874,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_56) ).

fof(c_0_2875,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_55) ).

fof(c_0_2876,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_54) ).

fof(c_0_2877,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_53) ).

fof(c_0_2878,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_52) ).

fof(c_0_2879,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_51) ).

fof(c_0_2880,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_50) ).

fof(c_0_2881,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_5) ).

fof(c_0_2882,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_49) ).

fof(c_0_2883,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_48) ).

fof(c_0_2884,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_47) ).

fof(c_0_2885,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_46) ).

fof(c_0_2886,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_45) ).

fof(c_0_2887,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_44) ).

fof(c_0_2888,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_43) ).

fof(c_0_2889,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_42) ).

fof(c_0_2890,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_41) ).

fof(c_0_2891,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_40) ).

fof(c_0_2892,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_4) ).

fof(c_0_2893,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_39) ).

fof(c_0_2894,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_38) ).

fof(c_0_2895,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_37) ).

fof(c_0_2896,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_36) ).

fof(c_0_2897,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_35) ).

fof(c_0_2898,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_34) ).

fof(c_0_2899,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_33) ).

fof(c_0_2900,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_32) ).

fof(c_0_2901,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_31) ).

fof(c_0_2902,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_30) ).

fof(c_0_2903,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_3) ).

fof(c_0_2904,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_29) ).

fof(c_0_2905,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_28) ).

fof(c_0_2906,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_27) ).

fof(c_0_2907,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_26) ).

fof(c_0_2908,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_25) ).

fof(c_0_2909,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_24) ).

fof(c_0_2910,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_23) ).

fof(c_0_2911,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_22) ).

fof(c_0_2912,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_21) ).

fof(c_0_2913,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_20) ).

fof(c_0_2914,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_2) ).

fof(c_0_2915,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_19) ).

fof(c_0_2916,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_18) ).

fof(c_0_2917,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_17) ).

fof(c_0_2918,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_16) ).

fof(c_0_2919,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_15) ).

fof(c_0_2920,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_14) ).

fof(c_0_2921,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_13) ).

fof(c_0_2922,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_12) ).

fof(c_0_2923,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_11) ).

fof(c_0_2924,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_10) ).

fof(c_0_2925,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_1) ).

fof(c_0_2926,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_0) ).

fof(c_0_2927,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    file('<stdin>',cls_Public_Okeymode_Odistinct__2_0) ).

fof(c_0_2928,axiom,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    file('<stdin>',cls_Public_Okeymode_Odistinct__1_0) ).

fof(c_0_2929,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('<stdin>',cls_Message_Oagent_Odistinct__4_0) ).

fof(c_0_2930,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('<stdin>',cls_Message_Oagent_Odistinct__3_0) ).

fof(c_0_2931,axiom,
    c_UNIV != c_emptyset,
    file('<stdin>',cls_Set_OUNIV__not__empty_0) ).

fof(c_0_2932,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    file('<stdin>',cls_Numeral_Obit_Odistinct__2_0) ).

fof(c_0_2933,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    file('<stdin>',cls_Numeral_Obit_Odistinct__1_0) ).

fof(c_0_2934,axiom,
    c_0 != c_1,
    file('<stdin>',cls_IntDef_Oint__0__neq__1_0) ).

fof(c_0_2935,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    file('<stdin>',cls_Extraction_Osumbool_Odistinct__2_0) ).

fof(c_0_2936,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    file('<stdin>',cls_Extraction_Osumbool_Odistinct__1_0) ).

fof(c_0_2937,axiom,
    ! [X1,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X1,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble8,X4) = X1,
    c_0_0 ).

fof(c_0_2938,axiom,
    ! [X1,X68,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X1,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble7,X4) = X1,
    c_0_1 ).

fof(c_0_2939,axiom,
    ! [X1,X68,X69,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X1,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble6,X4) = X1,
    c_0_2 ).

fof(c_0_2940,axiom,
    ! [X1,X68,X69,X70,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X1,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble5,X4) = X1,
    c_0_3 ).

fof(c_0_2941,axiom,
    ! [X1,X68,X69,X70,X71,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X1,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble4,X4) = X1,
    c_0_4 ).

fof(c_0_2942,axiom,
    ! [X1,X68,X69,X70,X71,X72,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X1,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble3,X4) = X1,
    c_0_5 ).

fof(c_0_2943,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X1,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble2,X4) = X1,
    c_0_6 ).

fof(c_0_2944,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X1,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble1,X4) = X1,
    c_0_7 ).

fof(c_0_2945,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X4] : c_List_Onibble_Onibble__rec(X1,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble0,X4) = X1,
    c_0_8 ).

fof(c_0_2946,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X1,c_List_Onibble_ONibbleF,X4) = X1,
    c_0_9 ).

fof(c_0_2947,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X1,X75,c_List_Onibble_ONibbleE,X4) = X1,
    c_0_10 ).

fof(c_0_2948,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X1,X76,X75,c_List_Onibble_ONibbleD,X4) = X1,
    c_0_11 ).

fof(c_0_2949,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X1,X77,X76,X75,c_List_Onibble_ONibbleC,X4) = X1,
    c_0_12 ).

fof(c_0_2950,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X80,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X1,X78,X77,X76,X75,c_List_Onibble_ONibbleB,X4) = X1,
    c_0_13 ).

fof(c_0_2951,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X81,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X1,X79,X78,X77,X76,X75,c_List_Onibble_ONibbleA,X4) = X1,
    c_0_14 ).

fof(c_0_2952,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X46,X4] : c_List_Onibble_Onibble__rec(X46,X45,X74,X73,X72,X71,X70,X69,X68,X1,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble9,X4) = X1,
    c_0_15 ).

fof(c_0_2953,axiom,
    ! [X1,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X1,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble8,X4) = X1,
    c_0_16 ).

fof(c_0_2954,axiom,
    ! [X1,X68,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X1,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble7,X4) = X1,
    c_0_17 ).

fof(c_0_2955,axiom,
    ! [X1,X68,X69,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X1,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble6,X4) = X1,
    c_0_18 ).

fof(c_0_2956,axiom,
    ! [X1,X68,X69,X70,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X1,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble5,X4) = X1,
    c_0_19 ).

fof(c_0_2957,axiom,
    ! [X1,X68,X69,X70,X71,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X1,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble4,X4) = X1,
    c_0_20 ).

fof(c_0_2958,axiom,
    ! [X1,X68,X69,X70,X71,X72,X74,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X1,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble3,X4) = X1,
    c_0_21 ).

fof(c_0_2959,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X45,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X1,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble2,X4) = X1,
    c_0_22 ).

fof(c_0_2960,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X75,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X1,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble1,X4) = X1,
    c_0_23 ).

fof(c_0_2961,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X81,X4] : c_List_Onibble_Onibble__case(X1,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble0,X4) = X1,
    c_0_24 ).

fof(c_0_2962,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X76,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X76,X1,c_List_Onibble_ONibbleF,X4) = X1,
    c_0_25 ).

fof(c_0_2963,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X77,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X77,X1,X75,c_List_Onibble_ONibbleE,X4) = X1,
    c_0_26 ).

fof(c_0_2964,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X78,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X78,X1,X76,X75,c_List_Onibble_ONibbleD,X4) = X1,
    c_0_27 ).

fof(c_0_2965,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X79,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X79,X1,X77,X76,X75,c_List_Onibble_ONibbleC,X4) = X1,
    c_0_28 ).

fof(c_0_2966,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X80,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X80,X1,X78,X77,X76,X75,c_List_Onibble_ONibbleB,X4) = X1,
    c_0_29 ).

fof(c_0_2967,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X81,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X81,X1,X79,X78,X77,X76,X75,c_List_Onibble_ONibbleA,X4) = X1,
    c_0_30 ).

fof(c_0_2968,axiom,
    ! [X1,X68,X69,X70,X71,X72,X73,X74,X45,X75,X76,X77,X78,X79,X80,X46,X4] : c_List_Onibble_Onibble__case(X46,X45,X74,X73,X72,X71,X70,X69,X68,X1,X80,X79,X78,X77,X76,X75,c_List_Onibble_ONibble9,X4) = X1,
    c_0_31 ).

fof(c_0_2969,plain,
    ! [X31,X5,X6,X32,X3,X4] :
      ( ~ c_in(X31,c_Relation_Orel__comp(X6,X5,X32,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(c_Main_Orel__compE__1(X6,X5,X31,X32,X3,X4),c_Main_Orel__compE__2(X6,X5,X31,X32,X3,X4),X4,X32),X5,tc_prod(X4,X32)) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_2970,plain,
    ! [X31,X5,X6,X32,X3,X4] :
      ( ~ c_in(X31,c_Relation_Orel__comp(X6,X5,X32,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(c_Main_Orel__compE__2(X6,X5,X31,X32,X3,X4),c_Main_Orel__compE__3(X6,X5,X31,X32,X3,X4),X32,X3),X6,tc_prod(X32,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_2971,plain,
    ! [X31,X5,X6,X32,X3,X4] :
      ( ~ c_in(X31,c_Relation_Orel__comp(X6,X5,X32,X3,X4),tc_prod(X4,X3))
      | X31 = c_Pair(c_Main_Orel__compE__1(X6,X5,X31,X32,X3,X4),c_Main_Orel__compE__3(X6,X5,X31,X32,X3,X4),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_2972,plain,
    ! [X5,X6,X7,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X7 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X7,X6,X5,X4,X3),c_Main_OdprodE__2(X7,X6,X5,X4,X3),X4,X3),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X7,X6,X5,X4,X3),c_Main_OdprodE__4(X7,X6,X5,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_2973,plain,
    ! [X5,X6,X7,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdprodE__1(X7,X6,X5,X4,X3),c_Main_OdprodE__3(X7,X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_2974,plain,
    ! [X5,X6,X7,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdprodE__2(X7,X6,X5,X4,X3),c_Main_OdprodE__4(X7,X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_2975,plain,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__1(X6,X12,X4,X3),c_Main_OdsumE__2(X6,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__3(X5,X12,X4,X3),c_Main_OdsumE__4(X5,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_2976,plain,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__1(X6,X12,X4,X3),c_Main_OdsumE__2(X6,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X12 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X5,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X5,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_2977,plain,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Main_OdsumE__3(X5,X12,X4,X3),c_Main_OdsumE__4(X5,X12,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X12 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_2978,plain,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X6,X24,X1,X26,X4),X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_2979,plain,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X26,X4),X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X26,c_Main_Olistrel__Cons1__2(X6,X24,X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_2980,plain,
    ! [X5,X6,X8,X9,X10,X11,X3,X4] :
      ( ~ c_in(c_Pair(X9,X8,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | ~ c_in(c_Pair(X11,X10,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X11,X9,X4,X3),c_Datatype__Universe_OScons(X10,X8,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_2981,plain,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X6,X24,X1,X26,X4),X1,X4,X4),X6,tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_2982,plain,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X26,X4),X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X6,X24,X1,X26,X4),X4,X4),X6,tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_2983,plain,
    ! [X12,X5,X6,X3,X4] :
      ( ~ c_in(X12,c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | X12 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X12 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X5,X12,X4,X3),X4,X3),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X5,X12,X4,X3),X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_2984,plain,
    ! [X6,X28,X14,X3,X4] :
      ( ~ c_in(X28,c_Relation_OImage(X6,X14,X3,X4),X4)
      | c_in(c_Pair(c_Main_OImageE__1(X14,X28,X6,X3,X4),X28,X3,X4),X6,tc_prod(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_2985,plain,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X6,X24,X1,X26,X4),c_Main_Olistrel__Cons2__2(X6,X24,X1,X26,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_2986,plain,
    ! [X26,X1,X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X26,X4),X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X6,X24,X1,X26,X4),c_Main_Olistrel__Cons1__2(X6,X24,X1,X26,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_2987,plain,
    ! [X7,X13,X14,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X7 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X14,X13,X7,X4,X3),c_Main_OuprodE__2(X14,X13,X7,X4,X3),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_2988,plain,
    ! [X5,X6,X7,X28,X19,X32,X3,X4] :
      ( ~ c_in(c_Pair(X28,X7,X3,X32),X6,tc_prod(X3,X32))
      | ~ c_in(c_Pair(X19,X28,X4,X3),X5,tc_prod(X4,X3))
      | c_in(c_Pair(X19,X7,X4,X32),c_Relation_Orel__comp(X6,X5,X3,X32,X4),tc_prod(X4,X32)) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_2989,plain,
    ! [X1,X2,X48,X15] :
      ( ~ c_in(c_Pair(c_Pair(X2,X1,tc_nat,tc_nat),c_Pair(X15,X48,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_plus(X2,X48,tc_nat) = c_plus(X15,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_2990,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_2991,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_2992,plain,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_2993,plain,
    ! [X5,X6,X8,X9,X3,X4] :
      ( ~ c_in(c_Pair(X9,X8,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X9,X4,X3),c_Datatype__Universe_OIn1(X8,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_2994,plain,
    ! [X5,X6,X10,X11,X3,X4] :
      ( ~ c_in(c_Pair(X11,X10,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X11,X4,X3),c_Datatype__Universe_OIn0(X10,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3)))) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_2995,plain,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_2996,plain,
    ! [X7,X13,X14,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OuprodE__1(X14,X13,X7,X4,X3),X14,tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_2997,plain,
    ! [X7,X13,X14,X3,X4] :
      ( ~ c_in(X7,c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OuprodE__2(X14,X13,X7,X4,X3),X13,tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_2998,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_2999,plain,
    ! [X12,X48] :
      ( ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_3000,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_3001,plain,
    ! [X12,X48] :
      ( ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_3002,plain,
    ! [X6,X28,X14,X3,X4] :
      ( ~ c_in(X28,c_Relation_OImage(X6,X14,X3,X4),X4)
      | c_in(c_Main_OImageE__1(X14,X28,X6,X3,X4),X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_3003,plain,
    ! [X12] :
      ( ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_3004,plain,
    ! [X12] :
      ( ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_3005,plain,
    ! [X1,X2,X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X19,X2,X4),c_List_Olist_OCons(X28,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(X2,X1,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_3006,plain,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X2,X1,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(X24,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_3007,axiom,
    ! [X1,X2] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X2,X1,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    c_0_70 ).

fof(c_0_3008,axiom,
    ! [X1,X2,X48,X15] :
      ( c_plus(X2,X48,tc_nat) != c_plus(X15,X1,tc_nat)
      | c_in(c_Pair(c_Pair(X2,X1,tc_nat,tc_nat),c_Pair(X15,X48,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    c_0_71 ).

fof(c_0_3009,plain,
    ! [X30,X6,X3,X4] :
      ( ~ c_in(X30,c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(c_Main_OconverseE__1(X6,X30,X3,X4),c_Main_OconverseE__2(X6,X30,X3,X4),X3,X4),X6,tc_prod(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_3010,plain,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_3011,plain,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_3012,plain,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X24,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_Nat_Osize(X24,tc_List_Olist(X4)) = c_Nat_Osize(X26,tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_3013,plain,
    ! [X1,X2,X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X19,X2,X4),c_List_Olist_OCons(X28,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_3014,plain,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(X2,X1,X4,X4),X6,tc_prod(X4,X4))
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_3015,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__1(X14,X15,X4,X3),X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__2(X13,X15,X4,X3),X13,tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_3016,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__1(X14,X15,X4,X3),X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X15 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X15,X4,X3),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_3017,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Main_OusumE__2(X13,X15,X4,X3),X13,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X15 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X14,X15,X4,X3),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_3018,plain,
    ! [X1,X63,X2,X6,X4] :
      ( ~ c_in(c_Pair(X63,X1,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_List_Olist_OCons(X2,X63,X4),c_List_Olist_OCons(X2,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_3019,plain,
    ! [X26,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(X24,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X2,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_3020,axiom,
    ! [X1,X2] :
      ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(X2,X1,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    c_0_83 ).

fof(c_0_3021,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | X15 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X14,X15,X4,X3),X4,X3)
      | X15 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X15,X4,X3),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_3022,plain,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(X2,X1,X4,X4),X6,tc_prod(X4,X4))
      | c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X4))
      | c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_3023,plain,
    ! [X1,X2] :
      ( ~ c_in(c_Pair(X2,X1,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_3024,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | X15 = c_Sum__Type_OInl(c_Main_OPlusE__1(X14,X15,X4,X3),X4,X3)
      | X15 = c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X15,X3,X4),X3,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_3025,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | c_in(c_Main_OPlusE__1(X14,X15,X4,X3),X14,X4)
      | X15 = c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X15,X3,X4),X3,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_3026,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | c_in(c_Main_OPlusE__2(X13,X15,X3,X4),X13,X3)
      | X15 = c_Sum__Type_OInl(c_Main_OPlusE__1(X14,X15,X4,X3),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_3027,plain,
    ! [X15,X13,X14,X3,X4] :
      ( ~ c_in(X15,c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3))
      | c_in(c_Main_OPlusE__1(X14,X15,X4,X3),X14,X4)
      | c_in(c_Main_OPlusE__2(X13,X15,X3,X4),X13,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_3028,axiom,
    ! [X17,X9,X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_OScons(X11,X9,X4,X3),X4,X3) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X17,X11,X4,X3),c_Datatype__Universe_Ontrunc(X17,X9,X4,X3),X4,X3),
    c_0_91 ).

fof(c_0_3029,plain,
    ! [X1,X2,X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(c_List_Olist_OCons(X19,X2,X4),c_List_Olist_OCons(X28,X1,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_3030,plain,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_Wellfounded__Recursion_Owf(X6,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_3031,plain,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_Wellfounded__Recursion_Oacyclic(X6,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_3032,plain,
    ! [X6,X28,X3,X4] :
      ( ~ c_in(X28,c_Relation_ORange(X6,X3,X4),X4)
      | c_in(c_Pair(c_Main_ORangeE__1(X28,X6,X4,X3),X28,X3,X4),X6,tc_prod(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_3033,plain,
    ! [X6,X19,X3,X4] :
      ( ~ c_in(X19,c_Relation_ODomain(X6,X4,X3),X4)
      | c_in(c_Pair(X19,c_Main_ODomainE__1(X19,X6,X4,X3),X4,X3),X6,tc_prod(X4,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_3034,plain,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_3035,plain,
    ! [X1,X2,X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X6,X4)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X2,X4,X4),X6,tc_prod(X4,X4)),X4)
      | c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_3036,plain,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(X28,c_Relation_OImage(X6,c_insert(X19,c_emptyset,X3),X3,X4),X4)
      | c_in(c_Pair(X19,X28,X3,X4),X6,tc_prod(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_3037,plain,
    ! [X26,X1,X24,X2,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X2 = X1
      | c_Nat_Osize(X24,tc_List_Olist(X4)) = c_Nat_Osize(X26,tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_3038,plain,
    ! [X22,X16,X17] :
      ( ~ c_Divides_Oop_Advd(X17,c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X17,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_3039,plain,
    ! [X22,X16,X17] :
      ( ~ c_Divides_Oop_Advd(X17,c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X17,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_3040,plain,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X3,X4),X6,tc_prod(X3,X4))
      | c_in(X28,c_Relation_OImage(X6,c_insert(X19,c_emptyset,X3),X3,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_3041,axiom,
    ! [X26,X24,X53,X54,X3,X4] :
      ( c_Nat_Osize(X26,tc_List_Olist(X4)) != c_Nat_Osize(X53,tc_List_Olist(X3))
      | c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X54,tc_List_Olist(X3))
      | c_List_Ozip(c_append(X24,X26,X4),c_append(X54,X53,X3),X4,X3) = c_append(c_List_Ozip(X24,X54,X4,X3),c_List_Ozip(X26,X53,X4,X3),tc_prod(X4,X3)) ),
    c_0_104 ).

fof(c_0_3042,plain,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X3),c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3))
      | c_in(c_Pair(X28,X19,X3,X4),X6,tc_prod(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_3043,axiom,
    ! [X5,X6,X3,X4] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X4,X3),
    c_0_106 ).

fof(c_0_3044,axiom,
    ! [X5,X6,X3,X4] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X6,X5,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X4,X3)),tc_set(tc_Datatype__Universe_Onode(X4,X3))),X4,X3),
    c_0_107 ).

fof(c_0_3045,plain,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X28,X19,X3,X4),X6,tc_prod(X3,X4))
      | c_in(c_Pair(X19,X28,X4,X3),c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_3046,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_3047,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_3048,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_3049,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_3050,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_3051,axiom,
    ! [X22,X86,X42] : c_Nat_Opower(X86,c_Suc(X22),tc_set(tc_prod(X42,X42))) = c_Relation_Orel__comp(X86,c_Nat_Opower(X86,X22,tc_set(tc_prod(X42,X42))),X42,X42,X42),
    c_0_114 ).

fof(c_0_3052,plain,
    ! [X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),c_Transitive__Closure_Otrancl(X6,X4),tc_prod(X4,X4))
      | c_in(c_Pair(X19,X28,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_3053,plain,
    ! [X6,X28,X19,X14,X3,X4] :
      ( ~ c_in(X19,X14,X4)
      | ~ c_in(c_Pair(X19,X28,X4,X3),X6,tc_prod(X4,X3))
      | c_in(X28,c_Relation_OImage(X6,X14,X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_3054,plain,
    ! [X30,X6,X3,X4] :
      ( ~ c_in(X30,c_Relation_Oconverse(X6,X3,X4),tc_prod(X4,X3))
      | X30 = c_Pair(c_Main_OconverseE__2(X6,X30,X3,X4),c_Main_OconverseE__1(X6,X30,X3,X4),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_3055,axiom,
    ! [X26,X1,X24,X2,X3,X4] : c_List_Ozip(c_List_Olist_OCons(X2,X24,X4),c_List_Olist_OCons(X1,X26,X3),X4,X3) = c_List_Olist_OCons(c_Pair(X2,X1,X4,X3),c_List_Ozip(X24,X26,X4,X3),tc_prod(X4,X3)),
    c_0_118 ).

fof(c_0_3056,plain,
    ! [X6,X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),X6,tc_prod(X4,X4))
      | c_in(c_Pair(X19,X28,X4,X4),c_Transitive__Closure_Otrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_3057,plain,
    ! [X9,X11,X13,X14,X3,X4] :
      ( ~ c_in(X9,X13,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | ~ c_in(X11,X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Datatype__Universe_OScons(X11,X9,X4,X3),c_Datatype__Universe_Ouprod(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_3058,plain,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_3059,plain,
    ! [X26,X24,X2,X3,X4] :
      ( ~ c_in(X2,c_List_Oset(X24,X4),X4)
      | c_Map_Omap__of(c_List_Ozip(X24,X26,X4,X3),X2,X4,X3) != c_Datatype_Ooption_ONone
      | c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_3060,plain,
    ! [X26,X24,X44,X3,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X26,tc_List_Olist(X3)),tc_nat)
      | ~ c_less(X44,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Onth(c_List_Ozip(X24,X26,X4,X3),X44,tc_prod(X4,X3)) = c_Pair(c_List_Onth(X24,X44,X4),c_List_Onth(X26,X44,X3),X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_3061,plain,
    ! [X12] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_3062,plain,
    ! [X12] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_3063,axiom,
    ! [X86,X4] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X86,X4),c_Transitive__Closure_Ortrancl(X86,X4),X4,X4,X4) = c_Transitive__Closure_Ortrancl(X86,X4),
    c_0_126 ).

fof(c_0_3064,axiom,
    ! [X1,X3,X4] : c_Relation_Orel__comp(X1,c_Relation_OId,X4,X3,X4) = X1,
    c_0_127 ).

fof(c_0_3065,axiom,
    ! [X1,X3,X4] : c_Relation_Orel__comp(c_Relation_OId,X1,X3,X3,X4) = X1,
    c_0_128 ).

fof(c_0_3066,plain,
    ! [X22,X16,X17] :
      ( ~ c_Divides_Oop_Advd(X17,X22,tc_nat)
      | ~ c_Divides_Oop_Advd(X17,X16,tc_nat)
      | c_Divides_Oop_Advd(X17,c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_3067,axiom,
    ! [X22,X16] : c_GCD_Ogcd(c_Pair(X16,c_plus(X22,X16,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),
    c_0_130 ).

fof(c_0_3068,axiom,
    ! [X22,X16] : c_GCD_Ogcd(c_Pair(X16,c_plus(X16,X22,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),
    c_0_131 ).

fof(c_0_3069,axiom,
    ! [X22,X16] : c_GCD_Ogcd(c_Pair(c_plus(X16,X22,tc_nat),X22,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),
    c_0_132 ).

fof(c_0_3070,axiom,
    ! [X1,X2,X60,X44,X3,X4] : c_List_Ozip(c_List_Oreplicate(X44,X2,X4),c_List_Oreplicate(X60,X1,X3),X4,X3) = c_List_Oreplicate(c_Orderings_Omin(X44,X60,tc_nat),c_Pair(X2,X1,X4,X3),tc_prod(X4,X3)),
    c_0_133 ).

fof(c_0_3071,plain,
    ! [X1,X24,X2,X44,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Olist__update(c_List_Olist__update(X24,X44,X2,X4),X44,X1,X4) = c_List_Olist__update(X24,X44,X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_3072,plain,
    ! [X1,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X1 = c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X4),c_Main_Olexord__Nil__left__2(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_3073,plain,
    ! [X12,X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_3074,plain,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X3),X6,tc_prod(X4,X3))
      | c_in(X28,c_Relation_ORange(X6,X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_3075,plain,
    ! [X6,X28,X19,X3,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X3),X6,tc_prod(X4,X3))
      | c_in(X19,c_Relation_ODomain(X6,X4,X3),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_3076,axiom,
    ! [X22,X16] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),X22,tc_nat),
    c_0_139 ).

fof(c_0_3077,axiom,
    ! [X22,X16] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X16,X22,tc_nat,tc_nat)),X16,tc_nat),
    c_0_140 ).

fof(c_0_3078,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_3079,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_3080,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_3081,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_3082,plain,
    ! [X24,X6,X4] :
      ( ~ c_in(c_Pair(X24,c_List_Olist_ONil,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_3083,plain,
    ! [X24,X6,X4] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X24,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))
      | X24 = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_3084,plain,
    ! [X2,X6,X4] : ~ c_in(c_Pair(X2,c_List_Olist_ONil,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_3085,plain,
    ! [X26,X6,X4] : ~ c_in(c_Pair(c_List_Olist_ONil,X26,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_3086,plain,
    ! [X24,X6,X4] : ~ c_in(c_Pair(X24,c_List_Olist_ONil,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olex(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_3087,plain,
    ! [X12] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_3088,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_3089,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_3090,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,X19,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_3091,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_0,X19,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_3092,plain,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_Nat_Opower(c_uminus(X19,X4),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X22,tc_nat),X4) = c_Nat_Opower(X19,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X22,tc_nat),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_3093,plain,
    ! [X1,X2] :
      ( ~ c_in(c_Pair(X2,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
      | c_less(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_3094,axiom,
    ! [X17,X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X17)),c_Datatype__Universe_OIn1(X11,X4,X3),X4,X3) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X17),X11,X4,X3),X4,X3),
    c_0_157 ).

fof(c_0_3095,axiom,
    ! [X17,X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X17)),c_Datatype__Universe_OIn0(X11,X4,X3),X4,X3) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X17),X11,X4,X3),X4,X3),
    c_0_158 ).

fof(c_0_3096,plain,
    ! [X6,X19,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | ~ c_in(c_Pair(X19,X19,X4,X4),X6,tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_3097,plain,
    ! [X16] :
      ( ~ c_less(c_0,c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
      | c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_3098,plain,
    ! [X28,X19,X4] :
      ( ~ c_in(c_Pair(X19,X28,X4,X4),c_Relation_OId,tc_prod(X4,X4))
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_3099,axiom,
    ! [X28] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X28,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X28,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    c_0_162 ).

fof(c_0_3100,plain,
    ! [X9,X13,X14,X3,X4] :
      ( ~ c_in(X9,X13,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Datatype__Universe_OIn1(X9,X4,X3),c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_3101,plain,
    ! [X11,X13,X14,X3,X4] :
      ( ~ c_in(X11,X14,tc_set(tc_Datatype__Universe_Onode(X4,X3)))
      | c_in(c_Datatype__Universe_OIn0(X11,X4,X3),c_Datatype__Universe_Ousum(X14,X13,X4,X3),tc_set(tc_Datatype__Universe_Onode(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_3102,axiom,
    ! [X87,X88,X89] : c_Message_Oparts(c_insert(c_Message_OHPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X88,X87),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oparts(c_insert(X87,X89,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    c_0_165 ).

fof(c_0_3103,axiom,
    ! [X87,X88,X89] : c_Message_Oanalz(c_insert(c_Message_OHPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X88,X87),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(c_insert(X87,X89,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    c_0_166 ).

fof(c_0_3104,axiom,
    ! [X26,X24,X2,X3,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X3))
      | c_in(X2,c_List_Oset(X24,X4),X4)
      | c_Map_Omap__of(c_List_Ozip(X24,X26,X4,X3),X2,X4,X3) = c_Datatype_Ooption_ONone ),
    c_0_167 ).

fof(c_0_3105,axiom,
    ! [X87,X88,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X88,X87),c_Message_Oparts(c_insert(X88,c_insert(X87,X89,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    c_0_168 ).

fof(c_0_3106,axiom,
    ! [X87,X88,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X88,X87),c_Message_Oanalz(c_insert(X88,c_insert(X87,X89,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    c_0_169 ).

fof(c_0_3107,axiom,
    ! [X6,X62,X25,X4] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X25,X62,X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olexord(X6,X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),
    c_0_170 ).

fof(c_0_3108,plain,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(c_minus(X14,c_insert(X19,X13,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_minus(X14,X13,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_171]) ).

fof(c_0_3109,axiom,
    ! [X26,X24,X22,X4] : c_List_Otake(X22,c_append(X24,X26,X4),X4) = c_append(c_List_Otake(X22,X24,X4),c_List_Otake(c_minus(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat),X26,X4),X4),
    c_0_172 ).

fof(c_0_3110,axiom,
    ! [X26,X24,X22,X4] : c_List_Odrop(X22,c_append(X24,X26,X4),X4) = c_append(c_List_Odrop(X22,X24,X4),c_List_Odrop(c_minus(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat),X26,X4),X4),
    c_0_173 ).

fof(c_0_3111,axiom,
    ! [X85,X28,X43,X19,X3,X4] :
      ( c_Pair(X19,X28,X4,X3) != c_Pair(X43,X85,X4,X3)
      | X28 = X85 ),
    c_0_174 ).

fof(c_0_3112,axiom,
    ! [X85,X28,X43,X19,X3,X4] :
      ( c_Pair(X19,X28,X4,X3) != c_Pair(X43,X85,X4,X3)
      | X19 = X43 ),
    c_0_175 ).

fof(c_0_3113,axiom,
    ! [X8,X9,X10,X11,X3,X4] :
      ( c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OScons(X10,X8,X4,X3)
      | X9 = X8 ),
    c_0_176 ).

fof(c_0_3114,axiom,
    ! [X8,X9,X10,X11,X3,X4] :
      ( c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OScons(X10,X8,X4,X3)
      | X11 = X10 ),
    c_0_177 ).

fof(c_0_3115,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_less(X28,X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_3116,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(X19,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_3117,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_less(X28,X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_3118,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(X19,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_3119,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(X28,X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_3120,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(X19,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_3121,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(X28,X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_3122,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(X19,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_185]) ).

fof(c_0_3123,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_3124,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_3125,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_3126,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_189]) ).

fof(c_0_3127,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_190]) ).

fof(c_0_3128,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_191]) ).

fof(c_0_3129,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_192]) ).

fof(c_0_3130,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | ~ c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_193]) ).

fof(c_0_3131,axiom,
    ! [X16] :
      ( c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1
      | c_less(c_0,c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    c_0_194 ).

fof(c_0_3132,axiom,
    ! [X26,X1,X24,X2,X4] : c_List_Olist__update(c_append(X24,c_List_Olist_OCons(X2,X26,X4),X4),c_Nat_Osize(X24,tc_List_Olist(X4)),X1,X4) = c_append(X24,c_List_Olist_OCons(X1,X26,X4),X4),
    c_0_195 ).

fof(c_0_3133,plain,
    ! [X28,X13,X14,X3,X4] :
      ( ~ c_in(X28,X13,X4)
      | c_in(c_Sum__Type_OInr(X28,X4,X3),c_Sum__Type_OPlus(X14,X13,X3,X4),tc_sum(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_196]) ).

fof(c_0_3134,plain,
    ! [X19,X13,X14,X3,X4] :
      ( ~ c_in(X19,X14,X4)
      | c_in(c_Sum__Type_OInl(X19,X4,X3),c_Sum__Type_OPlus(X14,X13,X4,X3),tc_sum(X4,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_197]) ).

fof(c_0_3135,axiom,
    ! [X6,X50] : c_IntDiv_OnegateSnd(c_Pair(X50,X6,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X50,c_uminus(X6,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    c_0_198 ).

fof(c_0_3136,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_199]) ).

fof(c_0_3137,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_200]) ).

fof(c_0_3138,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_201]) ).

fof(c_0_3139,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_202]) ).

fof(c_0_3140,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,X19,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_203]) ).

fof(c_0_3141,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X19,X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_204]) ).

fof(c_0_3142,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_lessequals(c_0,X19,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_205]) ).

fof(c_0_3143,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X19,X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_206]) ).

fof(c_0_3144,axiom,
    ! [X28] : c_IntDiv_OposDivAlg(c_Pair(c_0,X28,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    c_0_207 ).

fof(c_0_3145,axiom,
    ! [X1,X22] : c_GCD_Ogcd(c_Pair(X1,c_times(X1,X22,tc_nat),tc_nat,tc_nat)) = X1,
    c_0_208 ).

fof(c_0_3146,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_209]) ).

fof(c_0_3147,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_210]) ).

fof(c_0_3148,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_211]) ).

fof(c_0_3149,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_212]) ).

fof(c_0_3150,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_213]) ).

fof(c_0_3151,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_214]) ).

fof(c_0_3152,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_215]) ).

fof(c_0_3153,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | ~ c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_lessequals(X28,c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_216]) ).

fof(c_0_3154,axiom,
    ! [X26,X24,X3,X4] : c_Nat_Osize(c_List_Ozip(X24,X26,X4,X3),tc_List_Olist(tc_prod(X4,X3))) = c_Orderings_Omin(c_Nat_Osize(X24,tc_List_Olist(X4)),c_Nat_Osize(X26,tc_List_Olist(X3)),tc_nat),
    c_0_217 ).

fof(c_0_3155,plain,
    ! [X1,X24,X44,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Onth(c_List_Olist__update(X24,X44,X1,X4),X44,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_3156,plain,
    ! [X19,X14,X4] :
      ( ~ c_in(X19,X14,X4)
      | c_in(c_Pair(X19,X19,X4,X4),c_Relation_Odiag(X14,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_3157,plain,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(c_minus(X14,X13,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_minus(X14,c_insert(X19,X13,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_220]) ).

fof(c_0_3158,axiom,
    ! [X24,X2,X48,X4] :
      ( c_List_Otake(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_minus(c_Numeral_Onumber__of(X48,tc_nat),c_1,tc_nat),X24,X4),X4)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    c_0_221 ).

fof(c_0_3159,plain,
    ! [X1,X2] :
      ( ~ c_less(X2,X1,tc_nat)
      | c_in(c_Pair(X2,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(fof_simplification,[status(thm)],[c_0_222]) ).

fof(c_0_3160,axiom,
    ! [X2] :
      ( c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1 ),
    c_0_223 ).

fof(c_0_3161,plain,
    ! [X7,X14,X4] :
      ( ~ c_in(X7,c_Relation_Odiag(X14,X4),tc_prod(X4,X4))
      | X7 = c_Pair(c_Main_OdiagE__1(X14,X7,X4),c_Main_OdiagE__1(X14,X7,X4),X4,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_224]) ).

fof(c_0_3162,plain,
    ! [X24,X22,X44,X4] :
      ( ~ c_lessequals(c_plus(X22,X44,tc_nat),c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Onth(c_List_Odrop(X22,X24,X4),X44,X4) = c_List_Onth(X24,c_plus(X22,X44,tc_nat),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_225]) ).

fof(c_0_3163,axiom,
    ! [X16] : c_div(c_Suc(c_Suc(X16)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    c_0_226 ).

fof(c_0_3164,axiom,
    ! [X24,X2,X60,X44,X4] :
      ( X44 = X60
      | c_List_Onth(c_List_Olist__update(X24,X44,X2,X4),X60,X4) = c_List_Onth(X24,X60,X4) ),
    c_0_227 ).

fof(c_0_3165,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_plus(X16,c_times(X22,X17,tc_nat),tc_nat),X22,tc_nat) = c_plus(X17,c_div(X16,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_228]) ).

fof(c_0_3166,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_plus(X16,c_times(X17,X22,tc_nat),tc_nat),X22,tc_nat) = c_plus(X17,c_div(X16,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_229]) ).

fof(c_0_3167,axiom,
    ! [X6,X19,X4] : c_in(c_Pair(X19,X19,X4,X4),c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)),
    c_0_230 ).

fof(c_0_3168,axiom,
    ! [X48,X16] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X16))),c_Numeral_Onumber__of(X48,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X16,tc_nat),c_Numeral_Onumber__of(X48,tc_nat),tc_nat),
    c_0_231 ).

fof(c_0_3169,axiom,
    ! [X48,X16] : c_div(c_Suc(c_Suc(c_Suc(X16))),c_Numeral_Onumber__of(X48,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X16,tc_nat),c_Numeral_Onumber__of(X48,tc_nat),tc_nat),
    c_0_232 ).

fof(c_0_3170,axiom,
    ! [X103,X88,X13,X14] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X14,X13,X88),X103,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X88,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X103),tc_Message_Omsg),
    c_0_233 ).

fof(c_0_3171,plain,
    ! [X36,X37,X3,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X36,X3)
      | ~ c_Wellfounded__Recursion_Owf(X37,X4)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X37,X36,X4,X3),tc_prod(X4,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_234]) ).

fof(c_0_3172,plain,
    ! [X34,X35,X3,X4] :
      ( ~ c_Relation_Otrans(X34,X3)
      | ~ c_Relation_Otrans(X35,X4)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X35,X34,X4,X3),tc_prod(X4,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_235]) ).

fof(c_0_3173,plain,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X93)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oanalz(c_insert(X88,X89,tc_Message_Omsg)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_236]) ).

fof(c_0_3174,plain,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X28,X4)
      | ~ c_less(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4)
      | c_less(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_237]) ).

fof(c_0_3175,plain,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X28,X4)
      | ~ c_lessequals(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4)
      | c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_238]) ).

fof(c_0_3176,plain,
    ! [X48,X7,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Osemiring(X3)
      | c_times(c_Numeral_Onumber__of(X48,X3),c_plus(X28,X7,X3),X3) = c_plus(c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),c_times(c_Numeral_Onumber__of(X48,X3),X7,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_239]) ).

fof(c_0_3177,plain,
    ! [X48,X7,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oring(X3)
      | c_times(c_Numeral_Onumber__of(X48,X3),c_minus(X28,X7,X3),X3) = c_minus(c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),c_times(c_Numeral_Onumber__of(X48,X3),X7,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_240]) ).

fof(c_0_3178,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Osemiring(X3)
      | c_times(c_plus(X19,X28,X3),c_Numeral_Onumber__of(X48,X3),X3) = c_plus(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_241]) ).

fof(c_0_3179,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oring(X3)
      | c_times(c_minus(X19,X28,X3),c_Numeral_Onumber__of(X48,X3),X3) = c_minus(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_242]) ).

fof(c_0_3180,axiom,
    ! [X2,X4] : c_in(c_Pair(X2,X2,X4,X4),c_Relation_OId,tc_prod(X4,X4)),
    c_0_243 ).

fof(c_0_3181,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_244]) ).

fof(c_0_3182,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(X19,c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_245]) ).

fof(c_0_3183,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(X19,c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_246]) ).

fof(c_0_3184,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_247]) ).

fof(c_0_3185,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_0,X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_248]) ).

fof(c_0_3186,plain,
    ! [X6,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X6,X4)
      | c_less(c_0,c_divide(X6,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X4),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_249]) ).

fof(c_0_3187,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_250]) ).

fof(c_0_3188,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_251]) ).

fof(c_0_3189,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_252]) ).

fof(c_0_3190,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_3191,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_254]) ).

fof(c_0_3192,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_255]) ).

fof(c_0_3193,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X19,X28,X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_256]) ).

fof(c_0_3194,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_less(X28,X19,X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_257]) ).

fof(c_0_3195,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_3196,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_259]) ).

fof(c_0_3197,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X19,X28,X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_260]) ).

fof(c_0_3198,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_lessequals(X28,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_261]) ).

fof(c_0_3199,plain,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4))
      | c_lessequals(X60,X22,X4)
      | c_lessequals(X60,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_262]) ).

fof(c_0_3200,plain,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4))
      | c_lessequals(X16,X44,X4)
      | c_lessequals(X60,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_263]) ).

fof(c_0_3201,axiom,
    ! [X1,X19,X3,X4] : c_snd(c_Pair(X19,X1,X3,X4),X3,X4) = X1,
    c_0_264 ).

fof(c_0_3202,axiom,
    ! [X1,X28,X3,X4] : c_fst(c_Pair(X1,X28,X4,X3),X4,X3) = X1,
    c_0_265 ).

fof(c_0_3203,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(X16,c_Suc(c_Suc(c_Suc(X22))),tc_nat) = c_Divides_Oop_Amod(X16,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X22,tc_nat),tc_nat),
    c_0_266 ).

fof(c_0_3204,axiom,
    ! [X22,X16] : c_div(X16,c_Suc(c_Suc(c_Suc(X22))),tc_nat) = c_div(X16,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X22,tc_nat),tc_nat),
    c_0_267 ).

fof(c_0_3205,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_268]) ).

fof(c_0_3206,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_269]) ).

fof(c_0_3207,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(X19,c_Numeral_Onumber__of(X48,X3),X3),c_times(X28,c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_270]) ).

fof(c_0_3208,plain,
    ! [X48,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_less(c_0,c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_0,X3)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X48,X3),X19,X3),c_times(c_Numeral_Onumber__of(X48,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_271]) ).

fof(c_0_3209,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X17,tc_nat)
      | ~ c_lessequals(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_272]) ).

fof(c_0_3210,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_0,X17,tc_nat)
      | ~ c_lessequals(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_273]) ).

fof(c_0_3211,plain,
    ! [X24,X2,X59,X4] :
      ( ~ c_in(X2,c_List_Oset(c_List_Osublist(X24,X59,X4),X4),X4)
      | c_in(X2,c_List_Oset(X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_274]) ).

fof(c_0_3212,plain,
    ! [X1,X24,X2,X4] :
      ( ~ c_in(X2,c_List_Oset(c_List_Oremove1(X1,X24,X4),X4),X4)
      | c_in(X2,c_List_Oset(X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_275]) ).

fof(c_0_3213,plain,
    ! [X7,X89,X20] :
      ( ~ c_in(X7,c_Message_Oparts(c_union(X20,X89,tc_Message_Omsg)),tc_Message_Omsg)
      | c_in(X7,c_Message_Oparts(X89),tc_Message_Omsg)
      | c_in(X7,c_Message_Oparts(X20),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_276]) ).

fof(c_0_3214,axiom,
    ! [X24,X2,X44,X4] : c_Nat_Osize(c_List_Olist__update(X24,X44,X2,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    c_0_277 ).

fof(c_0_3215,axiom,
    ! [X28,X19,X3,X4] : c_Nat_Osize(c_Pair(X19,X28,X4,X3),tc_prod(X4,X3)) = c_0,
    c_0_278 ).

fof(c_0_3216,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_279]) ).

fof(c_0_3217,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_280]) ).

fof(c_0_3218,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_3219,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_282]) ).

fof(c_0_3220,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_283]) ).

fof(c_0_3221,plain,
    ! [X16,X17,X60] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_minus(c_Suc(c_minus(X60,X17,tc_nat)),X16,tc_nat) = c_minus(c_Suc(X60),c_plus(X17,X16,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_284]) ).

fof(c_0_3222,plain,
    ! [X16,X17,X60] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_minus(X16,c_Suc(c_minus(X60,X17,tc_nat)),tc_nat) = c_minus(c_plus(X16,X17,tc_nat),c_Suc(X60),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_285]) ).

fof(c_0_3223,axiom,
    ! [X26,X1,X24,X2,X4] :
      ( c_append(X24,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) != c_append(X26,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4)
      | X2 = X1 ),
    c_0_286 ).

fof(c_0_3224,axiom,
    ! [X26,X1,X24,X2,X4] :
      ( c_append(X24,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) != c_append(X26,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4)
      | X24 = X26 ),
    c_0_287 ).

fof(c_0_3225,plain,
    ! [X1,X44,X4] :
      ( ~ c_less(X44,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat)
      | c_List_Olist__update(X1,X44,c_List_Onth(X1,X44,X4),X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_288]) ).

fof(c_0_3226,axiom,
    ! [X16] : c_GCD_Ogcd(c_Pair(c_Suc(c_0),X16,tc_nat,tc_nat)) = c_1,
    c_0_289 ).

fof(c_0_3227,axiom,
    ! [X16] : c_GCD_Ogcd(c_Pair(X16,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
    c_0_290 ).

fof(c_0_3228,axiom,
    ! [X12,X48,X28] :
      ( c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | X28 = c_Numeral_Obit_OB0
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X48,X28),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_291 ).

fof(c_0_3229,axiom,
    ! [X1] : c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1,
    c_0_292 ).

fof(c_0_3230,axiom,
    ! [X1] : c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1,
    c_0_293 ).

fof(c_0_3231,axiom,
    ! [X1] : c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1,
    c_0_294 ).

fof(c_0_3232,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(c_0,X28,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_295]) ).

fof(c_0_3233,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(X28,c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_296]) ).

fof(c_0_3234,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(c_0,X28,X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_297]) ).

fof(c_0_3235,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_298]) ).

fof(c_0_3236,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(X28,c_0,X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_299]) ).

fof(c_0_3237,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(c_0,X28,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_300]) ).

fof(c_0_3238,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_301]) ).

fof(c_0_3239,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(c_0,X28,X3)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_302]) ).

fof(c_0_3240,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4)
      | c_less(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_303]) ).

fof(c_0_3241,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4)
      | c_less(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_304]) ).

fof(c_0_3242,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_305]) ).

fof(c_0_3243,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_306]) ).

fof(c_0_3244,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X19,c_0,X3)
      | c_less(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_307]) ).

fof(c_0_3245,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X19,c_0,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(X19,c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_308]) ).

fof(c_0_3246,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_309]) ).

fof(c_0_3247,plain,
    ! [X12,X28,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X19,X3)
      | c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_310]) ).

fof(c_0_3248,axiom,
    ! [X17,X9,X11,X3,X4] : c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_ONumb(X17,X4,X3),
    c_0_311 ).

fof(c_0_3249,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OLeaf(X19,X4,X3),
    c_0_312 ).

fof(c_0_3250,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OScons(X11,X9,X4,X3) != c_Datatype__Universe_OAtom(X19,X4,X3),
    c_0_313 ).

fof(c_0_3251,axiom,
    ! [X17,X9,X11,X3,X4] : c_Datatype__Universe_ONumb(X17,X4,X3) != c_Datatype__Universe_OScons(X11,X9,X4,X3),
    c_0_314 ).

fof(c_0_3252,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OLeaf(X19,X4,X3) != c_Datatype__Universe_OScons(X11,X9,X4,X3),
    c_0_315 ).

fof(c_0_3253,axiom,
    ! [X19,X9,X11,X3,X4] : c_Datatype__Universe_OAtom(X19,X4,X3) != c_Datatype__Universe_OScons(X11,X9,X4,X3),
    c_0_316 ).

fof(c_0_3254,plain,
    ! [X26,X24,X14,X4] :
      ( ~ c_in(X26,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | ~ c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(c_append(X24,X26,X4),c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_317]) ).

fof(c_0_3255,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_OHPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_318]) ).

fof(c_0_3256,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_319]) ).

fof(c_0_3257,plain,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_320]) ).

fof(c_0_3258,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_321]) ).

fof(c_0_3259,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_322]) ).

fof(c_0_3260,axiom,
    ! [X49,X3,X4] : X49 = c_Pair(c_Main_Osurj__pair__1(X49,X4,X3),c_Main_Osurj__pair__2(X49,X4,X3),X4,X3),
    c_0_323 ).

fof(c_0_3261,axiom,
    ! [X1,X3,X4] : c_Pair(c_fst(X1,X4,X3),c_snd(X1,X4,X3),X4,X3) = X1,
    c_0_324 ).

fof(c_0_3262,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat)
      | c_less(c_0,X17,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_325]) ).

fof(c_0_3263,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat)
      | c_less(c_0,X17,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_326]) ).

fof(c_0_3264,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_less(X28,c_0,X3)
      | c_less(c_0,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_327]) ).

fof(c_0_3265,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_0,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_328]) ).

fof(c_0_3266,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_less(X28,c_0,X3)
      | c_less(c_0,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_329]) ).

fof(c_0_3267,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3)
      | c_lessequals(X28,c_0,X3)
      | c_lessequals(c_0,X28,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_330]) ).

fof(c_0_3268,axiom,
    ! [X6,X4] : c_Relation_OImage(c_List_Olistrel(X6,X4),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X4)),tc_List_Olist(X4),tc_List_Olist(X4)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X4)),
    c_0_331 ).

fof(c_0_3269,plain,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X60,X22,X4)
      | ~ c_lessequals(X16,X44,X4)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_332]) ).

fof(c_0_3270,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | c_Numeral_Onumber__of(X2,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_333]) ).

fof(c_0_3271,plain,
    ! [X6,X3,X4] :
      ( ~ c_in(c_Relation_Oconverse(X6,X3,X4),c_Finite__Set_OFinites,tc_set(tc_prod(X4,X3)))
      | c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X3,X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_334]) ).

fof(c_0_3272,axiom,
    ! [X88,X93,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oparts(c_insert(X88,X89,tc_Message_Omsg)),tc_Message_Omsg),
    c_0_335 ).

fof(c_0_3273,plain,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(X2,X1,tc_nat)
      | ~ c_less(c_1,X28,X4)
      | c_less(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_336]) ).

fof(c_0_3274,plain,
    ! [X1,X2,X28,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X28,X4)
      | ~ c_lessequals(X2,X1,tc_nat)
      | c_lessequals(c_Nat_Opower(X28,X2,X4),c_Nat_Opower(X28,X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_337]) ).

fof(c_0_3275,plain,
    ! [X66,X61,X19,X42] :
      ( ~ c_in(X19,c_List_Oset(X66,X42),X42)
      | c_List_Olist__inter(c_List_Olist_OCons(X19,X61,X42),X66,X42) = c_List_Olist_OCons(X19,c_List_Olist__inter(X61,X66,X42),X42) ),
    inference(fof_simplification,[status(thm)],[c_0_338]) ).

fof(c_0_3276,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X2)),X4),X4)
      | ~ c_lessequals(c_Numeral_Onumber__of(X2,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_339]) ).

fof(c_0_3277,plain,
    ! [X22,X16,X44] :
      ( ~ c_lessequals(c_plus(X44,X16,tc_nat),X22,tc_nat)
      | c_List_Otake(X16,c_List_Oupt(X44,X22),tc_nat) = c_List_Oupt(X44,c_plus(X44,X16,tc_nat)) ),
    inference(fof_simplification,[status(thm)],[c_0_340]) ).

fof(c_0_3278,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_0,X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_341]) ).

fof(c_0_3279,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X28,X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_342]) ).

fof(c_0_3280,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_0,X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_343]) ).

fof(c_0_3281,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X28,X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_344]) ).

fof(c_0_3282,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(c_0,X28,X3)
      | ~ c_less(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_3283,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_less(X28,c_0,X3)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_less(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_346]) ).

fof(c_0_3284,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(c_0,X28,X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X12,X3),c_0,X3)
      | c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_347]) ).

fof(c_0_3285,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Oordered__field(X3)
      | ~ c_lessequals(X28,c_0,X3)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,X3),X3)
      | c_lessequals(c_divide(c_Numeral_Onumber__of(X12,X3),X28,X3),c_0,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_3286,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_0,X2,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_349]) ).

fof(c_0_3287,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(X2,c_Main_OMin__gr__iff__1(X14,X2,X4),X4)
      | c_less(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_350]) ).

fof(c_0_3288,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X14,X2,X4),X4)
      | c_lessequals(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_351]) ).

fof(c_0_3289,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(c_Main_OMax__less__iff__1(X14,X2,X4),X2,X4)
      | c_less(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_352]) ).

fof(c_0_3290,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(c_Main_OMax__le__iff__1(X14,X2,X4),X2,X4)
      | c_lessequals(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_353]) ).

fof(c_0_3291,axiom,
    ! [X19,X14,X4] : c_insert(X19,c_minus(X14,c_insert(X19,c_emptyset,X4),tc_set(X4)),X4) = c_insert(X19,X14,X4),
    c_0_354 ).

fof(c_0_3292,axiom,
    ! [X26,X1,X4] : c_List_Orev(c_append(c_List_Orev(X26,X4),c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4),X4) = c_List_Olist_OCons(X1,X26,X4),
    c_0_355 ).

fof(c_0_3293,axiom,
    ! [X19,X13,X14,X4] : c_inter(c_insert(X19,X14,X4),c_insert(X19,X13,X4),X4) = c_insert(X19,c_inter(X14,X13,X4),X4),
    c_0_356 ).

fof(c_0_3294,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X15,X27,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
    c_0_357 ).

fof(c_0_3295,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_0,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_358]) ).

fof(c_0_3296,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(X2,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_359]) ).

fof(c_0_3297,axiom,
    ! [X103,X88,X14] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X14,X88),X103,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X88,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X103),tc_Message_Omsg),
    c_0_360 ).

fof(c_0_3298,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(X16,X22,tc_nat)
      | ~ c_less(c_0,X17,tc_nat)
      | c_less(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_361]) ).

fof(c_0_3299,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(X16,X22,tc_nat)
      | ~ c_less(c_0,X17,tc_nat)
      | c_less(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_362]) ).

fof(c_0_3300,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X15,c_plus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
    c_0_363 ).

fof(c_0_3301,plain,
    ! [X29,X4] :
      ( ~ c_in(X29,c_Relation_OId,tc_prod(X4,X4))
      | X29 = c_Pair(c_Main_OIdE__1(X29,X4),c_Main_OIdE__1(X29,X4),X4,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_3302,plain,
    ! [X22,X16,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X44,X22,X4)
      | c_minus(c_SetInterval_OatLeastLessThan(X44,X16,X4),c_SetInterval_OatLeastLessThan(X44,X22,X4),tc_set(X4)) = c_SetInterval_OatLeastLessThan(X22,X16,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_3303,axiom,
    ! [X16] : c_Divides_Oop_Amod(c_Suc(c_Suc(X16)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X16,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    c_0_366 ).

fof(c_0_3304,axiom,
    ! [X22,X16,X17] : c_Divides_Oop_Amod(c_plus(X16,c_times(X22,X17,tc_nat),tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    c_0_367 ).

fof(c_0_3305,axiom,
    ! [X22,X16,X17] : c_Divides_Oop_Amod(c_plus(X16,c_times(X17,X22,tc_nat),tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    c_0_368 ).

fof(c_0_3306,plain,
    ! [X27,X19,X14,X4] :
      ( ~ c_in(X19,X14,X4)
      | ~ c_in(X27,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(c_List_Olist_OCons(X19,X27,X4),c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_369]) ).

fof(c_0_3307,axiom,
    ! [X17,X44,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_ONumb(X44,X4,X3),X4,X3) = c_Datatype__Universe_ONumb(X44,X4,X3),
    c_0_370 ).

fof(c_0_3308,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_OLeaf(X19,X4,X3),X4,X3) = c_Datatype__Universe_OLeaf(X19,X4,X3),
    c_0_371 ).

fof(c_0_3309,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(X17),c_Datatype__Universe_OAtom(X19,X4,X3),X4,X3) = c_Datatype__Universe_OAtom(X19,X4,X3),
    c_0_372 ).

fof(c_0_3310,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_1,X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_373]) ).

fof(c_0_3311,axiom,
    ! [X26,X1,X24,X4] : c_List_Onth(c_append(X24,c_List_Olist_OCons(X1,X26,X4),X4),c_Nat_Osize(X24,tc_List_Olist(X4)),X4) = X1,
    c_0_374 ).

fof(c_0_3312,plain,
    ! [X12,X48,X28] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X48,X28),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_375]) ).

fof(c_0_3313,axiom,
    ! [X103,X88,X13,X14] : c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X14,X13,X88),X103,tc_Event_Oevent)) = c_insert(X88,c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg),
    c_0_376 ).

fof(c_0_3314,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_less(c_1,c_divide(X28,X19,X4),X4)
      | c_less(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_377]) ).

fof(c_0_3315,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_less(c_1,c_divide(X28,X19,X4),X4)
      | c_less(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_378]) ).

fof(c_0_3316,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(c_1,c_divide(X28,X19,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_379]) ).

fof(c_0_3317,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(c_1,c_divide(X28,X19,X4),X4)
      | c_lessequals(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_3318,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_less(c_divide(X28,X19,X4),c_1,X4)
      | c_less(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_381]) ).

fof(c_0_3319,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_less(c_divide(X28,X19,X4),c_1,X4)
      | c_less(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_382]) ).

fof(c_0_3320,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(c_divide(X28,X19,X4),c_1,X4)
      | c_lessequals(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_383]) ).

fof(c_0_3321,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(c_divide(X28,X19,X4),c_1,X4)
      | c_lessequals(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_384]) ).

fof(c_0_3322,plain,
    ! [X12,X48,X7,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_minus(X7,c_Numeral_Onumber__of(X12,X4),X4),X4) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X12)),X4),X7,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_385]) ).

fof(c_0_3323,axiom,
    ! [X2] :
      ( c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
      | c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1 ),
    c_0_386 ).

fof(c_0_3324,plain,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_387]) ).

fof(c_0_3325,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4)
      | c_less(c_1,c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_388]) ).

fof(c_0_3326,axiom,
    ! [X24,X2,X48,X4] :
      ( c_List_Onth(c_List_Olist_OCons(X2,X24,X4),c_Numeral_Onumber__of(X48,tc_nat),X4) = c_List_Onth(X24,c_minus(c_Numeral_Onumber__of(X48,tc_nat),c_1,tc_nat),X4)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    c_0_389 ).

fof(c_0_3327,axiom,
    ! [X24,X2,X48,X4] :
      ( c_List_Odrop(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X48,tc_nat),c_1,tc_nat),X24,X4)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    c_0_390 ).

fof(c_0_3328,plain,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | c_less(c_0,c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_391]) ).

fof(c_0_3329,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_less(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_392]) ).

fof(c_0_3330,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_less(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_393]) ).

fof(c_0_3331,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_lessequals(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_394]) ).

fof(c_0_3332,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4)
      | c_lessequals(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_395]) ).

fof(c_0_3333,plain,
    ! [X17,X60,X44] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_minus(X44,c_minus(X60,X17,tc_nat),tc_nat) = c_minus(c_plus(X44,X17,tc_nat),X60,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_396]) ).

fof(c_0_3334,plain,
    ! [X17,X60,X44] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_plus(X44,c_minus(X60,X17,tc_nat),tc_nat) = c_minus(c_plus(X44,X60,tc_nat),X17,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_397]) ).

fof(c_0_3335,plain,
    ! [X17,X60,X44] :
      ( ~ c_lessequals(X17,X60,tc_nat)
      | c_plus(c_minus(X60,X17,tc_nat),X44,tc_nat) = c_minus(c_plus(X60,X44,tc_nat),X17,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_398]) ).

fof(c_0_3336,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | X2 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_399]) ).

fof(c_0_3337,axiom,
    ! [X26,X24,X22,X4] : c_List_Onth(c_append(X24,X26,X4),c_plus(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat),X4) = c_List_Onth(X26,X22,X4),
    c_0_400 ).

fof(c_0_3338,plain,
    ! [X7,X28,X19] :
      ( ~ c_less(c_0,X7,tc_nat)
      | c_div(c_times(X19,X7,tc_nat),c_times(X28,X7,tc_nat),tc_nat) = c_div(X19,X28,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_401]) ).

fof(c_0_3339,plain,
    ! [X7,X28,X19] :
      ( ~ c_less(c_0,X7,tc_nat)
      | c_div(c_times(X7,X19,tc_nat),c_times(X7,X28,tc_nat),tc_nat) = c_div(X19,X28,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_402]) ).

fof(c_0_3340,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | ~ c_less(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_403]) ).

fof(c_0_3341,plain,
    ! [X6,X3,X4] :
      ( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X3,X4)))
      | c_in(c_Relation_Oconverse(X6,X3,X4),c_Finite__Set_OFinites,tc_set(tc_prod(X4,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_3342,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_405]) ).

fof(c_0_3343,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_lessequals(X2,c_0,X4)
      | X2 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_406]) ).

fof(c_0_3344,axiom,
    ! [X89,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X89,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X89,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg),
    c_0_407 ).

fof(c_0_3345,plain,
    ! [X1,X2,X44,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X44,tc_nat)
      | c_List_Olist__update(X1,X44,X2,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_408]) ).

fof(c_0_3346,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_less(X2,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_409]) ).

fof(c_0_3347,plain,
    ! [X26,X24,X14,X4] :
      ( ~ c_in(c_append(X24,X26,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X26,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_410]) ).

fof(c_0_3348,plain,
    ! [X26,X24,X14,X4] :
      ( ~ c_in(c_append(X24,X26,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_411]) ).

fof(c_0_3349,plain,
    ! [X2,X27,X14,X4] :
      ( ~ c_in(c_List_Olist_OCons(X2,X27,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X27,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_412]) ).

fof(c_0_3350,axiom,
    ! [X48] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_413 ).

fof(c_0_3351,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_414]) ).

fof(c_0_3352,plain,
    ! [X2,X12] :
      ( ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),tc_nat),tc_nat)
      | c_less(c_0,X2,tc_nat)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_415]) ).

fof(c_0_3353,plain,
    ! [X17,X60,X44] :
      ( ~ c_less(c_plus(X44,X17,tc_nat),X60,tc_nat)
      | c_List_Onth(c_List_Oupt(X44,X60),X17,tc_nat) = c_plus(X44,X17,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_416]) ).

fof(c_0_3354,plain,
    ! [X49,X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_Numeral_Onumber__of(X48,X4),c_times(c_Numeral_Onumber__of(X12,X4),X49,X4),X4) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X48,X12),X4),X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_417]) ).

fof(c_0_3355,plain,
    ! [X49,X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_plus(c_Numeral_Onumber__of(X12,X4),X49,X4),X4) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,X12),X4),X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_418]) ).

fof(c_0_3356,plain,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(X2,c_Finite__Set_OMin(X14,X4),X4)
      | c_less(X2,X25,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_419]) ).

fof(c_0_3357,plain,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(X2,c_Finite__Set_OMin(X14,X4),X4)
      | c_lessequals(X2,X25,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_420]) ).

fof(c_0_3358,plain,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_less(c_Finite__Set_OMax(X14,X4),X2,X4)
      | c_less(X25,X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_421]) ).

fof(c_0_3359,plain,
    ! [X2,X25,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X25,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_lessequals(c_Finite__Set_OMax(X14,X4),X2,X4)
      | c_lessequals(X25,X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_422]) ).

fof(c_0_3360,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    c_0_423 ).

fof(c_0_3361,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4)
      | c_lessequals(c_1,c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_424]) ).

fof(c_0_3362,plain,
    ! [X22,X16,X60,X44,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X60,X44,X4)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X44,X60,X4),c_SetInterval_OatLeastLessThan(X16,X22,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_425]) ).

fof(c_0_3363,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_426]) ).

fof(c_0_3364,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_427]) ).

fof(c_0_3365,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_428]) ).

fof(c_0_3366,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_429]) ).

fof(c_0_3367,plain,
    ! [X2,X14,X4] :
      ( ~ c_lessequals(X14,c_insert(X2,c_emptyset,X4),tc_set(X4))
      | c_insert(X2,X14,X4) = c_insert(X2,c_emptyset,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_430]) ).

fof(c_0_3368,plain,
    ! [X2,X14,X4] :
      ( ~ c_lessequals(X14,c_insert(X2,c_emptyset,X4),tc_set(X4))
      | c_insert(X2,c_emptyset,X4) = c_insert(X2,X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_431]) ).

fof(c_0_3369,plain,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X4),X4)
      | ~ c_lessequals(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_432]) ).

fof(c_0_3370,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_union(X14,X13,X4),X4)
      | c_in(X7,X13,X4)
      | c_in(X7,X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_433]) ).

fof(c_0_3371,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_434]) ).

fof(c_0_3372,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_435]) ).

fof(c_0_3373,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_plus(X19,X7,X4),c_plus(X28,X7,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_436]) ).

fof(c_0_3374,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_plus(X7,X19,X4),c_plus(X7,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_437]) ).

fof(c_0_3375,plain,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X13,X33,tc_set(X4))
      | ~ c_lessequals(X14,X33,tc_set(X4))
      | c_lessequals(c_union(X14,X13,X4),X33,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_438]) ).

fof(c_0_3376,plain,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X33,X13,tc_set(X4))
      | ~ c_lessequals(X33,X14,tc_set(X4))
      | c_lessequals(X33,c_inter(X14,X13,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_439]) ).

fof(c_0_3377,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X13,X4)
      | ~ c_in(X7,c_minus(X14,X13,tc_set(X4)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_440]) ).

fof(c_0_3378,plain,
    ! [X2,X27,X14,X4] :
      ( ~ c_in(c_List_Olist_OCons(X2,X27,X4),c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(X2,X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_441]) ).

fof(c_0_3379,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) != c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_442]) ).

fof(c_0_3380,axiom,
    ! [X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X11,X4,X3),X4,X3) = c_emptyset,
    c_0_443 ).

fof(c_0_3381,axiom,
    ! [X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X11,X4,X3),X4,X3) = c_emptyset,
    c_0_444 ).

fof(c_0_3382,plain,
    ! [X20,X21,X4] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X4))
      | ~ c_in(X21,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_union(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_445]) ).

fof(c_0_3383,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(X2,c_0,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_446]) ).

fof(c_0_3384,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X84),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_447]) ).

fof(c_0_3385,plain,
    ! [X2,X13,X14,X4] :
      ( ~ c_in(X2,X13,X4)
      | ~ c_lessequals(X14,X13,tc_set(X4))
      | c_lessequals(c_insert(X2,X14,X4),X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_448]) ).

fof(c_0_3386,plain,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Power_Orecpower(X3)
      | c_Nat_Opower(c_Numeral_Onumber__of(X12,X3),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3) = c_times(c_Numeral_Onumber__of(X12,X3),c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_449]) ).

fof(c_0_3387,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_plus(X16,X22,tc_nat),tc_nat)
      | c_less(c_0,X22,tc_nat)
      | c_less(c_0,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_450]) ).

fof(c_0_3388,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,X28,X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_1,c_divide(X28,X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_451]) ).

fof(c_0_3389,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_1,c_divide(X28,X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_452]) ).

fof(c_0_3390,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_1,c_divide(X28,X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_453]) ).

fof(c_0_3391,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_1,c_divide(X28,X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_454]) ).

fof(c_0_3392,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,X19,X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_divide(X28,X19,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_455]) ).

fof(c_0_3393,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,X28,X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_divide(X28,X19,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_456]) ).

fof(c_0_3394,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | ~ c_lessequals(X28,X19,X4)
      | c_lessequals(c_divide(X28,X19,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_457]) ).

fof(c_0_3395,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_divide(X28,X19,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_458]) ).

fof(c_0_3396,plain,
    ! [X22,X16,X17] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_3397,plain,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_plus(X17,X16,tc_nat),c_plus(X17,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_460]) ).

fof(c_0_3398,plain,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_3399,plain,
    ! [X22,X16,X17] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_462]) ).

fof(c_0_3400,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMin__gr__iff__1(X14,X2,X4),X14,X4)
      | c_less(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_463]) ).

fof(c_0_3401,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMin__ge__iff__1(X14,X2,X4),X14,X4)
      | c_lessequals(X2,c_Finite__Set_OMin(X14,X4),X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_464]) ).

fof(c_0_3402,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMax__less__iff__1(X14,X2,X4),X14,X4)
      | c_less(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_465]) ).

fof(c_0_3403,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Main_OMax__le__iff__1(X14,X2,X4),X14,X4)
      | c_lessequals(c_Finite__Set_OMax(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_466]) ).

fof(c_0_3404,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_OHPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_467]) ).

fof(c_0_3405,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X44,X15,X4)
      | ~ c_less(X27,X44,X4)
      | c_in(X44,c_SetInterval_OgreaterThanLessThan(X27,X15,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_468]) ).

fof(c_0_3406,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X27,X44,X4)
      | ~ c_lessequals(X44,X15,X4)
      | c_in(X44,c_SetInterval_OgreaterThanAtMost(X27,X15,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_469]) ).

fof(c_0_3407,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X44,X15,X4)
      | ~ c_lessequals(X27,X44,X4)
      | c_in(X44,c_SetInterval_OatLeastLessThan(X27,X15,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_470]) ).

fof(c_0_3408,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_lessequals(X44,X15,X4)
      | ~ c_lessequals(X27,X44,X4)
      | c_in(X44,c_SetInterval_OatLeastAtMost(X27,X15,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_471]) ).

fof(c_0_3409,plain,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X1,X49,X3)
      | ~ c_lessequals(X2,X49,X3)
      | c_lessequals(c_Orderings_Omax(X2,X1,X3),X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_472]) ).

fof(c_0_3410,plain,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,X49,X3)
      | ~ c_lessequals(X2,X1,X3)
      | c_lessequals(X2,c_Orderings_Omin(X1,X49,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_473]) ).

fof(c_0_3411,plain,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X49,X1,X4)
      | ~ c_less(X49,X2,X4)
      | c_less(X49,c_Orderings_Omin(X2,X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_474]) ).

fof(c_0_3412,plain,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X1,X49,X4)
      | ~ c_less(X2,X49,X4)
      | c_less(c_Orderings_Omax(X2,X1,X4),X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_475]) ).

fof(c_0_3413,plain,
    ! [X24,X14,X4] :
      ( ~ c_in(c_Main_Oin__listsI__1(X14,X24,X4),X14,X4)
      | c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_476]) ).

fof(c_0_3414,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_Message_Osynth(c_Message_Oanalz(c_insert(X88,X89,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X89)) ),
    inference(fof_simplification,[status(thm)],[c_0_477]) ).

fof(c_0_3415,plain,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(X19,X13,X4)
      | c_emptyset != c_inter(c_insert(X19,X14,X4),X13,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_478]) ).

fof(c_0_3416,plain,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(X19,X13,X4)
      | c_inter(c_insert(X19,X14,X4),X13,X4) != c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_479]) ).

fof(c_0_3417,plain,
    ! [X28,X13,X14,X4] :
      ( ~ c_in(X28,X14,X4)
      | c_emptyset != c_inter(X14,c_insert(X28,X13,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_480]) ).

fof(c_0_3418,plain,
    ! [X19,X13,X14,X4] :
      ( ~ c_in(X19,X13,X4)
      | c_inter(X13,c_insert(X19,X14,X4),X4) != c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_481]) ).

fof(c_0_3419,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,X2,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_482]) ).

fof(c_0_3420,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,X2,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_483]) ).

fof(c_0_3421,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(X2,c_0,X4)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_484]) ).

fof(c_0_3422,plain,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X4),X22,X4),X4)
      | X22 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_485]) ).

fof(c_0_3423,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X19,X7,X4),c_times(X28,X7,X4),X4) = c_divide(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_486]) ).

fof(c_0_3424,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X7,X19,X4),c_times(X7,X28,X4),X4) = c_divide(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_487]) ).

fof(c_0_3425,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_plus(c_HOL_Oabs(X19,X4),c_HOL_Oabs(X28,X4),X4),X4) = c_plus(c_HOL_Oabs(X19,X4),c_HOL_Oabs(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_488]) ).

fof(c_0_3426,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_divide(X28,X7,X4),X4) = c_divide(c_times(X19,X7,X4),X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_489]) ).

fof(c_0_3427,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_divide(X19,X28,X4),X7,X4) = c_divide(X19,c_times(X28,X7,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_490]) ).

fof(c_0_3428,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | ~ c_in(X28,c_IntDef_ONats,X4)
      | ~ c_in(X19,c_IntDef_ONats,X4)
      | c_in(c_times(X19,X28,X4),c_IntDef_ONats,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_491]) ).

fof(c_0_3429,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | ~ c_in(X28,c_IntDef_ONats,X4)
      | ~ c_in(X19,c_IntDef_ONats,X4)
      | c_in(c_plus(X19,X28,X4),c_IntDef_ONats,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_492]) ).

fof(c_0_3430,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X28,c_IntDef_OInts,X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_times(X19,X28,X4),c_IntDef_OInts,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_493]) ).

fof(c_0_3431,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X28,c_IntDef_OInts,X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_minus(X19,X28,X4),c_IntDef_OInts,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_494]) ).

fof(c_0_3432,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X28,c_IntDef_OInts,X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_plus(X19,X28,X4),c_IntDef_OInts,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_495]) ).

fof(c_0_3433,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_496]) ).

fof(c_0_3434,plain,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Main_OInter__iff__1(X14,X33,X4),X4)
      | c_in(X14,c_Inter(X33,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_497]) ).

fof(c_0_3435,plain,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Main_OInterI__1(X14,X33,X4),X4)
      | c_in(X14,c_Inter(X33,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_498]) ).

fof(c_0_3436,plain,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(X26,X4)
      | ~ c_List_Odistinct(X24,X4)
      | c_inter(c_List_Oset(X24,X4),c_List_Oset(X26,X4),X4) != c_emptyset
      | c_List_Odistinct(c_append(X24,X26,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_499]) ).

fof(c_0_3437,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X13,X4)
      | ~ c_in(X7,X14,X4)
      | c_in(X7,c_inter(X14,X13,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_500]) ).

fof(c_0_3438,axiom,
    ! [X12,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_nat),tc_IntDef_Oint)) ),
    c_0_501 ).

fof(c_0_3439,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    c_0_502 ).

fof(c_0_3440,plain,
    ! [X24,X2,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Oset(c_List_Oremove1(X2,X24,X4),X4) = c_minus(c_List_Oset(X24,X4),c_insert(X2,c_emptyset,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_503]) ).

fof(c_0_3441,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X19,X14,X4) != c_insert(X28,c_emptyset,X4)
      | c_lessequals(X14,c_insert(X28,c_emptyset,X4),tc_set(X4)) ),
    c_0_504 ).

fof(c_0_3442,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X28,c_emptyset,X4) != c_insert(X19,X14,X4)
      | c_lessequals(X14,c_insert(X28,c_emptyset,X4),tc_set(X4)) ),
    c_0_505 ).

fof(c_0_3443,plain,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(tc_set(X4)))
      | ~ c_in(c_Main_Ofinite__Union__1(X14,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Union(X14,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_506]) ).

fof(c_0_3444,axiom,
    ! [X22,X16,X17] : c_minus(c_minus(c_Suc(X16),X22,tc_nat),c_Suc(X17),tc_nat) = c_minus(c_minus(X16,X22,tc_nat),X17,tc_nat),
    c_0_507 ).

fof(c_0_3445,plain,
    ! [X24,X22,X4] :
      ( ~ c_less(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_in(c_List_Onth(X24,X22,X4),c_List_Oset(X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_508]) ).

fof(c_0_3446,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_divide(X28,X7,X4),X19,X4) = c_divide(c_times(X28,X19,X4),X7,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_509]) ).

fof(c_0_3447,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X19,c_divide(X28,X7,X4),X4) = c_divide(c_times(X19,X28,X4),X7,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_510]) ).

fof(c_0_3448,plain,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3)
      | c_less(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_511]) ).

fof(c_0_3449,plain,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3)
      | c_lessequals(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_512]) ).

fof(c_0_3450,plain,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_less(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_513]) ).

fof(c_0_3451,plain,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3)
      | c_lessequals(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_514]) ).

fof(c_0_3452,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4)
      | c_1 = c_Numeral_Onumber__of(X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_515]) ).

fof(c_0_3453,axiom,
    ! [X1,X24,X4] : c_List_Olast(c_append(X24,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4),X4) = X1,
    c_0_516 ).

fof(c_0_3454,axiom,
    ! [X1,X2,X4] : c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4),X4) = X1,
    c_0_517 ).

fof(c_0_3455,plain,
    ! [X7,X14,X4] :
      ( ~ c_in(X7,c_Relation_Odiag(X14,X4),tc_prod(X4,X4))
      | c_in(c_Main_OdiagE__1(X14,X7,X4),X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_518]) ).

fof(c_0_3456,axiom,
    ! [X24,X2,X22,X4] : c_List_Otake(c_Suc(X22),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X22,X24,X4),X4),
    c_0_519 ).

fof(c_0_3457,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_minus(X14,X13,tc_set(X4)),X4)
      | c_in(X7,X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_520]) ).

fof(c_0_3458,axiom,
    ! [X13,X14,X4] : c_Relation_OImage(c_Relation_Odiag(X14,X4),X13,X4,X4) = c_inter(X14,X13,X4),
    c_0_521 ).

fof(c_0_3459,plain,
    ! [X1,X2] :
      ( ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | c_IntDef_OAbs__Integ(X2) != c_IntDef_OAbs__Integ(X1)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_522]) ).

fof(c_0_3460,plain,
    ! [X103,X88,X14] :
      ( ~ c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X14,X88),X103,tc_Event_Oevent)) = c_insert(X88,c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_523]) ).

fof(c_0_3461,axiom,
    ! [X1,X24,X2,X42] :
      ( X2 = X1
      | c_List_Oremove1(X2,c_List_Olist_OCons(X1,X24,X42),X42) = c_List_Olist_OCons(X1,c_List_Oremove1(X2,X24,X42),X42) ),
    c_0_524 ).

fof(c_0_3462,plain,
    ! [X2,X13,X14,X4] :
      ( ~ c_lessequals(c_insert(X2,X14,X4),X13,tc_set(X4))
      | c_lessequals(X14,X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_525]) ).

fof(c_0_3463,plain,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(c_union(X14,X13,X4),X33,tc_set(X4))
      | c_lessequals(X13,X33,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_526]) ).

fof(c_0_3464,plain,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(c_union(X14,X13,X4),X33,tc_set(X4))
      | c_lessequals(X14,X33,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_527]) ).

fof(c_0_3465,plain,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X33,c_inter(X14,X13,X4),tc_set(X4))
      | c_lessequals(X33,X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_528]) ).

fof(c_0_3466,plain,
    ! [X33,X13,X14,X4] :
      ( ~ c_lessequals(X33,c_inter(X14,X13,X4),tc_set(X4))
      | c_lessequals(X33,X14,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_529]) ).

fof(c_0_3467,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(c_1,X22,tc_nat)
      | ~ c_lessequals(c_1,X16,tc_nat)
      | c_lessequals(c_Suc(c_0),c_times(X16,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_530]) ).

fof(c_0_3468,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | ~ c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_531]) ).

fof(c_0_3469,axiom,
    ! [X88,X93,X89] :
      ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X93)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    c_0_532 ).

fof(c_0_3470,axiom,
    ! [X19,X13,X14,X4] : c_union(X14,c_insert(X19,X13,X4),X4) = c_insert(X19,c_union(X14,X13,X4),X4),
    c_0_533 ).

fof(c_0_3471,axiom,
    ! [X19,X33,X13,X4] : c_union(c_insert(X19,X13,X4),X33,X4) = c_insert(X19,c_union(X13,X33,X4),X4),
    c_0_534 ).

fof(c_0_3472,axiom,
    ! [X26,X24,X2,X42] : c_append(c_List_Olist_OCons(X2,X24,X42),X26,X42) = c_List_Olist_OCons(X2,c_append(X24,X26,X42),X42),
    c_0_535 ).

fof(c_0_3473,axiom,
    ! [X26,X24,X2,X42] : c_List_Oitrev(c_List_Olist_OCons(X2,X24,X42),X26,X42) = c_List_Oitrev(X24,c_List_Olist_OCons(X2,X26,X42),X42),
    c_0_536 ).

fof(c_0_3474,axiom,
    ! [X52,X26,X24,X4] : c_append(c_append(X24,X26,X4),X52,X4) = c_append(X24,c_append(X26,X52,X4),X4),
    c_0_537 ).

fof(c_0_3475,plain,
    ! [X19,X14,X4] :
      ( ~ c_in(c_insert(X19,X14,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X14,c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_538]) ).

fof(c_0_3476,plain,
    ! [X20,X21,X4] :
      ( ~ c_in(c_union(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X20,c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_539]) ).

fof(c_0_3477,plain,
    ! [X20,X21,X4] :
      ( ~ c_in(c_union(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X21,c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_540]) ).

fof(c_0_3478,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X16,tc_nat)
      | ~ c_less(c_0,X22,tc_nat)
      | c_less(c_minus(X16,X22,tc_nat),X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_541]) ).

fof(c_0_3479,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X16,tc_nat)
      | ~ c_less(c_1,X22,tc_nat)
      | c_less(c_div(X16,X22,tc_nat),X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_542]) ).

fof(c_0_3480,axiom,
    ! [X24,X22,X16,X4] : c_List_Otake(X22,c_List_Otake(X16,X24,X4),X4) = c_List_Otake(c_Orderings_Omin(X22,X16,tc_nat),X24,X4),
    c_0_543 ).

fof(c_0_3481,axiom,
    ! [X2,X17,X44,X4] : c_List_Otake(X44,c_List_Oreplicate(X17,X2,X4),X4) = c_List_Oreplicate(c_Orderings_Omin(X44,X17,tc_nat),X2,X4),
    c_0_544 ).

fof(c_0_3482,axiom,
    ! [X2,X17,X44,X4] : c_List_Odrop(X44,c_List_Oreplicate(X17,X2,X4),X4) = c_List_Oreplicate(c_minus(X17,X44,tc_nat),X2,X4),
    c_0_545 ).

fof(c_0_3483,axiom,
    ! [X24,X22,X16,X4] : c_List_Odrop(X22,c_List_Odrop(X16,X24,X4),X4) = c_List_Odrop(c_plus(X22,X16,tc_nat),X24,X4),
    c_0_546 ).

fof(c_0_3484,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ class_Orderings_Olinorder(X4)
      | ~ c_less(c_plus(X19,X19,X4),c_0,X4)
      | c_less(X19,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_547]) ).

fof(c_0_3485,plain,
    ! [X2,X13,X14,X4] :
      ( ~ c_lessequals(c_insert(X2,X14,X4),X13,tc_set(X4))
      | c_in(X2,X13,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_548]) ).

fof(c_0_3486,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | ~ c_less(c_0,X16,tc_nat)
      | c_less(c_0,c_times(X16,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_549]) ).

fof(c_0_3487,plain,
    ! [X24,X25,X14,X4] :
      ( ~ c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | ~ c_in(X25,c_List_Oset(X24,X4),X4)
      | c_in(X25,X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_550]) ).

fof(c_0_3488,plain,
    ! [X24,X2,X42] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X2,X24,X42),X42)
      | ~ c_in(X2,c_List_Oset(X24,X42),X42) ),
    inference(fof_simplification,[status(thm)],[c_0_551]) ).

fof(c_0_3489,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanLessThan(X27,X15,X4),X4)
      | c_less(X44,X15,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_552]) ).

fof(c_0_3490,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanLessThan(X27,X15,X4),X4)
      | c_less(X27,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_553]) ).

fof(c_0_3491,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanAtMost(X27,X15,X4),X4)
      | c_lessequals(X44,X15,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_554]) ).

fof(c_0_3492,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThanAtMost(X27,X15,X4),X4)
      | c_less(X27,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_555]) ).

fof(c_0_3493,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastLessThan(X27,X15,X4),X4)
      | c_less(X44,X15,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_556]) ).

fof(c_0_3494,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastLessThan(X27,X15,X4),X4)
      | c_lessequals(X27,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_557]) ).

fof(c_0_3495,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastAtMost(X27,X15,X4),X4)
      | c_lessequals(X44,X15,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_558]) ).

fof(c_0_3496,plain,
    ! [X15,X27,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeastAtMost(X27,X15,X4),X4)
      | c_lessequals(X27,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_559]) ).

fof(c_0_3497,plain,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_Orderings_Omax(X2,X1,X3),X49,X3)
      | c_lessequals(X1,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_560]) ).

fof(c_0_3498,plain,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_Orderings_Omax(X2,X1,X3),X49,X3)
      | c_lessequals(X2,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_561]) ).

fof(c_0_3499,plain,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,c_Orderings_Omin(X1,X49,X3),X3)
      | c_lessequals(X2,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_562]) ).

fof(c_0_3500,plain,
    ! [X49,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,c_Orderings_Omin(X1,X49,X3),X3)
      | c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_563]) ).

fof(c_0_3501,plain,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X49,c_Orderings_Omin(X2,X1,X4),X4)
      | c_less(X49,X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_564]) ).

fof(c_0_3502,plain,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X49,c_Orderings_Omin(X2,X1,X4),X4)
      | c_less(X49,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_565]) ).

fof(c_0_3503,plain,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(c_Orderings_Omax(X2,X1,X4),X49,X4)
      | c_less(X1,X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_566]) ).

fof(c_0_3504,plain,
    ! [X49,X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_less(c_Orderings_Omax(X2,X1,X4),X49,X4)
      | c_less(X2,X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_567]) ).

fof(c_0_3505,plain,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Oanalz(X89),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X93)),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_568]) ).

fof(c_0_3506,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_lessequals(X22,X16,tc_nat)
      | c_NatArith_Oof__nat(c_minus(X16,X22,tc_nat),X4) = c_minus(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_569]) ).

fof(c_0_3507,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | c_in(X7,X13,X4)
      | c_in(X7,c_minus(X14,X13,tc_set(X4)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_570]) ).

fof(c_0_3508,plain,
    ! [X13,X14,X4] :
      ( ~ c_in(c_Main_OsubsetI__1(X14,X13,X4),X13,X4)
      | c_lessequals(X14,X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_571]) ).

fof(c_0_3509,plain,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3)
      | c_less(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_572]) ).

fof(c_0_3510,plain,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(X19,X3),c_Numeral_Onumber__of(X48,X3),X3)
      | c_lessequals(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_573]) ).

fof(c_0_3511,plain,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3)
      | c_less(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_574]) ).

fof(c_0_3512,plain,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_Numeral_Onumber__of(X48,X3),c_uminus(X28,X3),X3)
      | c_lessequals(X28,c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_575]) ).

fof(c_0_3513,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,c_divide(c_1,X28,X4),X4)
      | c_less(c_0,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_576]) ).

fof(c_0_3514,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,c_divide(c_1,X28,X4),X4)
      | c_lessequals(c_0,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_577]) ).

fof(c_0_3515,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_divide(c_1,X28,X4),c_0,X4)
      | c_less(X28,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_578]) ).

fof(c_0_3516,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_divide(c_1,X28,X4),c_0,X4)
      | c_lessequals(X28,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_579]) ).

fof(c_0_3517,plain,
    ! [X2,X13,X14,X4] :
      ( ~ c_in(X2,X13,X4)
      | c_minus(c_insert(X2,X14,X4),X13,tc_set(X4)) = c_minus(X14,X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_580]) ).

fof(c_0_3518,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_581]) ).

fof(c_0_3519,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_582]) ).

fof(c_0_3520,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_minus(X19,X28,X4),c_0,X4)
      | c_less(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_583]) ).

fof(c_0_3521,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_minus(X19,X28,X4),c_0,X4)
      | c_lessequals(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_584]) ).

fof(c_0_3522,axiom,
    ! [X17,X60,X44] : c_minus(c_minus(X44,X60,tc_nat),X17,tc_nat) = c_minus(X44,c_plus(X60,X17,tc_nat),tc_nat),
    c_0_585 ).

fof(c_0_3523,axiom,
    ! [X28,X19] :
      ( X19 = c_0
      | c_div(c_plus(X28,X19,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_plus(c_div(X28,X19,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    c_0_586 ).

fof(c_0_3524,axiom,
    ! [X28,X19] :
      ( X19 = c_0
      | c_div(c_plus(X19,X28,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_plus(c_div(X28,X19,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    c_0_587 ).

fof(c_0_3525,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X2)),X4),X4)
      | ~ c_lessequals(c_Numeral_Onumber__of(X2,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_588]) ).

fof(c_0_3526,axiom,
    ! [X22,X16,X17] :
      ( c_less(c_0,X17,tc_nat)
      | c_lessequals(c_times(X16,X17,tc_nat),c_times(X22,X17,tc_nat),tc_nat) ),
    c_0_589 ).

fof(c_0_3527,axiom,
    ! [X22,X16,X17] :
      ( c_less(c_0,X17,tc_nat)
      | c_lessequals(c_times(X17,X16,tc_nat),c_times(X17,X22,tc_nat),tc_nat) ),
    c_0_590 ).

fof(c_0_3528,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,c_plus(X19,X19,X4),X4)
      | c_lessequals(c_0,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_591]) ).

fof(c_0_3529,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_plus(X19,X19,X4),c_0,X4)
      | c_lessequals(X19,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_592]) ).

fof(c_0_3530,plain,
    ! [X28,X19,X14,X4] :
      ( ~ c_in(X19,c_insert(X28,X14,X4),X4)
      | c_in(X19,X14,X4)
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_593]) ).

fof(c_0_3531,plain,
    ! [X26,X1,X2,X42] :
      ( ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X26,X42),X42)
      | c_List_Oop_Amem(X2,X26,X42)
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_594]) ).

fof(c_0_3532,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_595]) ).

fof(c_0_3533,axiom,
    ! [X19,X13,X14,X4] :
      ( c_emptyset != c_inter(c_insert(X19,X14,X4),X13,X4)
      | c_emptyset = c_inter(X14,X13,X4) ),
    c_0_596 ).

fof(c_0_3534,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(c_insert(X19,X14,X4),X13,X4) != c_emptyset
      | c_inter(X14,X13,X4) = c_emptyset ),
    c_0_597 ).

fof(c_0_3535,axiom,
    ! [X28,X13,X14,X4] :
      ( c_emptyset != c_inter(X14,c_insert(X28,X13,X4),X4)
      | c_emptyset = c_inter(X14,X13,X4) ),
    c_0_598 ).

fof(c_0_3536,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(X13,c_insert(X19,X14,X4),X4) != c_emptyset
      | c_inter(X13,X14,X4) = c_emptyset ),
    c_0_599 ).

fof(c_0_3537,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_inter(X14,X13,X4),X4)
      | c_in(X7,X13,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_600]) ).

fof(c_0_3538,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,c_inter(X14,X13,X4),X4)
      | c_in(X7,X14,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_601]) ).

fof(c_0_3539,plain,
    ! [X22] :
      ( ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | X22 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_602]) ).

fof(c_0_3540,axiom,
    ! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X1,
    c_0_603 ).

fof(c_0_3541,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(X2,X4) != c_1
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_604]) ).

fof(c_0_3542,axiom,
    ! [X24,X2,X42] : c_List_Orev(c_List_Olist_OCons(X2,X24,X42),X42) = c_append(c_List_Orev(X24,X42),c_List_Olist_OCons(X2,c_List_Olist_ONil,X42),X42),
    c_0_605 ).

fof(c_0_3543,plain,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_606]) ).

fof(c_0_3544,plain,
    ! [X84,X48] :
      ( ~ c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_607]) ).

fof(c_0_3545,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(c_Suc(c_0),c_times(X16,X22,tc_nat),tc_nat)
      | c_lessequals(c_1,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_608]) ).

fof(c_0_3546,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(c_Suc(c_0),c_times(X16,X22,tc_nat),tc_nat)
      | c_lessequals(c_1,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_609]) ).

fof(c_0_3547,plain,
    ! [X2,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Finite__Set_OMin(c_insert(X2,X14,X3),X3) = c_Orderings_Omin(X2,c_Finite__Set_OMin(X14,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_610]) ).

fof(c_0_3548,plain,
    ! [X2,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Finite__Set_OMax(c_insert(X2,X14,X3),X3) = c_Orderings_Omax(X2,c_Finite__Set_OMax(X14,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_611]) ).

fof(c_0_3549,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_612]) ).

fof(c_0_3550,axiom,
    ! [X19,X13,X14,X4] :
      ( c_emptyset != c_inter(X14,X13,X4)
      | c_in(X19,X13,X4)
      | c_emptyset = c_inter(c_insert(X19,X14,X4),X13,X4) ),
    c_0_613 ).

fof(c_0_3551,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(X14,X13,X4) != c_emptyset
      | c_in(X19,X13,X4)
      | c_inter(c_insert(X19,X14,X4),X13,X4) = c_emptyset ),
    c_0_614 ).

fof(c_0_3552,axiom,
    ! [X28,X13,X14,X4] :
      ( c_emptyset != c_inter(X14,X13,X4)
      | c_in(X28,X14,X4)
      | c_emptyset = c_inter(X14,c_insert(X28,X13,X4),X4) ),
    c_0_615 ).

fof(c_0_3553,axiom,
    ! [X19,X13,X14,X4] :
      ( c_inter(X13,X14,X4) != c_emptyset
      | c_in(X19,X13,X4)
      | c_inter(X13,c_insert(X19,X14,X4),X4) = c_emptyset ),
    c_0_616 ).

fof(c_0_3554,plain,
    ! [X24,X22,X44,X4] :
      ( ~ c_less(X44,X22,tc_nat)
      | c_List_Onth(c_List_Otake(X22,X24,X4),X44,X4) = c_List_Onth(X24,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_617]) ).

fof(c_0_3555,plain,
    ! [X2,X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(X2,X14,X4)
      | c_Finite__Set_Ocard(c_insert(X2,X14,X4),X4) = c_Suc(c_Finite__Set_Ocard(X14,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_618]) ).

fof(c_0_3556,plain,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_619]) ).

fof(c_0_3557,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_minus(X22,X16,tc_nat),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_620]) ).

fof(c_0_3558,plain,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(c_append(X24,X26,X4),X4)
      | c_inter(c_List_Oset(X24,X4),c_List_Oset(X26,X4),X4) = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_621]) ).

fof(c_0_3559,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_OHPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_622]) ).

fof(c_0_3560,axiom,
    ! [X66,X61,X19,X42] :
      ( c_in(X19,c_List_Oset(X66,X42),X42)
      | c_List_Olist__inter(c_List_Olist_OCons(X19,X61,X42),X66,X42) = c_List_Olist__inter(X61,X66,X42) ),
    c_0_623 ).

fof(c_0_3561,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_times(X16,X22,tc_nat),tc_nat)
      | c_less(c_0,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_624]) ).

fof(c_0_3562,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,c_times(X16,X22,tc_nat),tc_nat)
      | c_less(c_0,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_625]) ).

fof(c_0_3563,plain,
    ! [X49,X12] :
      ( ~ c_lessequals(X12,c_minus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(X12,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_626]) ).

fof(c_0_3564,plain,
    ! [X49,X12] :
      ( ~ c_less(X12,c_plus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(X12,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_627]) ).

fof(c_0_3565,plain,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(c_Main_OUnion__iff__1(X14,X33,X4),X33,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_628]) ).

fof(c_0_3566,plain,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(c_Main_OUnionE__1(X14,X33,X4),X33,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_629]) ).

fof(c_0_3567,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_630]) ).

fof(c_0_3568,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_631]) ).

fof(c_0_3569,axiom,
    ! [X26,X1,X24,X4] :
      ( c_List_Orev(X24,X4) != c_List_Olist_OCons(X1,X26,X4)
      | X24 = c_append(c_List_Orev(X26,X4),c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) ),
    c_0_632 ).

fof(c_0_3570,plain,
    ! [X2,X14,X4] :
      ( ~ c_in(c_0,X14,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X14,X4) = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_633]) ).

fof(c_0_3571,axiom,
    ! [X100,X102] : c_Nat_Osize(c_Message_Omsg_OMPair(X102,X100),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X102,tc_Message_Omsg),c_Nat_Osize(X100,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
    c_0_634 ).

fof(c_0_3572,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X2)),X4),X4)
      | c_lessequals(c_Numeral_Onumber__of(X2,X4),c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_635]) ).

fof(c_0_3573,axiom,
    ! [X12,X48] : c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X48,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_636 ).

fof(c_0_3574,plain,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(X14,c_Main_OUnion__iff__1(X14,X33,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_637]) ).

fof(c_0_3575,plain,
    ! [X33,X14,X4] :
      ( ~ c_in(X14,c_Union(X33,X4),X4)
      | c_in(X14,c_Main_OUnionE__1(X14,X33,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_638]) ).

fof(c_0_3576,plain,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4),c_0,X4)
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_639]) ).

fof(c_0_3577,plain,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(tc_set(X4)))
      | c_in(c_Main_Ofinite__Union__1(X14,X4),X14,tc_set(X4))
      | c_in(c_Union(X14,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_640]) ).

fof(c_0_3578,plain,
    ! [X60,X44] :
      ( ~ c_lessequals(X44,X60,tc_nat)
      | c_List_Oupt(X44,c_Suc(X60)) = c_append(c_List_Oupt(X44,X60),c_List_Olist_OCons(X60,c_List_Olist_ONil,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_641]) ).

fof(c_0_3579,plain,
    ! [X93,X89] :
      ( ~ c_in(X93,c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat)
      | c_in(X93,c_Message_OkeysFor(X89),tc_nat)
      | c_in(c_Message_Omsg_OKey(v_sko__uhi(X89,X93)),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_642]) ).

fof(c_0_3580,axiom,
    ! [X2,X13,X14,X4] :
      ( c_in(X2,X14,X4)
      | c_minus(X14,c_insert(X2,X13,X4),tc_set(X4)) = c_minus(X14,X13,tc_set(X4)) ),
    c_0_643 ).

fof(c_0_3581,plain,
    ! [X2,X12] :
      ( ~ c_less(c_0,X2,tc_nat)
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_644]) ).

fof(c_0_3582,axiom,
    ! [X24,X2,X42] :
      ( c_in(X2,c_List_Oset(X24,X42),X42)
      | c_List_Oremdups(c_List_Olist_OCons(X2,X24,X42),X42) = c_List_Olist_OCons(X2,c_List_Oremdups(X24,X42),X42) ),
    c_0_645 ).

fof(c_0_3583,plain,
    ! [X48] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_646]) ).

fof(c_0_3584,plain,
    ! [X103,X28,X14] :
      ( ~ c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X28,X14))),c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_647]) ).

fof(c_0_3585,plain,
    ! [X24,X22,X4] :
      ( ~ c_less(X22,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | c_List_Olast(c_List_Odrop(X22,X24,X4),X4) = c_List_Olast(X24,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_648]) ).

fof(c_0_3586,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4)
      | X2 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_649]) ).

fof(c_0_3587,plain,
    ! [X25,X33,X14,X4] :
      ( ~ c_in(X25,X33,tc_set(X4))
      | ~ c_in(X14,c_Inter(X33,X4),X4)
      | c_in(X14,X25,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_650]) ).

fof(c_0_3588,axiom,
    ! [X2,X22,X4] :
      ( X22 = c_0
      | c_List_Otl(c_List_Oreplicate(X22,X2,X4),X4) = c_List_Oreplicate(c_minus(X22,c_1,tc_nat),X2,X4) ),
    c_0_651 ).

fof(c_0_3589,plain,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),tc_set(X4))
      | c_lessequals(X13,X14,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_652]) ).

fof(c_0_3590,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(X19,c_0,X4),c_times(X28,c_0,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_653]) ).

fof(c_0_3591,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(c_0,X19,X4),c_times(c_0,X28,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_654]) ).

fof(c_0_3592,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_655]) ).

fof(c_0_3593,plain,
    ! [X12,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | X19 = c_divide(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_656]) ).

fof(c_0_3594,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0
      | c_times(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_657]) ).

fof(c_0_3595,plain,
    ! [X12,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0
      | c_divide(c_times(X19,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_658]) ).

fof(c_0_3596,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | X28 = c_times(c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3)
      | c_Numeral_Onumber__of(X12,X3) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_659]) ).

fof(c_0_3597,axiom,
    ! [X24,X14,X4] :
      ( c_in(X24,c_List_Olists(X14,X4),tc_List_Olist(X4))
      | c_in(c_Main_Oin__listsI__1(X14,X24,X4),c_List_Oset(X24,X4),X4) ),
    c_0_660 ).

fof(c_0_3598,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_661]) ).

fof(c_0_3599,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X87,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_662]) ).

fof(c_0_3600,plain,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_663]) ).

fof(c_0_3601,plain,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_664]) ).

fof(c_0_3602,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_665]) ).

fof(c_0_3603,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(X87,c_Message_Osynth(X89),tc_Message_Omsg)
      | ~ c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_666]) ).

fof(c_0_3604,plain,
    ! [X88,X93,X89] :
      ( ~ c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_667]) ).

fof(c_0_3605,plain,
    ! [X22,X16,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,X19,X4)
      | c_Nat_Opower(X19,X16,X4) != c_Nat_Opower(X19,X22,X4)
      | X16 = X22 ),
    inference(fof_simplification,[status(thm)],[c_0_668]) ).

fof(c_0_3606,plain,
    ! [X47,X13,X4] :
      ( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_minus(X13,X47,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_669]) ).

fof(c_0_3607,plain,
    ! [X1,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X1,X14,X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Orderings_Omax(X1,c_Finite__Set_OMin(X14,X3),X3) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_670]) ).

fof(c_0_3608,plain,
    ! [X1,X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X1,X14,X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | X14 = c_emptyset
      | c_Orderings_Omin(X1,c_Finite__Set_OMax(X14,X3),X3) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_671]) ).

fof(c_0_3609,plain,
    ! [X88,X93,X89] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X93,X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_672]) ).

fof(c_0_3610,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X2,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_lessequals(c_Finite__Set_OMin(X14,X4),X2,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_673]) ).

fof(c_0_3611,plain,
    ! [X2,X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X2,X14,X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_lessequals(X2,c_Finite__Set_OMax(X14,X4),X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_674]) ).

fof(c_0_3612,axiom,
    ! [X1,X22,X4] : c_append(c_List_Otake(X22,X1,X4),c_List_Odrop(X22,X1,X4),X4) = X1,
    c_0_675 ).

fof(c_0_3613,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_less(c_0,c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_676]) ).

fof(c_0_3614,axiom,
    ! [X84] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    c_0_677 ).

fof(c_0_3615,plain,
    ! [X25,X33,X14,X4] :
      ( ~ c_in(X14,X25,X4)
      | ~ c_in(X25,X33,tc_set(X4))
      | c_in(X14,c_Union(X33,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_678]) ).

fof(c_0_3616,plain,
    ! [X24,X2,X42] :
      ( ~ c_in(X2,c_List_Oset(X24,X42),X42)
      | c_List_Oremdups(c_List_Olist_OCons(X2,X24,X42),X42) = c_List_Oremdups(X24,X42) ),
    inference(fof_simplification,[status(thm)],[c_0_679]) ).

fof(c_0_3617,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X84),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_680]) ).

fof(c_0_3618,plain,
    ! [X20,X21,X4] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_inter(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_681]) ).

fof(c_0_3619,plain,
    ! [X20,X21,X4] :
      ( ~ c_in(X21,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_inter(X21,X20,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_682]) ).

fof(c_0_3620,plain,
    ! [X19,X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_insert(X19,X14,X4),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_683]) ).

fof(c_0_3621,axiom,
    ! [X24,X2,X48,X4] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_List_Odrop(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_OCons(X2,X24,X4) ),
    c_0_684 ).

fof(c_0_3622,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ class_Orderings_Olinorder(X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_plus(X19,X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_685]) ).

fof(c_0_3623,plain,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_686]) ).

fof(c_0_3624,plain,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_divide(c_times(c_0,c_Numeral_Onumber__of(X12,X3),X3),c_Numeral_Onumber__of(X12,X3),X3) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_687]) ).

fof(c_0_3625,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_688]) ).

fof(c_0_3626,axiom,
    ! [X13,X14,X4] : c_uminus(c_union(X14,X13,X4),tc_set(X4)) = c_inter(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),X4),
    c_0_689 ).

fof(c_0_3627,axiom,
    ! [X13,X14,X4] : c_uminus(c_inter(X14,X13,X4),tc_set(X4)) = c_union(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),X4),
    c_0_690 ).

fof(c_0_3628,axiom,
    ! [X93,X89] :
      ( c_in(X93,c_Message_OkeysFor(c_Message_Oanalz(X89)),tc_nat)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X93),c_Message_Oanalz(X89),tc_Message_Omsg) ),
    c_0_691 ).

fof(c_0_3629,axiom,
    ! [X26,X24,X4] : c_Nat_Osize(c_append(X24,X26,X4),tc_List_Olist(X4)) = c_plus(c_Nat_Osize(X24,tc_List_Olist(X4)),c_Nat_Osize(X26,tc_List_Olist(X4)),tc_nat),
    c_0_692 ).

fof(c_0_3630,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X28,X4)
      | c_less(c_0,c_divide(c_1,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_693]) ).

fof(c_0_3631,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,X28,X4)
      | c_lessequals(c_0,c_divide(c_1,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_694]) ).

fof(c_0_3632,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X28,c_0,X4)
      | c_less(c_divide(c_1,X28,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_695]) ).

fof(c_0_3633,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(X28,c_0,X4)
      | c_lessequals(c_divide(c_1,X28,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_696]) ).

fof(c_0_3634,axiom,
    ! [X1,X2] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) != c_0
      | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    c_0_697 ).

fof(c_0_3635,plain,
    ! [X1,X2] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_698]) ).

fof(c_0_3636,axiom,
    ! [X1,X2] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_699 ).

fof(c_0_3637,plain,
    ! [X1,X2] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_700]) ).

fof(c_0_3638,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_minus(X19,X28,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_701]) ).

fof(c_0_3639,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_minus(X19,X28,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_702]) ).

fof(c_0_3640,plain,
    ! [X28,X19,X4] :
      ( ~ c_in(X28,c_insert(X19,c_emptyset,X4),X4)
      | X28 = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_703]) ).

fof(c_0_3641,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_Nat_Opower(c_HOL_Oabs(X2,X4),c_Numeral_Onumber__of(X12,tc_nat),X4) = c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_704]) ).

fof(c_0_3642,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,X19,X4)
      | c_lessequals(c_0,c_plus(X19,X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_705]) ).

fof(c_0_3643,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_lessequals(c_plus(X19,X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_706]) ).

fof(c_0_3644,plain,
    ! [X22,X44] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_minus(X22,c_Suc(X44),tc_nat),X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_707]) ).

fof(c_0_3645,plain,
    ! [X17,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | c_minus(c_insert(X17,c_emptyset,X4),c_SetInterval_OlessThan(X17,X4),tc_set(X4)) = c_insert(X17,c_emptyset,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_708]) ).

fof(c_0_3646,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_709]) ).

fof(c_0_3647,axiom,
    ! [X33,X14,X4] :
      ( c_in(X14,c_Inter(X33,X4),X4)
      | c_in(c_Main_OInter__iff__1(X14,X33,X4),X33,tc_set(X4)) ),
    c_0_710 ).

fof(c_0_3648,axiom,
    ! [X33,X14,X4] :
      ( c_in(X14,c_Inter(X33,X4),X4)
      | c_in(c_Main_OInterI__1(X14,X33,X4),X33,tc_set(X4)) ),
    c_0_711 ).

fof(c_0_3649,plain,
    ! [X28,X19,X14,X4] :
      ( ~ c_in(X19,X14,X4)
      | c_in(X19,c_insert(X28,X14,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_712]) ).

fof(c_0_3650,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X13,X4)
      | c_in(X7,c_union(X14,X13,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_713]) ).

fof(c_0_3651,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | c_in(X7,c_union(X14,X13,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_714]) ).

fof(c_0_3652,plain,
    ! [X26,X1,X2,X42] :
      ( ~ c_List_Oop_Amem(X2,X26,X42)
      | c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X26,X42),X42) ),
    inference(fof_simplification,[status(thm)],[c_0_715]) ).

fof(c_0_3653,axiom,
    ! [X1,X46,X4] : c_Public_Okeymode_Okeymode__rec(X46,X1,c_Public_Okeymode_OEncryption,X4) = X1,
    c_0_716 ).

fof(c_0_3654,axiom,
    ! [X1,X45,X4] : c_Public_Okeymode_Okeymode__rec(X1,X45,c_Public_Okeymode_OSignature,X4) = X1,
    c_0_717 ).

fof(c_0_3655,axiom,
    ! [X1,X46,X4] : c_Public_Okeymode_Okeymode__case(X46,X1,c_Public_Okeymode_OEncryption,X4) = X1,
    c_0_718 ).

fof(c_0_3656,axiom,
    ! [X1,X45,X4] : c_Public_Okeymode_Okeymode__case(X1,X45,c_Public_Okeymode_OSignature,X4) = X1,
    c_0_719 ).

fof(c_0_3657,axiom,
    ! [X1,X4] : c_Relation_OImage(c_Relation_OId,X1,X4,X4) = X1,
    c_0_720 ).

fof(c_0_3658,axiom,
    ! [X1,X46,X4] : c_Numeral_Obit_Obit__rec(X46,X1,c_Numeral_Obit_OB1,X4) = X1,
    c_0_721 ).

fof(c_0_3659,axiom,
    ! [X1,X45,X4] : c_Numeral_Obit_Obit__rec(X1,X45,c_Numeral_Obit_OB0,X4) = X1,
    c_0_722 ).

fof(c_0_3660,axiom,
    ! [X1,X46,X4] : c_Numeral_Obit_Obit__case(X46,X1,c_Numeral_Obit_OB1,X4) = X1,
    c_0_723 ).

fof(c_0_3661,axiom,
    ! [X1,X45,X4] : c_Numeral_Obit_Obit__case(X1,X45,c_Numeral_Obit_OB0,X4) = X1,
    c_0_724 ).

fof(c_0_3662,axiom,
    ! [X1,X46,X4] : c_Extraction_Osumbool_Osumbool__rec(X46,X1,c_Extraction_Osumbool_ORight,X4) = X1,
    c_0_725 ).

fof(c_0_3663,axiom,
    ! [X1,X45,X4] : c_Extraction_Osumbool_Osumbool__rec(X1,X45,c_Extraction_Osumbool_OLeft,X4) = X1,
    c_0_726 ).

fof(c_0_3664,axiom,
    ! [X1,X46,X4] : c_Extraction_Osumbool_Osumbool__case(X46,X1,c_Extraction_Osumbool_ORight,X4) = X1,
    c_0_727 ).

fof(c_0_3665,axiom,
    ! [X1,X45,X4] : c_Extraction_Osumbool_Osumbool__case(X1,X45,c_Extraction_Osumbool_OLeft,X4) = X1,
    c_0_728 ).

fof(c_0_3666,plain,
    ! [X60,X44] : ~ c_less(c_plus(X60,X44,tc_nat),X44,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_729]) ).

fof(c_0_3667,plain,
    ! [X60,X44] : ~ c_less(c_plus(X44,X60,tc_nat),X44,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_730]) ).

fof(c_0_3668,axiom,
    ! [X86,X3,X4] : c_Relation_OImage(X86,c_emptyset,X3,X4) = c_emptyset,
    c_0_731 ).

fof(c_0_3669,axiom,
    ! [X26,X3,X4] : c_List_Ozip(c_List_Olist_ONil,X26,X4,X3) = c_List_Olist_ONil,
    c_0_732 ).

fof(c_0_3670,axiom,
    ! [X24,X83,X42] : c_List_Ozip(X24,c_List_Olist_ONil,X42,X83) = c_List_Olist_ONil,
    c_0_733 ).

fof(c_0_3671,plain,
    ! [X1,X22,X44,X4] :
      ( ~ c_less(X44,X22,tc_nat)
      | c_List_Onth(c_List_Oreplicate(X22,X1,X4),X44,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_734]) ).

fof(c_0_3672,axiom,
    ! [X48,X44,X42] : c_List_Olist__update(c_List_Olist_ONil,X44,X48,X42) = c_List_Olist_ONil,
    c_0_735 ).

fof(c_0_3673,axiom,
    ! [X11,X3,X4] : c_Datatype__Universe_Ontrunc(c_0,X11,X4,X3) = c_emptyset,
    c_0_736 ).

fof(c_0_3674,axiom,
    ! [X3,X4] : c_Sum__Type_OPlus(c_UNIV,c_UNIV,X4,X3) = c_UNIV,
    c_0_737 ).

fof(c_0_3675,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_738]) ).

fof(c_0_3676,plain,
    ! [X1,X22] :
      ( ~ c_lessequals(X22,X1,tc_nat)
      | c_plus(X22,c_minus(X1,X22,tc_nat),tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_739]) ).

fof(c_0_3677,plain,
    ! [X1,X22] :
      ( ~ c_lessequals(X22,X1,tc_nat)
      | c_plus(c_minus(X1,X22,tc_nat),X22,tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_740]) ).

fof(c_0_3678,plain,
    ! [X1,X22] :
      ( ~ c_lessequals(X1,X22,tc_nat)
      | c_minus(X22,c_minus(X22,X1,tc_nat),tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_741]) ).

fof(c_0_3679,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_times(X19,X28,X4),X4) = c_times(c_HOL_Oinverse(X19,X4),c_HOL_Oinverse(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_742]) ).

fof(c_0_3680,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_HOL_Oabs(c_divide(X19,X28,X4),X4) = c_divide(c_HOL_Oabs(X19,X4),c_HOL_Oabs(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_743]) ).

fof(c_0_3681,plain,
    ! [X22,X44] :
      ( ~ c_lessequals(c_1,X44,tc_nat)
      | c_lessequals(c_Suc(c_0),c_Nat_Opower(X44,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_744]) ).

fof(c_0_3682,plain,
    ! [X22] :
      ( ~ c_less(c_0,c_Nat_Opower(c_0,X22,tc_nat),tc_nat)
      | X22 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_745]) ).

fof(c_0_3683,plain,
    ! [X2,X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Numeral_Onumber__of(X12,tc_nat) != c_0
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_746]) ).

fof(c_0_3684,axiom,
    ! [X13,X14,X4] : c_minus(c_minus(X14,X13,tc_set(X4)),X13,tc_set(X4)) = c_minus(X14,X13,tc_set(X4)),
    c_0_747 ).

fof(c_0_3685,axiom,
    ! [X13,X14,X4] : c_Union(c_union(X14,X13,tc_set(X4)),X4) = c_union(c_Union(X14,X4),c_Union(X13,X4),X4),
    c_0_748 ).

fof(c_0_3686,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OlessThan(X2,X4),c_SetInterval_OlessThan(X1,X4),tc_set(X4))
      | c_lessequals(X2,X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_749]) ).

fof(c_0_3687,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X4),c_SetInterval_OgreaterThan(X1,X4),tc_set(X4))
      | c_lessequals(X1,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_750]) ).

fof(c_0_3688,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(c_SetInterval_OatMost(X2,X4),c_SetInterval_OatMost(X1,X4),tc_set(X4))
      | c_lessequals(X2,X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_751]) ).

fof(c_0_3689,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(c_SetInterval_OatLeast(X2,X4),c_SetInterval_OatLeast(X1,X4),tc_set(X4))
      | c_lessequals(X1,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_752]) ).

fof(c_0_3690,plain,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_0,c_minus(X22,X16,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_753]) ).

fof(c_0_3691,axiom,
    ! [X26,X24,X4] : c_List_Oconcat(c_append(X24,X26,tc_List_Olist(X4)),X4) = c_append(c_List_Oconcat(X24,X4),c_List_Oconcat(X26,X4),X4),
    c_0_754 ).

fof(c_0_3692,plain,
    ! [X1,X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_times(X1,X22,tc_nat),X22,tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_755]) ).

fof(c_0_3693,plain,
    ! [X1,X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(c_times(X22,X1,tc_nat),X22,tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_756]) ).

fof(c_0_3694,axiom,
    ! [X1,X4] :
      ( X1 = c_List_Olist_ONil
      | c_append(c_List_Obutlast(X1,X4),c_List_Olist_OCons(c_List_Olast(X1,X4),c_List_Olist_ONil,X4),X4) = X1 ),
    c_0_757 ).

fof(c_0_3695,plain,
    ! [X28,X19] :
      ( ~ c_less(c_0,X28,tc_IntDef_Oint)
      | c_less(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_758]) ).

fof(c_0_3696,plain,
    ! [X28,X19] :
      ( ~ c_less(X28,c_0,tc_IntDef_Oint)
      | c_less(X28,c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_759]) ).

fof(c_0_3697,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_760]) ).

fof(c_0_3698,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_lessequals(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_761]) ).

fof(c_0_3699,plain,
    ! [X49,X12] :
      ( ~ c_less(X12,X49,tc_IntDef_Oint)
      | c_lessequals(X12,c_minus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_762]) ).

fof(c_0_3700,plain,
    ! [X49,X12] :
      ( ~ c_lessequals(X12,X49,tc_IntDef_Oint)
      | c_less(X12,c_plus(X49,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_763]) ).

fof(c_0_3701,plain,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X4),X4)
      | c_lessequals(c_Numeral_Onumber__of(X2,X4),c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_764]) ).

fof(c_0_3702,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X54,tc_List_Olist(X4)) != c_Nat_Osize(X53,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X54 = X53 ),
    c_0_765 ).

fof(c_0_3703,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X54,tc_List_Olist(X4)) != c_Nat_Osize(X53,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X24 = X26 ),
    c_0_766 ).

fof(c_0_3704,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X54 = X53 ),
    c_0_767 ).

fof(c_0_3705,axiom,
    ! [X26,X24,X53,X54,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_Nat_Osize(X26,tc_List_Olist(X4))
      | c_append(X24,X54,X4) != c_append(X26,X53,X4)
      | X24 = X26 ),
    c_0_768 ).

fof(c_0_3706,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_0,c_plus(X16,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_769]) ).

fof(c_0_3707,plain,
    ! [X22,X16] :
      ( ~ c_less(c_0,X16,tc_nat)
      | c_less(c_0,c_plus(X16,X22,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_770]) ).

fof(c_0_3708,plain,
    ! [X28,X19] :
      ( ~ c_less(c_0,X28,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_771]) ).

fof(c_0_3709,plain,
    ! [X28,X19] :
      ( ~ c_less(X28,c_0,tc_IntDef_Oint)
      | c_lessequals(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_772]) ).

fof(c_0_3710,plain,
    ! [X7,X13,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | ~ c_lessequals(X14,X13,tc_set(X4))
      | c_in(X7,X13,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_773]) ).

fof(c_0_3711,plain,
    ! [X2,X22] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_774]) ).

fof(c_0_3712,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat)
      | c_less(c_0,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_775]) ).

fof(c_0_3713,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_uminus(c_LOrder_Omeet(X19,X28,X4),X4) = c_LOrder_Ojoin(c_uminus(X19,X4),c_uminus(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_776]) ).

fof(c_0_3714,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_uminus(c_LOrder_Ojoin(X19,X28,X4),X4) = c_LOrder_Omeet(c_uminus(X19,X4),c_uminus(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_777]) ).

fof(c_0_3715,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_plus(X19,X28,X4),X4) = c_plus(c_uminus(X19,X4),c_uminus(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_778]) ).

fof(c_0_3716,plain,
    ! [X6,X29,X4] :
      ( ~ c_in(X29,X6,tc_prod(X4,X4))
      | c_in(X29,c_Transitive__Closure_Ortrancl(X6,X4),tc_prod(X4,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_779]) ).

fof(c_0_3717,axiom,
    ! [X13,X14,X4] : c_Pow(c_inter(X14,X13,X4),X4) = c_inter(c_Pow(X14,X4),c_Pow(X13,X4),tc_set(X4)),
    c_0_780 ).

fof(c_0_3718,axiom,
    ! [X13,X14,X4] : c_List_Olists(c_inter(X14,X13,X4),X4) = c_inter(c_List_Olists(X14,X4),c_List_Olists(X13,X4),tc_List_Olist(X4)),
    c_0_781 ).

fof(c_0_3719,plain,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X13,X14,tc_set(X4))
      | c_lessequals(c_uminus(X14,tc_set(X4)),c_uminus(X13,tc_set(X4)),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_782]) ).

fof(c_0_3720,axiom,
    ! [X103,X88,X14] :
      ( c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X14,X88),X103,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X103) ),
    c_0_783 ).

fof(c_0_3721,plain,
    ! [X7,X14,X4] :
      ( ~ c_in(X7,X14,X4)
      | ~ c_in(X7,c_uminus(X14,tc_set(X4)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_784]) ).

fof(c_0_3722,plain,
    ! [X49,X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_uminus(c_Numeral_Onumber__of(X12,X4),X4),X49,X4) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X12),X4),X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_785]) ).

fof(c_0_3723,axiom,
    ! [X13,X14,X4] : c_uminus(c_minus(X14,X13,tc_set(X4)),tc_set(X4)) = c_union(c_uminus(X14,tc_set(X4)),X13,X4),
    c_0_786 ).

fof(c_0_3724,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_NatArith_Oof__nat(c_times(X16,X22,tc_nat),X4) = c_times(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_787]) ).

fof(c_0_3725,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_NatArith_Oof__nat(c_plus(X16,X22,tc_nat),X4) = c_plus(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_788]) ).

fof(c_0_3726,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_times(X12,X49,tc_IntDef_Oint),X4) = c_times(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_789]) ).

fof(c_0_3727,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_minus(X12,X49,tc_IntDef_Oint),X4) = c_minus(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_790]) ).

fof(c_0_3728,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_plus(X12,X49,tc_IntDef_Oint),X4) = c_plus(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_791]) ).

fof(c_0_3729,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X84),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_792]) ).

fof(c_0_3730,plain,
    ! [X49,X12] :
      ( ~ c_less(X12,X49,tc_IntDef_Oint)
      | ~ c_less(c_0,X49,tc_IntDef_Oint)
      | c_less(c_IntDef_Onat(X12),c_IntDef_Onat(X49),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_793]) ).

fof(c_0_3731,plain,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(X7,c_times(X28,X7,X4),X4) = c_divide(c_1,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_794]) ).

fof(c_0_3732,plain,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(X7,c_times(X7,X28,X4),X4) = c_divide(c_1,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_795]) ).

fof(c_0_3733,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_uminus(X28,X4),c_uminus(X19,X4),X4)
      | c_less(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_796]) ).

fof(c_0_3734,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_uminus(X28,X4),c_uminus(X19,X4),X4)
      | c_lessequals(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_797]) ).

fof(c_0_3735,axiom,
    ! [X84] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)),
    c_0_798 ).

fof(c_0_3736,plain,
    ! [X12,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_799]) ).

fof(c_0_3737,plain,
    ! [X2,X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_Parity_Oeven(X22,tc_nat)
      | c_Nat_Opower(c_uminus(X2,X4),X22,X4) = c_uminus(c_Nat_Opower(X2,X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_800]) ).

fof(c_0_3738,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_801]) ).

fof(c_0_3739,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4)
      | c_lessequals(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_802]) ).

fof(c_0_3740,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4)
      | c_less(X12,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_803]) ).

fof(c_0_3741,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4)
      | c_lessequals(X12,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_804]) ).

fof(c_0_3742,axiom,
    ! [X89,X20] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X89,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X89,tc_Message_Omsg)),
    c_0_805 ).

fof(c_0_3743,axiom,
    ! [X13,X14,X4] : c_union(X14,c_minus(X13,X14,tc_set(X4)),X4) = c_union(X14,X13,X4),
    c_0_806 ).

fof(c_0_3744,axiom,
    ! [X13,X14,X4] : c_union(c_minus(X13,X14,tc_set(X4)),X14,X4) = c_union(X13,X14,X4),
    c_0_807 ).

fof(c_0_3745,plain,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X19,X4),X22,X4),X4)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_808]) ).

fof(c_0_3746,axiom,
    ! [X26,X24,X4] : c_List_Oset(c_append(X24,X26,X4),X4) = c_union(c_List_Oset(X24,X4),c_List_Oset(X26,X4),X4),
    c_0_809 ).

fof(c_0_3747,axiom,
    ! [X26,X24,X4] : c_List_Orev(c_append(X24,X26,X4),X4) = c_append(c_List_Orev(X26,X4),c_List_Orev(X24,X4),X4),
    c_0_810 ).

fof(c_0_3748,plain,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X19,X4),X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_811]) ).

fof(c_0_3749,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_1 != c_Numeral_Onumber__of(X1,X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_812]) ).

fof(c_0_3750,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X87,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_813]) ).

fof(c_0_3751,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(c_Message_Oanalz(X89)),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_814]) ).

fof(c_0_3752,axiom,
    ! [X88,X93,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X93,X88),X89,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X93),c_Message_OkeysFor(X89),tc_nat),
    c_0_815 ).

fof(c_0_3753,plain,
    ! [X103,X7] :
      ( ~ c_in(X7,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X103)),tc_Message_Omsg)
      | c_in(X7,c_Event_Oused(X103),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_816]) ).

fof(c_0_3754,plain,
    ! [X24,X2,X42] :
      ( ~ c_List_Odistinct(X24,X42)
      | c_List_Odistinct(c_List_Olist_OCons(X2,X24,X42),X42)
      | c_in(X2,c_List_Oset(X24,X42),X42) ),
    inference(fof_simplification,[status(thm)],[c_0_817]) ).

fof(c_0_3755,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X15,X27,tc_IntDef_Oint)),
    c_0_818 ).

fof(c_0_3756,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X27,X15,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X15,X27,tc_IntDef_Oint)),
    c_0_819 ).

fof(c_0_3757,plain,
    ! [X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X19,X4),c_0,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_820]) ).

fof(c_0_3758,axiom,
    ! [X84,X48] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_Numeral_Onumber__of(X84,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X84)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_821 ).

fof(c_0_3759,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omax(X2,c_Orderings_Omax(X2,X1,X3),X3) = c_Orderings_Omax(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_822]) ).

fof(c_0_3760,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omin(X2,c_Orderings_Omin(X2,X1,X3),X3) = c_Orderings_Omin(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_823]) ).

fof(c_0_3761,axiom,
    ! [X13,X14,X4] :
      ( c_in(c_Main_OsubsetI__1(X14,X13,X4),X14,X4)
      | c_lessequals(X14,X13,tc_set(X4)) ),
    c_0_824 ).

fof(c_0_3762,plain,
    ! [X88,X89] :
      ( ~ c_in(c_Message_Omsg_OHash(X88),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_825]) ).

fof(c_0_3763,axiom,
    ! [X2,X22,X42] : c_List_Oreplicate(c_Suc(X22),X2,X42) = c_List_Olist_OCons(X2,c_List_Oreplicate(X22,X2,X42),X42),
    c_0_826 ).

fof(c_0_3764,axiom,
    ! [X24,X2,X22,X4] : c_List_Onth(c_List_Olist_OCons(X2,X24,X4),c_Suc(X22),X4) = c_List_Onth(X24,X22,X4),
    c_0_827 ).

fof(c_0_3765,axiom,
    ! [X24,X2,X22,X4] : c_List_Odrop(c_Suc(X22),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Odrop(X22,X24,X4),
    c_0_828 ).

fof(c_0_3766,axiom,
    ! [X2,X12] :
      ( c_Numeral_Onumber__of(X12,tc_nat) != c_0
      | c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X12,tc_nat),tc_nat),tc_nat) ),
    c_0_829 ).

fof(c_0_3767,axiom,
    ! [X65,X19,X4] : c_Nat_Osize(c_List_Olist_OCons(X19,X65,X4),tc_List_Olist(X4)) = c_plus(c_Nat_Osize(X65,tc_List_Olist(X4)),c_Suc(c_0),tc_nat),
    c_0_830 ).

fof(c_0_3768,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X2,X4),X4) = c_uminus(c_Numeral_Onumber__of(X2,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_831]) ).

fof(c_0_3769,plain,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_Numeral_Onumber__of(X2,X4) = c_Numeral_Onumber__of(X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_832]) ).

fof(c_0_3770,plain,
    ! [X2,X22] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | ~ c_less(c_0,X22,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X2,X22,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_833]) ).

fof(c_0_3771,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | ~ c_less(c_0,X1,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_834]) ).

fof(c_0_3772,axiom,
    ! [X24,X22,X4] : c_Nat_Osize(c_List_Otake(X22,X24,X4),tc_List_Olist(X4)) = c_Orderings_Omin(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat),
    c_0_835 ).

fof(c_0_3773,axiom,
    ! [X24,X22,X4] : c_Nat_Osize(c_List_Odrop(X22,X24,X4),tc_List_Olist(X4)) = c_minus(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat),
    c_0_836 ).

fof(c_0_3774,plain,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_minus(c_Numeral_Onumber__of(X48,X4),c_1,X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_837]) ).

fof(c_0_3775,plain,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(X19,X3),c_1,X3)
      | c_less(c_uminus(c_1,X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_838]) ).

fof(c_0_3776,plain,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(X19,X3),c_1,X3)
      | c_lessequals(c_uminus(c_1,X3),X19,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_839]) ).

fof(c_0_3777,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X2,X4) = c_uminus(c_divide(c_1,X2,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_840]) ).

fof(c_0_3778,plain,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_1,c_uminus(X28,X3),X3)
      | c_less(X28,c_uminus(c_1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_841]) ).

fof(c_0_3779,plain,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_1,c_uminus(X28,X3),X3)
      | c_lessequals(X28,c_uminus(c_1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_842]) ).

fof(c_0_3780,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_843]) ).

fof(c_0_3781,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_844]) ).

fof(c_0_3782,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_845]) ).

fof(c_0_3783,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_846]) ).

fof(c_0_3784,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_847]) ).

fof(c_0_3785,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_848]) ).

fof(c_0_3786,plain,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(c_uminus(c_1,X3),X19,X3)
      | c_less(c_uminus(X19,X3),c_1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_849]) ).

fof(c_0_3787,plain,
    ! [X19,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(c_uminus(c_1,X3),X19,X3)
      | c_lessequals(c_uminus(X19,X3),c_1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_850]) ).

fof(c_0_3788,plain,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_less(X28,c_uminus(c_1,X3),X3)
      | c_less(c_1,c_uminus(X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_851]) ).

fof(c_0_3789,plain,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | ~ c_lessequals(X28,c_uminus(c_1,X3),X3)
      | c_lessequals(c_1,c_uminus(X28,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_852]) ).

fof(c_0_3790,axiom,
    ! [X13,X14,X4] : c_union(X14,c_union(X13,X14,X4),X4) = c_union(X13,X14,X4),
    c_0_853 ).

fof(c_0_3791,axiom,
    ! [X2,X14,X4] : c_insert(X2,c_insert(X2,X14,X4),X4) = c_insert(X2,X14,X4),
    c_0_854 ).

fof(c_0_3792,axiom,
    ! [X29,X22] : c_Nat_Opower(X29,c_Suc(X22),tc_nat) = c_times(X29,c_Nat_Opower(X29,X22,tc_nat),tc_nat),
    c_0_855 ).

fof(c_0_3793,axiom,
    ! [X22,X16] : c_times(c_Suc(X16),X22,tc_nat) = c_plus(X22,c_times(X16,X22,tc_nat),tc_nat),
    c_0_856 ).

fof(c_0_3794,axiom,
    ! [X22,X16] : c_times(X16,c_Suc(X22),tc_nat) = c_plus(X16,c_times(X16,X22,tc_nat),tc_nat),
    c_0_857 ).

fof(c_0_3795,axiom,
    ! [X29,X22] : c_Nat_Opower(X29,c_Suc(X22),tc_IntDef_Oint) = c_times(X29,c_Nat_Opower(X29,X22,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_858 ).

fof(c_0_3796,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_uminus(X28,X4),X4) = c_uminus(c_divide(X19,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_859]) ).

fof(c_0_3797,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_uminus(X19,tc_IntDef_Oint),c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_860 ).

fof(c_0_3798,axiom,
    ! [X19,X13,X4] : c_Union(c_insert(X19,X13,tc_set(X4)),X4) = c_union(X19,c_Union(X13,X4),X4),
    c_0_861 ).

fof(c_0_3799,axiom,
    ! [X19,X13,X4] : c_Inter(c_insert(X19,X13,tc_set(X4)),X4) = c_inter(X19,c_Inter(X13,X4),X4),
    c_0_862 ).

fof(c_0_3800,axiom,
    ! [X67,X14,X42] : c_List_Olistset(c_List_Olist_OCons(X14,X67,tc_set(X42)),X42) = c_List_Oset__Cons(X14,c_List_Olistset(X67,X42),X42),
    c_0_863 ).

fof(c_0_3801,axiom,
    ! [X24,X2,X42] : c_List_Oconcat(c_List_Olist_OCons(X2,X24,tc_List_Olist(X42)),X42) = c_append(X2,c_List_Oconcat(X24,X42),X42),
    c_0_864 ).

fof(c_0_3802,plain,
    ! [X14,X4] :
      ( ~ c_in(c_Pow(X14,X4),c_Finite__Set_OFinites,tc_set(tc_set(X4)))
      | c_in(X14,c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_865]) ).

fof(c_0_3803,plain,
    ! [X12,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,c_Numeral_Onumber__of(X12,tc_nat),X4) != c_0
      | c_less(c_0,c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_866]) ).

fof(c_0_3804,axiom,
    ! [X22] : c_plus(X22,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(X22)),
    c_0_867 ).

fof(c_0_3805,axiom,
    ! [X22] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X22,tc_nat) = c_Suc(c_Suc(X22)),
    c_0_868 ).

fof(c_0_3806,axiom,
    ! [X2,X14,X4] :
      ( c_in(c_0,X14,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X14,X4) = c_List_Olist_ONil ),
    c_0_869 ).

fof(c_0_3807,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_plus(X28,X19,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_Divides_Oop_Amod(X28,X19,tc_IntDef_Oint),
    c_0_870 ).

fof(c_0_3808,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_plus(X19,X28,tc_IntDef_Oint),X19,tc_IntDef_Oint) = c_Divides_Oop_Amod(X28,X19,tc_IntDef_Oint),
    c_0_871 ).

fof(c_0_3809,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),
    c_0_872 ).

fof(c_0_3810,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    c_0_873 ).

fof(c_0_3811,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_plus(X16,X22,tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    c_0_874 ).

fof(c_0_3812,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_plus(X22,X16,tc_nat),X22,tc_nat) = c_Divides_Oop_Amod(X16,X22,tc_nat),
    c_0_875 ).

fof(c_0_3813,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_876]) ).

fof(c_0_3814,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_times(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X1,tc_nat)
      | c_Parity_Oeven(X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_877]) ).

fof(c_0_3815,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,X84),tc_nat) ),
    c_0_878 ).

fof(c_0_3816,plain,
    ! [X14,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X3))
      | c_lessequals(c_Finite__Set_OMin(X14,X3),c_Finite__Set_OMax(X14,X3),X3)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_879]) ).

fof(c_0_3817,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oring(X4)
      | c_times(X19,c_uminus(X28,X4),X4) = c_uminus(c_times(X19,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_880]) ).

fof(c_0_3818,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oring(X4)
      | c_times(c_uminus(X19,X4),X28,X4) = c_uminus(c_times(X19,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_881]) ).

fof(c_0_3819,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_uminus(X19,X4),X28,X4) = c_uminus(c_divide(X19,X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_882]) ).

fof(c_0_3820,plain,
    ! [X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_883]) ).

fof(c_0_3821,plain,
    ! [X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_884]) ).

fof(c_0_3822,plain,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X12,tc_nat),tc_nat)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_885]) ).

fof(c_0_3823,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X2,X1,X4)
      | c_lessequals(c_SetInterval_OlessThan(X2,X4),c_SetInterval_OlessThan(X1,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_886]) ).

fof(c_0_3824,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_lessequals(X1,X2,X4)
      | c_lessequals(c_SetInterval_OgreaterThan(X2,X4),c_SetInterval_OgreaterThan(X1,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_887]) ).

fof(c_0_3825,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X2,X1,X4)
      | c_lessequals(c_SetInterval_OatMost(X2,X4),c_SetInterval_OatMost(X1,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_888]) ).

fof(c_0_3826,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X1,X2,X4)
      | c_lessequals(c_SetInterval_OatLeast(X2,X4),c_SetInterval_OatLeast(X1,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_889]) ).

fof(c_0_3827,axiom,
    ! [X24,X2,X48,X4] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_List_Onth(c_List_Olist_OCons(X2,X24,X4),c_Numeral_Onumber__of(X48,tc_nat),X4) = X2 ),
    c_0_890 ).

fof(c_0_3828,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg)
      | c_Message_Oparts(c_insert(X88,X89,tc_Message_Omsg)) = c_Message_Oparts(X89) ),
    inference(fof_simplification,[status(thm)],[c_0_891]) ).

fof(c_0_3829,plain,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X4,X4),X4)
      | c_Wellfounded__Recursion_Oacyclic(X6,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_892]) ).

fof(c_0_3830,plain,
    ! [X24,X22,X4] :
      ( ~ c_List_Odistinct(c_List_Orotate(X22,X24,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_893]) ).

fof(c_0_3831,plain,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(c_append(X24,X26,X4),X4)
      | c_List_Odistinct(X26,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_894]) ).

fof(c_0_3832,plain,
    ! [X26,X24,X4] :
      ( ~ c_List_Odistinct(c_append(X24,X26,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_895]) ).

fof(c_0_3833,plain,
    ! [X24,X2,X42] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X2,X24,X42),X42)
      | c_List_Odistinct(X24,X42) ),
    inference(fof_simplification,[status(thm)],[c_0_896]) ).

fof(c_0_3834,axiom,
    ! [X24,X2,X48,X4] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_List_Otake(c_Numeral_Onumber__of(X48,tc_nat),c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olist_ONil ),
    c_0_897 ).

fof(c_0_3835,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X2)),X4),X4)
      | c_lessequals(c_Numeral_Onumber__of(X2,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_898]) ).

fof(c_0_3836,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(X48,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_899]) ).

fof(c_0_3837,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(X48,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_900]) ).

fof(c_0_3838,plain,
    ! [X93,X89] :
      ( ~ c_in(X93,c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat)
      | c_in(X93,c_Message_OkeysFor(X89),tc_nat)
      | X93 = c_Message_OinvKey(v_sko__uhi(X89,X93)) ),
    inference(fof_simplification,[status(thm)],[c_0_901]) ).

fof(c_0_3839,axiom,
    ! [X26,X24,X4] :
      ( X24 = c_List_Olist_ONil
      | c_List_Otl(c_append(X24,X26,X4),X4) = c_append(c_List_Otl(X24,X4),X26,X4) ),
    c_0_902 ).

fof(c_0_3840,axiom,
    ! [X24,X2,X42] :
      ( X24 = c_List_Olist_ONil
      | c_List_Obutlast(c_List_Olist_OCons(X2,X24,X42),X42) = c_List_Olist_OCons(X2,c_List_Obutlast(X24,X42),X42) ),
    c_0_903 ).

fof(c_0_3841,axiom,
    ! [X2,X22] :
      ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,tc_IntDef_Oint),X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | X2 = c_0 ),
    c_0_904 ).

fof(c_0_3842,axiom,
    ! [X24,X2,X42] : c_List_Oset(c_List_Olist_OCons(X2,X24,X42),X42) = c_insert(X2,c_List_Oset(X24,X42),X42),
    c_0_905 ).

fof(c_0_3843,axiom,
    ! [X2,X22] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X2,tc_IntDef_Oint),X22,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_906 ).

fof(c_0_3844,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_OrderedGroup_Opprt(X19,X4),c_OrderedGroup_Opprt(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_907]) ).

fof(c_0_3845,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_OrderedGroup_Onprt(X19,X4),c_OrderedGroup_Onprt(X28,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_908]) ).

fof(c_0_3846,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(X19,X28,X4)
      | c_less(c_uminus(X28,X4),c_uminus(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_909]) ).

fof(c_0_3847,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(X19,X28,X4)
      | c_lessequals(c_uminus(X28,X4),c_uminus(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_910]) ).

fof(c_0_3848,plain,
    ! [X2,X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X12,X2),X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_911]) ).

fof(c_0_3849,plain,
    ! [X1,X22,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X22,tc_nat)
      | c_List_Otake(X22,X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_912]) ).

fof(c_0_3850,axiom,
    ! [X1,X22,X4] :
      ( c_Divides_Oop_Amod(X22,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) != c_0
      | c_List_Orotate(X22,X1,X4) = X1 ),
    c_0_913 ).

fof(c_0_3851,plain,
    ! [X24,X22,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat)
      | c_List_Odrop(X22,X24,X4) = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_914]) ).

fof(c_0_3852,axiom,
    ! [X2] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_915 ).

fof(c_0_3853,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_916]) ).

fof(c_0_3854,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(X16,X22,tc_nat)
      | c_less(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_917]) ).

fof(c_0_3855,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_NatArith_Oof__nat(X16,X4),c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_918]) ).

fof(c_0_3856,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(X12,X49,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_919]) ).

fof(c_0_3857,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(X12,X49,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X12,X4),c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_920]) ).

fof(c_0_3858,plain,
    ! [X13,X14,X4] :
      ( ~ c_in(X14,c_Pow(X13,X4),tc_set(X4))
      | c_lessequals(X14,X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_921]) ).

fof(c_0_3859,plain,
    ! [X1,X2,X23,X4] :
      ( ~ c_Infinite__Set_Oatmost__one(X23,X4)
      | ~ c_in(X1,X23,X4)
      | ~ c_in(X2,X23,X4)
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_922]) ).

fof(c_0_3860,plain,
    ! [X1,X22,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),c_1,tc_nat)
      | c_List_Orotate(X22,X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_923]) ).

fof(c_0_3861,axiom,
    ! [X16,X60,X44] : c_List_Odrop(X16,c_List_Oupt(X44,X60),tc_nat) = c_List_Oupt(c_plus(X44,X16,tc_nat),X60),
    c_0_924 ).

fof(c_0_3862,plain,
    ! [X1] :
      ( ~ c_less(c_0,X1,tc_nat)
      | c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_925]) ).

fof(c_0_3863,plain,
    ! [X103,X25] :
      ( ~ c_in(c_Message_Omsg_ONonce(X25),c_Event_Oused(X103),tc_Message_Omsg)
      | ~ c_lessequals(v_sko__urX(X103),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_926]) ).

fof(c_0_3864,plain,
    ! [X2,X22] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X22,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_927]) ).

fof(c_0_3865,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat)
      | c_Parity_Oeven(X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_928]) ).

fof(c_0_3866,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4)
      | c_0 = c_Numeral_Onumber__of(X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_929]) ).

fof(c_0_3867,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_930]) ).

fof(c_0_3868,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_931]) ).

fof(c_0_3869,plain,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X13,X14,tc_set(X4))
      | ~ c_lessequals(X14,X13,tc_set(X4))
      | X14 = X13 ),
    inference(fof_simplification,[status(thm)],[c_0_932]) ).

fof(c_0_3870,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Event_Oused(X89),tc_Message_Omsg)
      | c_in(X88,c_Event_Oused(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_933]) ).

fof(c_0_3871,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Event_Oused(X89),tc_Message_Omsg)
      | c_in(X87,c_Event_Oused(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_934]) ).

fof(c_0_3872,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_935]) ).

fof(c_0_3873,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X87,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_936]) ).

fof(c_0_3874,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oparts(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_937]) ).

fof(c_0_3875,plain,
    ! [X87,X88,X89] :
      ( ~ c_in(c_Message_Omsg_OMPair(X88,X87),c_Message_Oparts(X89),tc_Message_Omsg)
      | c_in(X87,c_Message_Oparts(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_938]) ).

fof(c_0_3876,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,c_HOL_Oinverse(X19,X4),X4)
      | c_less(c_0,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_939]) ).

fof(c_0_3877,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_HOL_Oinverse(X19,X4),c_0,X4)
      | c_lessequals(X19,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_940]) ).

fof(c_0_3878,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,c_HOL_Oinverse(X19,X4),X4)
      | c_lessequals(c_0,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_941]) ).

fof(c_0_3879,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_HOL_Oinverse(X19,X4),c_0,X4)
      | c_less(X19,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_942]) ).

fof(c_0_3880,plain,
    ! [X13,X14,X4] :
      ( ~ c_less(X14,X13,tc_set(X4))
      | ~ c_lessequals(X13,X14,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_943]) ).

fof(c_0_3881,plain,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Pow(X14,X4),c_Finite__Set_OFinites,tc_set(tc_set(X4))) ),
    inference(fof_simplification,[status(thm)],[c_0_944]) ).

fof(c_0_3882,plain,
    ! [X24,X2,X42] : ~ c_List_Onull(c_List_Olist_OCons(X2,X24,X42),X42),
    inference(fof_simplification,[status(thm)],[c_0_945]) ).

fof(c_0_3883,plain,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),X4),X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_946]) ).

fof(c_0_3884,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_divide(X19,X28,X4),X4) = c_divide(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_947]) ).

fof(c_0_3885,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,X7,X4) != c_divide(X28,X7,X4)
      | X19 = X28
      | X7 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_948]) ).

fof(c_0_3886,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X7,X19,X4) != c_divide(X7,X28,X4)
      | X19 = X28
      | X7 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_949]) ).

fof(c_0_3887,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OlessThan(X17,X4),X4)
      | c_less(X44,X17,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_950]) ).

fof(c_0_3888,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OgreaterThan(X17,X4),X4)
      | c_less(X17,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_951]) ).

fof(c_0_3889,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatMost(X17,X4),X4)
      | c_lessequals(X44,X17,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_952]) ).

fof(c_0_3890,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_in(X44,c_SetInterval_OatLeast(X17,X4),X4)
      | c_lessequals(X17,X44,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_953]) ).

fof(c_0_3891,plain,
    ! [X22,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X22,X4),X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_954]) ).

fof(c_0_3892,plain,
    ! [X48] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X48,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X48,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_955]) ).

fof(c_0_3893,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4)
      | c_Numeral_Onumber__of(X2,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_956]) ).

fof(c_0_3894,axiom,
    ! [X9,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X9),c_Message_Oparts(X89),tc_Message_Omsg),
    c_0_957 ).

fof(c_0_3895,axiom,
    ! [X9,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X9),c_Message_Oparts(X89),tc_Message_Omsg),
    c_0_958 ).

fof(c_0_3896,axiom,
    ! [X93,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X93),c_Message_Oparts(X89),tc_Message_Omsg),
    c_0_959 ).

fof(c_0_3897,axiom,
    ! [X88,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X88),c_Message_Oparts(X89),tc_Message_Omsg),
    c_0_960 ).

fof(c_0_3898,axiom,
    ! [X111,X89] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X111),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X111),c_Message_Oparts(X89),tc_Message_Omsg),
    c_0_961 ).

fof(c_0_3899,axiom,
    ! [X9,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X9),c_Message_Oanalz(X89),tc_Message_Omsg),
    c_0_962 ).

fof(c_0_3900,axiom,
    ! [X9,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X9),c_Message_Oanalz(X89),tc_Message_Omsg),
    c_0_963 ).

fof(c_0_3901,axiom,
    ! [X88,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X88),c_Message_Oanalz(X89),tc_Message_Omsg),
    c_0_964 ).

fof(c_0_3902,axiom,
    ! [X111,X89] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X111),X89,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X111),c_Message_Oanalz(X89),tc_Message_Omsg),
    c_0_965 ).

fof(c_0_3903,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_uminus(X19,X4),c_0,X4)
      | c_less(c_0,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_966]) ).

fof(c_0_3904,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_uminus(X19,X4),c_0,X4)
      | c_lessequals(c_0,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_967]) ).

fof(c_0_3905,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_0,c_uminus(X19,X4),X4)
      | c_less(X19,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_968]) ).

fof(c_0_3906,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_0,c_uminus(X19,X4),X4)
      | c_lessequals(X19,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_969]) ).

fof(c_0_3907,axiom,
    ! [X6,X4] : c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X4,X4)),X4) = c_Transitive__Closure_Ortrancl(X6,X4),
    c_0_970 ).

fof(c_0_3908,axiom,
    ! [X86,X4] : c_Transitive__Closure_Ortrancl(c_union(X86,c_Relation_OId,tc_prod(X4,X4)),X4) = c_Transitive__Closure_Ortrancl(X86,X4),
    c_0_971 ).

fof(c_0_3909,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_0,c_NatArith_Oof__nat(X22,X4),X4)
      | c_less(c_0,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_972]) ).

fof(c_0_3910,plain,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_IntDef_Oof__int(X12,X4),c_0,X4)
      | c_less(X12,c_0,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_973]) ).

fof(c_0_3911,plain,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_IntDef_Oof__int(X12,X4),c_0,X4)
      | c_lessequals(X12,c_0,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_974]) ).

fof(c_0_3912,plain,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,c_IntDef_Oof__int(X49,X4),X4)
      | c_less(c_0,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_975]) ).

fof(c_0_3913,plain,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,c_IntDef_Oof__int(X49,X4),X4)
      | c_lessequals(c_0,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_976]) ).

fof(c_0_3914,plain,
    ! [X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Finite__Set_OMin(X14,X4),X14,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_977]) ).

fof(c_0_3915,plain,
    ! [X14,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_in(c_Finite__Set_OMax(X14,X4),X14,X4)
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_978]) ).

fof(c_0_3916,plain,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X14,X13,tc_set(X4))
      | c_in(X14,c_Pow(X13,X4),tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_979]) ).

fof(c_0_3917,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_minus(X19,X28,X4),X4) = c_minus(X28,X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_980]) ).

fof(c_0_3918,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X19,X7,X4) != c_times(X28,X7,X4)
      | X19 = X28
      | X7 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_981]) ).

fof(c_0_3919,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X7,X19,X4) != c_times(X7,X28,X4)
      | X19 = X28
      | X7 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_982]) ).

fof(c_0_3920,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X28,X14))),c_Event_Oused(X103),tc_Message_Omsg),
    c_0_983 ).

fof(c_0_3921,axiom,
    ! [X28,X14] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X28,X14))),c_Event_OinitState(X14),tc_Message_Omsg),
    c_0_984 ).

fof(c_0_3922,axiom,
    ! [X24,X22,X4] : c_List_Orotate(c_Suc(X22),X24,X4) = c_List_Orotate1(c_List_Orotate(X22,X24,X4),X4),
    c_0_985 ).

fof(c_0_3923,axiom,
    ! [X24,X4] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X24,X4),tc_List_Olist(X4)),c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat),
    c_0_986 ).

fof(c_0_3924,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
      | c_plus(X28,X19,X4) != c_plus(X7,X19,X4)
      | X28 = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_987]) ).

fof(c_0_3925,plain,
    ! [X7,X28,X19,X4] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
      | c_plus(X19,X28,X4) != c_plus(X19,X7,X4)
      | X28 = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_988]) ).

fof(c_0_3926,axiom,
    ! [X103,X88,X14] : c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X14,X88),X103,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X103),
    c_0_989 ).

fof(c_0_3927,plain,
    ! [X51,X25,X4] :
      ( ~ c_in(X25,c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Oconcat(X51,X4) != c_List_Olist_ONil
      | X25 = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_990]) ).

fof(c_0_3928,plain,
    ! [X51,X25,X4] :
      ( ~ c_in(X25,c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Olist_ONil != c_List_Oconcat(X51,X4)
      | X25 = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_991]) ).

fof(c_0_3929,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(X19,c_divide(X28,X19,X4),X4) = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_992]) ).

fof(c_0_3930,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(c_divide(X28,X19,X4),X19,X4) = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_993]) ).

fof(c_0_3931,plain,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X19,X7,X4),X7,X4) = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_994]) ).

fof(c_0_3932,plain,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | X7 = c_0
      | c_divide(c_times(X7,X19,X4),X7,X4) = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_995]) ).

fof(c_0_3933,plain,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_minus(c_1,c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X12)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_996]) ).

fof(c_0_3934,axiom,
    ! [X24,X22,X4] :
      ( c_List_Odrop(X22,X24,X4) != c_List_Olist_ONil
      | c_lessequals(c_Nat_Osize(X24,tc_List_Olist(X4)),X22,tc_nat) ),
    c_0_997 ).

fof(c_0_3935,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_0,c_HOL_Oinverse(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_998]) ).

fof(c_0_3936,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_lessequals(c_HOL_Oinverse(X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_999]) ).

fof(c_0_3937,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_lessequals(c_0,X19,X4)
      | c_lessequals(c_0,c_HOL_Oinverse(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1000]) ).

fof(c_0_3938,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_HOL_Oinverse(X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1001]) ).

fof(c_0_3939,plain,
    ! [X103,X14] :
      ( ~ c_in(X14,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1002]) ).

fof(c_0_3940,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_nat),tc_nat) = c_minus(X15,c_Suc(X27),tc_nat),
    c_0_1003 ).

fof(c_0_3941,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X27,X15,tc_nat),tc_nat) = c_minus(c_Suc(X15),X27,tc_nat),
    c_0_1004 ).

fof(c_0_3942,axiom,
    ! [X2,X22,X4] :
      ( X22 = c_0
      | c_List_Oset(c_List_Oreplicate(X22,X2,X4),X4) = c_insert(X2,c_emptyset,X4) ),
    c_0_1005 ).

fof(c_0_3943,axiom,
    ! [X2,X22,X4] : c_List_Orev(c_List_Oreplicate(X22,X2,X4),X4) = c_List_Oreplicate(X22,X2,X4),
    c_0_1006 ).

fof(c_0_3944,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_uminus(X19,X4),c_uminus(X28,X4),X4) = c_divide(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1007]) ).

fof(c_0_3945,plain,
    ! [X22] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X22)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(fof_simplification,[status(thm)],[c_0_1008]) ).

fof(c_0_3946,plain,
    ! [X89,X20] :
      ( ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(X20,c_Message_Osynth(X89),tc_set(tc_Message_Omsg)) ),
    inference(fof_simplification,[status(thm)],[c_0_1009]) ).

fof(c_0_3947,plain,
    ! [X89,X20] :
      ( ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(X20,c_Message_Oparts(X89),tc_set(tc_Message_Omsg)) ),
    inference(fof_simplification,[status(thm)],[c_0_1010]) ).

fof(c_0_3948,plain,
    ! [X89,X20] :
      ( ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(X20,c_Message_Oanalz(X89),tc_set(tc_Message_Omsg)) ),
    inference(fof_simplification,[status(thm)],[c_0_1011]) ).

fof(c_0_3949,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X44,X17,X4)
      | c_in(X44,c_SetInterval_OlessThan(X17,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1012]) ).

fof(c_0_3950,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_less(X17,X44,X4)
      | c_in(X44,c_SetInterval_OgreaterThan(X17,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1013]) ).

fof(c_0_3951,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_lessequals(X44,X17,X4)
      | c_in(X44,c_SetInterval_OatMost(X17,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1014]) ).

fof(c_0_3952,plain,
    ! [X17,X44,X4] :
      ( ~ class_Orderings_Oord(X4)
      | ~ c_lessequals(X17,X44,X4)
      | c_in(X44,c_SetInterval_OatLeast(X17,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1015]) ).

fof(c_0_3953,axiom,
    ! [X13,X14,X4] : c_inter(X14,c_minus(X13,X14,tc_set(X4)),X4) = c_emptyset,
    c_0_1016 ).

fof(c_0_3954,plain,
    ! [X60,X44] :
      ( ~ c_less(X44,X60,tc_nat)
      | c_List_Olast(c_List_Oupt(X44,X60),tc_nat) = c_minus(X60,c_1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1017]) ).

fof(c_0_3955,axiom,
    ! [X97,X98,X106,X104,X107,X105] :
      ( c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OSays(X107,X106,X97)
      | X98 = X97 ),
    c_0_1018 ).

fof(c_0_3956,axiom,
    ! [X97,X98,X106,X104,X107,X105] :
      ( c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OSays(X107,X106,X97)
      | X104 = X106 ),
    c_0_1019 ).

fof(c_0_3957,axiom,
    ! [X97,X98,X106,X104,X107,X105] :
      ( c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OSays(X107,X106,X97)
      | X105 = X107 ),
    c_0_1020 ).

fof(c_0_3958,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Sum__Type_OInr(X2,X3,X4) != c_Sum__Type_OInr(X1,X3,X4)
      | X2 = X1 ),
    c_0_1021 ).

fof(c_0_3959,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Sum__Type_OInl(X2,X4,X3) != c_Sum__Type_OInl(X1,X4,X3)
      | X2 = X1 ),
    c_0_1022 ).

fof(c_0_3960,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1023]) ).

fof(c_0_3961,axiom,
    ! [X52,X26,X24,X4] :
      ( c_append(X24,X26,X4) != c_append(X24,X52,X4)
      | X26 = X52 ),
    c_0_1024 ).

fof(c_0_3962,axiom,
    ! [X64,X65,X43,X19,X4] :
      ( c_List_Olist_OCons(X19,X65,X4) != c_List_Olist_OCons(X43,X64,X4)
      | X65 = X64 ),
    c_0_1025 ).

fof(c_0_3963,axiom,
    ! [X64,X65,X43,X19,X4] :
      ( c_List_Olist_OCons(X19,X65,X4) != c_List_Olist_OCons(X43,X64,X4)
      | X19 = X43 ),
    c_0_1026 ).

fof(c_0_3964,axiom,
    ! [X52,X26,X24,X4] :
      ( c_append(X26,X24,X4) != c_append(X52,X24,X4)
      | X26 = X52 ),
    c_0_1027 ).

fof(c_0_3965,axiom,
    ! [X9,X11,X3,X4] :
      ( c_Datatype__Universe_OIn1(X11,X4,X3) != c_Datatype__Universe_OIn1(X9,X4,X3)
      | X11 = X9 ),
    c_0_1028 ).

fof(c_0_3966,axiom,
    ! [X9,X11,X3,X4] :
      ( c_Datatype__Universe_OIn0(X11,X4,X3) != c_Datatype__Universe_OIn0(X9,X4,X3)
      | X11 = X9 ),
    c_0_1029 ).

fof(c_0_3967,axiom,
    ! [X28,X19,X3,X4] :
      ( c_Datatype__Universe_OAtom(X19,X4,X3) != c_Datatype__Universe_OAtom(X28,X4,X3)
      | X19 = X28 ),
    c_0_1030 ).

fof(c_0_3968,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Datatype__Universe_ONumb(X2,X4,X3) != c_Datatype__Universe_ONumb(X1,X4,X3)
      | X2 = X1 ),
    c_0_1031 ).

fof(c_0_3969,axiom,
    ! [X1,X2,X3,X4] :
      ( c_Datatype__Universe_OLeaf(X2,X4,X3) != c_Datatype__Universe_OLeaf(X1,X4,X3)
      | X2 = X1 ),
    c_0_1032 ).

fof(c_0_3970,plain,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(c_uminus(X49,tc_IntDef_Oint),X12,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1033]) ).

fof(c_0_3971,plain,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(X49,c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1034]) ).

fof(c_0_3972,axiom,
    ! [X89,X20] : c_Message_Oparts(c_union(X20,X89,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X89),tc_Message_Omsg),
    c_0_1035 ).

fof(c_0_3973,axiom,
    ! [X94,X89] : c_Message_OkeysFor(c_union(X89,X94,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X89),c_Message_OkeysFor(X94),tc_nat),
    c_0_1036 ).

fof(c_0_3974,axiom,
    ! [X22,X16] : c_Orderings_Omin(c_Suc(X16),c_Suc(X22),tc_nat) = c_Suc(c_Orderings_Omin(X16,X22,tc_nat)),
    c_0_1037 ).

fof(c_0_3975,axiom,
    ! [X22,X16] : c_Orderings_Omax(c_Suc(X16),c_Suc(X22),tc_nat) = c_Suc(c_Orderings_Omax(X16,X22,tc_nat)),
    c_0_1038 ).

fof(c_0_3976,axiom,
    ! [X84,X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X48,X84),tc_nat) ),
    c_0_1039 ).

fof(c_0_3977,axiom,
    ! [X22,X16] : c_IntDef_Oint(c_plus(X16,X22,tc_nat)) = c_plus(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint),
    c_0_1040 ).

fof(c_0_3978,plain,
    ! [X28,X14] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X28,X14)),c_Message_OsymKeys,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_1041]) ).

fof(c_0_3979,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Osynth(c_Message_Osynth(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1042]) ).

fof(c_0_3980,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oparts(c_Message_Oparts(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1043]) ).

fof(c_0_3981,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oanalz(c_Message_Oanalz(X89)),tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1044]) ).

fof(c_0_3982,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_0,c_divide(X28,c_0,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1045]) ).

fof(c_0_3983,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_divide(X28,c_0,X4),c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1046]) ).

fof(c_0_3984,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(X19,c_0,X4),c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1047]) ).

fof(c_0_3985,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,c_times(X28,c_0,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1048]) ).

fof(c_0_3986,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_times(c_0,X19,X4),c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1049]) ).

fof(c_0_3987,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,c_times(c_0,X28,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1050]) ).

fof(c_0_3988,axiom,
    ! [X28,X19,X3,X4] : c_Sum__Type_OInr(X28,X3,X4) != c_Sum__Type_OInl(X19,X4,X3),
    c_0_1051 ).

fof(c_0_3989,axiom,
    ! [X28,X19,X3,X4] : c_Sum__Type_OInl(X19,X4,X3) != c_Sum__Type_OInr(X28,X3,X4),
    c_0_1052 ).

fof(c_0_3990,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_ONumb(X17,X4,X3) != c_Datatype__Universe_OLeaf(X19,X4,X3),
    c_0_1053 ).

fof(c_0_3991,axiom,
    ! [X17,X19,X3,X4] : c_Datatype__Universe_OLeaf(X19,X4,X3) != c_Datatype__Universe_ONumb(X17,X4,X3),
    c_0_1054 ).

fof(c_0_3992,axiom,
    ! [X9,X11,X3,X4] : c_Datatype__Universe_OIn1(X9,X4,X3) != c_Datatype__Universe_OIn0(X11,X4,X3),
    c_0_1055 ).

fof(c_0_3993,axiom,
    ! [X9,X11,X3,X4] : c_Datatype__Universe_OIn0(X11,X4,X3) != c_Datatype__Universe_OIn1(X9,X4,X3),
    c_0_1056 ).

fof(c_0_3994,plain,
    ! [X25,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(X25),X89,tc_Message_Omsg)
      | c_in(c_Message_OinvKey(X25),c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1057]) ).

fof(c_0_3995,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X19,X14,X4) != c_insert(X28,c_emptyset,X4)
      | X19 = X28 ),
    c_0_1058 ).

fof(c_0_3996,axiom,
    ! [X28,X19,X14,X4] :
      ( c_insert(X28,c_emptyset,X4) != c_insert(X19,X14,X4)
      | X19 = X28 ),
    c_0_1059 ).

fof(c_0_3997,plain,
    ! [X89,X20] :
      ( ~ c_lessequals(X20,c_Message_Osynth(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X89),tc_set(tc_Message_Omsg)) ),
    inference(fof_simplification,[status(thm)],[c_0_1060]) ).

fof(c_0_3998,plain,
    ! [X89,X20] :
      ( ~ c_lessequals(X20,c_Message_Oparts(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X89),tc_set(tc_Message_Omsg)) ),
    inference(fof_simplification,[status(thm)],[c_0_1061]) ).

fof(c_0_3999,plain,
    ! [X89,X20] :
      ( ~ c_lessequals(X20,c_Message_Oanalz(X89),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X89),tc_set(tc_Message_Omsg)) ),
    inference(fof_simplification,[status(thm)],[c_0_1062]) ).

fof(c_0_4000,axiom,
    ! [X2,X4] : c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) = c_List_Orev(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4),
    c_0_1063 ).

fof(c_0_4001,axiom,
    ! [X2,X4] : c_List_Orev(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),
    c_0_1064 ).

fof(c_0_4002,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(c_0,X19,X4)
      | c_less(c_uminus(X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1065]) ).

fof(c_0_4003,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(c_0,X19,X4)
      | c_lessequals(c_uminus(X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1066]) ).

fof(c_0_4004,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_less(X19,c_0,X4)
      | c_less(c_0,c_uminus(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1067]) ).

fof(c_0_4005,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_lessequals(c_0,c_uminus(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1068]) ).

fof(c_0_4006,axiom,
    ! [X22,X16,X17] :
      ( c_times(X16,X17,tc_nat) != c_times(X22,X17,tc_nat)
      | X16 = X22
      | X17 = c_0 ),
    c_0_1069 ).

fof(c_0_4007,axiom,
    ! [X22,X16,X17] :
      ( c_times(X17,X16,tc_nat) != c_times(X17,X22,tc_nat)
      | X16 = X22
      | X17 = c_0 ),
    c_0_1070 ).

fof(c_0_4008,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_in(X19,c_IntDef_OInts,X4)
      | c_in(c_uminus(X19,X4),c_IntDef_OInts,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1071]) ).

fof(c_0_4009,plain,
    ! [X2,X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X4),X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X12,X2),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1072]) ).

fof(c_0_4010,plain,
    ! [X2,X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_Parity_Oeven(X22,tc_nat)
      | c_Nat_Opower(c_uminus(X2,X4),X22,X4) = c_Nat_Opower(X2,X22,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1073]) ).

fof(c_0_4011,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_nat),tc_nat) = c_minus(X15,X27,tc_nat),
    c_0_1074 ).

fof(c_0_4012,axiom,
    ! [X15,X27] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X27,X15,tc_nat),tc_nat) = c_minus(X15,X27,tc_nat),
    c_0_1075 ).

fof(c_0_4013,axiom,
    ! [X22,X16,X17] :
      ( c_plus(X16,X17,tc_nat) != c_plus(X22,X17,tc_nat)
      | X16 = X22 ),
    c_0_1076 ).

fof(c_0_4014,axiom,
    ! [X22,X16,X17] :
      ( c_plus(X17,X16,tc_nat) != c_plus(X17,X22,tc_nat)
      | X16 = X22 ),
    c_0_1077 ).

fof(c_0_4015,axiom,
    ! [X28,X19,X4] :
      ( c_insert(X19,c_emptyset,X4) != c_insert(X28,c_emptyset,X4)
      | X19 = X28 ),
    c_0_1078 ).

fof(c_0_4016,plain,
    ! [X1,X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(X2,X4) != c_Numeral_Onumber__of(X1,X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(X1)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1079]) ).

fof(c_0_4017,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oring(X4)
      | c_times(c_uminus(X19,X4),c_uminus(X28,X4),X4) = c_times(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1080]) ).

fof(c_0_4018,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_0,X22,tc_nat)
      | c_less(c_0,c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1081]) ).

fof(c_0_4019,plain,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(X12,c_0,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X12,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1082]) ).

fof(c_0_4020,plain,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(X12,c_0,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X12,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1083]) ).

fof(c_0_4021,plain,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,X49,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1084]) ).

fof(c_0_4022,plain,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_lessequals(c_0,X49,tc_IntDef_Oint)
      | c_lessequals(c_0,c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1085]) ).

fof(c_0_4023,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1086]) ).

fof(c_0_4024,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) != c_Numeral_Onumber__of(X84,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1087]) ).

fof(c_0_4025,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) != c_Numeral_Onumber__of(X84,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1088]) ).

fof(c_0_4026,plain,
    ! [X1] :
      ( ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1089]) ).

fof(c_0_4027,axiom,
    ! [X22,X16] : c_plus(c_Suc(X16),X22,tc_nat) = c_Suc(c_plus(X16,X22,tc_nat)),
    c_0_1090 ).

fof(c_0_4028,axiom,
    ! [X22,X16] : c_plus(X16,c_Suc(X22),tc_nat) = c_Suc(c_plus(X16,X22,tc_nat)),
    c_0_1091 ).

fof(c_0_4029,plain,
    ! [X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_minus(c_Numeral_Onumber__of(X48,X4),c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_Obin__minus(X12)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1092]) ).

fof(c_0_4030,plain,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_1,X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1093]) ).

fof(c_0_4031,plain,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_1,c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X12),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1094]) ).

fof(c_0_4032,plain,
    ! [X48] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X48,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X48),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1095]) ).

fof(c_0_4033,plain,
    ! [X93,X89] :
      ( ~ c_in(X93,c_Message_OkeysFor(X89),tc_nat)
      | c_in(X93,c_Message_OkeysFor(c_Message_Osynth(X89)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1096]) ).

fof(c_0_4034,plain,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X4),X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB0),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1097]) ).

fof(c_0_4035,axiom,
    ! [X87,X88,X89] : c_Message_OkeysFor(c_insert(c_Message_OHPair(X88,X87),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1098 ).

fof(c_0_4036,axiom,
    ! [X103,X88,X14] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X14,X88),X103,tc_Event_Oevent)) = c_Event_Oused(X103),
    c_0_1099 ).

fof(c_0_4037,axiom,
    ! [X87,X88,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X88,X87),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1100 ).

fof(c_0_4038,axiom,
    ! [X16,X18] :
      ( c_Divides_Oop_Amod(X16,X18,tc_IntDef_Oint) != c_0
      | X16 = c_times(X18,c_Main_Ozmod__eq__0D__dest__1(X18,X16),tc_IntDef_Oint) ),
    c_0_1101 ).

fof(c_0_4039,axiom,
    ! [X16,X18] :
      ( c_Divides_Oop_Amod(X16,X18,tc_nat) != c_0
      | X16 = c_times(X18,c_Main_Omod__eq__0D__dest__1(X18,X16),tc_nat) ),
    c_0_1102 ).

fof(c_0_4040,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X103)),tc_Message_Omsg),
    c_0_1103 ).

fof(c_0_4041,plain,
    ! [X9,X89] :
      ( ~ c_in(c_Message_Omsg_ONonce(X9),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1104]) ).

fof(c_0_4042,plain,
    ! [X93,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(X93),c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1105]) ).

fof(c_0_4043,axiom,
    ! [X1,X3,X4] : c_Relation_Oconverse(c_Relation_Oconverse(X1,X4,X3),X3,X4) = X1,
    c_0_1106 ).

fof(c_0_4044,axiom,
    ! [X24,X2,X4] : c_List_Oremove1(X2,c_List_Olist_OCons(X2,X24,X4),X4) = X24,
    c_0_1107 ).

fof(c_0_4045,axiom,
    ! [X2,X14,X4] : c_in(X2,c_insert(X2,X14,X4),X4),
    c_0_1108 ).

fof(c_0_4046,axiom,
    ! [X26,X2,X4] : c_List_Oop_Amem(X2,c_List_Olist_OCons(X2,X26,X4),X4),
    c_0_1109 ).

fof(c_0_4047,axiom,
    ! [X1,X24,X4] : c_List_Onth(c_List_Olist_OCons(X1,X24,X4),c_0,X4) = X1,
    c_0_1110 ).

fof(c_0_4048,plain,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X49,tc_IntDef_Oint),X12,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1111]) ).

fof(c_0_4049,plain,
    ! [X49,X12] :
      ( ~ c_Divides_Oop_Advd(X49,X12,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X49,c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1112]) ).

fof(c_0_4050,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_1113 ).

fof(c_0_4051,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanLessThan(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1114 ).

fof(c_0_4052,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_1115 ).

fof(c_0_4053,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OgreaterThanAtMost(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1116 ).

fof(c_0_4054,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastLessThan(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_1117 ).

fof(c_0_4055,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastLessThan(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1118 ).

fof(c_0_4056,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastAtMost(X27,X15,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_1119 ).

fof(c_0_4057,axiom,
    ! [X15,X27] : c_in(c_SetInterval_OatLeastAtMost(X27,X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1120 ).

fof(c_0_4058,axiom,
    ! [X24,X2,X4] :
      ( c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) != c_List_Orev(X24,X4)
      | X24 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) ),
    c_0_1121 ).

fof(c_0_4059,axiom,
    ! [X24,X2,X4] :
      ( c_List_Orev(X24,X4) != c_List_Olist_OCons(X2,c_List_Olist_ONil,X4)
      | X24 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X4) ),
    c_0_1122 ).

fof(c_0_4060,axiom,
    ! [X1,X28] :
      ( X28 = c_0
      | c_div(c_times(X28,X1,tc_IntDef_Oint),X28,tc_IntDef_Oint) = X1 ),
    c_0_1123 ).

fof(c_0_4061,axiom,
    ! [X1,X28] :
      ( X28 = c_0
      | c_div(c_times(X1,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = X1 ),
    c_0_1124 ).

fof(c_0_4062,plain,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X14,X13,tc_set(X4))
      | c_less(X14,X13,tc_set(X4))
      | X14 = X13 ),
    inference(fof_simplification,[status(thm)],[c_0_1125]) ).

fof(c_0_4063,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X88),c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1126]) ).

fof(c_0_4064,plain,
    ! [X9,X89] :
      ( ~ c_in(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X9),c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1127]) ).

fof(c_0_4065,plain,
    ! [X93,X89] :
      ( ~ c_in(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X93),c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1128]) ).

fof(c_0_4066,axiom,
    ! [X19,X4] : c_in(X19,c_insert(X19,c_emptyset,X4),X4),
    c_0_1129 ).

fof(c_0_4067,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1130]) ).

fof(c_0_4068,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_nat)
      | ~ c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1131]) ).

fof(c_0_4069,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1132]) ).

fof(c_0_4070,axiom,
    ! [X22,X16] : c_lessequals(X22,c_plus(X16,X22,tc_nat),tc_nat),
    c_0_1133 ).

fof(c_0_4071,axiom,
    ! [X22,X16] : c_lessequals(X22,c_plus(X22,X16,tc_nat),tc_nat),
    c_0_1134 ).

fof(c_0_4072,axiom,
    ! [X2,X22] :
      ( c_less(c_0,c_Nat_Opower(X2,X22,tc_nat),tc_nat)
      | X2 = c_0 ),
    c_0_1135 ).

fof(c_0_4073,axiom,
    ! [X22,X16] : c_lessequals(c_minus(X16,X22,tc_nat),X16,tc_nat),
    c_0_1136 ).

fof(c_0_4074,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_times(X28,X19,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_0,
    c_0_1137 ).

fof(c_0_4075,axiom,
    ! [X28,X19] : c_Divides_Oop_Amod(c_times(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_0,
    c_0_1138 ).

fof(c_0_4076,axiom,
    ! [X28,X19] : c_div(c_Divides_Oop_Amod(X19,X28,tc_IntDef_Oint),X28,tc_IntDef_Oint) = c_0,
    c_0_1139 ).

fof(c_0_4077,axiom,
    ! [X22,X16] : c_div(c_Divides_Oop_Amod(X16,X22,tc_nat),X22,tc_nat) = c_0,
    c_0_1140 ).

fof(c_0_4078,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_times(X16,X22,tc_nat),X22,tc_nat) = c_0,
    c_0_1141 ).

fof(c_0_4079,axiom,
    ! [X22,X16] : c_Divides_Oop_Amod(c_times(X22,X16,tc_nat),X22,tc_nat) = c_0,
    c_0_1142 ).

fof(c_0_4080,axiom,
    ! [X22,X16] : c_lessequals(c_div(X16,X22,tc_nat),X16,tc_nat),
    c_0_1143 ).

fof(c_0_4081,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X16,X17,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_1144 ).

fof(c_0_4082,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X17,X16,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_1145 ).

fof(c_0_4083,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X16,X17,tc_nat),tc_nat),
    c_0_1146 ).

fof(c_0_4084,axiom,
    ! [X16,X17] : c_Divides_Oop_Advd(X17,c_times(X17,X16,tc_nat),tc_nat),
    c_0_1147 ).

fof(c_0_4085,plain,
    ! [X13,X14,X4] :
      ( ~ c_lessequals(X14,X13,tc_set(X4))
      | c_minus(X14,X13,tc_set(X4)) = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1148]) ).

fof(c_0_4086,axiom,
    ! [X13,X14,X4] :
      ( c_minus(X14,X13,tc_set(X4)) != c_emptyset
      | c_lessequals(X14,X13,tc_set(X4)) ),
    c_0_1149 ).

fof(c_0_4087,plain,
    ! [X13,X14,X4] :
      ( ~ c_less(X14,X13,tc_set(X4))
      | c_lessequals(X14,X13,tc_set(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_1150]) ).

fof(c_0_4088,plain,
    ! [X1,X4] :
      ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),c_1,tc_nat)
      | c_List_Orotate1(X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1151]) ).

fof(c_0_4089,plain,
    ! [X22,X16] :
      ( ~ c_less(c_Suc(X16),c_Suc(X22),tc_nat)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1152]) ).

fof(c_0_4090,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(c_Suc(X22),c_Suc(X16),tc_nat)
      | c_lessequals(X22,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1153]) ).

fof(c_0_4091,plain,
    ! [X49,X12] :
      ( ~ c_less(c_IntDef_Onat(X12),c_IntDef_Onat(X49),tc_nat)
      | c_less(X12,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1154]) ).

fof(c_0_4092,plain,
    ! [X22,X16] :
      ( ~ c_less(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint)
      | c_less(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1155]) ).

fof(c_0_4093,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint)
      | c_lessequals(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1156]) ).

fof(c_0_4094,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1157]) ).

fof(c_0_4095,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1158]) ).

fof(c_0_4096,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X48,tc_nat),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1159]) ).

fof(c_0_4097,plain,
    ! [X49,X12] :
      ( ~ c_less(c_IntDef_Onat(X12),c_IntDef_Onat(X49),tc_nat)
      | c_less(c_0,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1160]) ).

fof(c_0_4098,plain,
    ! [X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_Numeral_Onumber__of(X48,X4),c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X48,X12),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1161]) ).

fof(c_0_4099,plain,
    ! [X12,X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_Numeral_Onumber__of(X48,X4),c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X48,X12),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1162]) ).

fof(c_0_4100,axiom,
    ! [X13,X14,X4] : c_minus(X14,c_uminus(X13,tc_set(X4)),tc_set(X4)) = c_inter(X14,X13,X4),
    c_0_1163 ).

fof(c_0_4101,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1164]) ).

fof(c_0_4102,plain,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,X22,X4) != c_0
      | c_less(c_0,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1165]) ).

fof(c_0_4103,axiom,
    ! [X2] : c_less(c_0,c_Nat_Opower(X2,c_0,tc_nat),tc_nat),
    c_0_1166 ).

fof(c_0_4104,axiom,
    ! [X28,X19] : c_div(c_uminus(X19,tc_IntDef_Oint),c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X19,X28,tc_IntDef_Oint),
    c_0_1167 ).

fof(c_0_4105,plain,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X48),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,c_Numeral_Onumber__of(X48,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1168]) ).

fof(c_0_4106,plain,
    ! [X49] :
      ( ~ c_less(c_Suc(c_0),c_IntDef_Onat(X49),tc_nat)
      | c_less(c_1,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1169]) ).

fof(c_0_4107,plain,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X12,c_Numeral_Obit_OB1),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1170]) ).

fof(c_0_4108,plain,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_Suc(X16),c_Suc(X22),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1171]) ).

fof(c_0_4109,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(X22,X16,tc_nat)
      | c_lessequals(c_Suc(X22),c_Suc(X16),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1172]) ).

fof(c_0_4110,plain,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_less(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1173]) ).

fof(c_0_4111,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_lessequals(c_IntDef_Oint(X16),c_IntDef_Oint(X22),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1174]) ).

fof(c_0_4112,plain,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_less(c_0,X22,tc_nat)
      | c_Nat_Opower(c_0,X22,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1175]) ).

fof(c_0_4113,plain,
    ! [X22,X16] : ~ c_less(c_IntDef_Oint(X22),c_uminus(c_IntDef_Oint(X16),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(fof_simplification,[status(thm)],[c_0_1176]) ).

fof(c_0_4114,plain,
    ! [X27,X17,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X27,X17,X4)
      | c_SetInterval_OgreaterThanAtMost(X17,X27,X4) = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1177]) ).

fof(c_0_4115,plain,
    ! [X22,X16,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_lessequals(X22,X16,X4)
      | c_SetInterval_OatLeastLessThan(X16,X22,X4) = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1178]) ).

fof(c_0_4116,plain,
    ! [X22,X16,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_less(X22,X16,X4)
      | c_SetInterval_OatLeastAtMost(X16,X22,X4) = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1179]) ).

fof(c_0_4117,axiom,
    ! [X7,X14,X4] :
      ( c_in(X7,X14,X4)
      | c_in(X7,c_uminus(X14,tc_set(X4)),X4) ),
    c_0_1180 ).

fof(c_0_4118,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_less(c_Numeral_Onumber__of(X2,X4),c_0,X4)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X2,X4),X4) = c_Numeral_Onumber__of(X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1181]) ).

fof(c_0_4119,axiom,
    ! [X24,X22,X4] : c_Nat_Osize(c_List_Orotate(X22,X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    c_0_1182 ).

fof(c_0_4120,axiom,
    ! [X28,X3,X4] : c_Nat_Osize(c_Sum__Type_OInr(X28,X3,X4),tc_sum(X4,X3)) = c_0,
    c_0_1183 ).

fof(c_0_4121,axiom,
    ! [X19,X3,X4] : c_Nat_Osize(c_Sum__Type_OInl(X19,X4,X3),tc_sum(X4,X3)) = c_0,
    c_0_1184 ).

fof(c_0_4122,plain,
    ! [X22,X16] :
      ( ~ c_less(X16,c_Suc(X22),tc_nat)
      | c_lessequals(X16,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1185]) ).

fof(c_0_4123,plain,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X6,X4)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X4,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1186]) ).

fof(c_0_4124,plain,
    ! [X24,X44,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Otake(X44,X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1187]) ).

fof(c_0_4125,plain,
    ! [X24,X59,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Osublist(X24,X59,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1188]) ).

fof(c_0_4126,plain,
    ! [X24,X22,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Orotate(X22,X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1189]) ).

fof(c_0_4127,plain,
    ! [X24,X2,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Oremove1(X2,X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1190]) ).

fof(c_0_4128,plain,
    ! [X24,X44,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Odrop(X44,X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1191]) ).

fof(c_0_4129,plain,
    ! [X49] :
      ( ~ c_less(c_1,X49,tc_IntDef_Oint)
      | c_less(c_Suc(c_0),c_IntDef_Onat(X49),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1192]) ).

fof(c_0_4130,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_less(X16,c_Suc(X22),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1193]) ).

fof(c_0_4131,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,X89,tc_Message_Omsg)
      | c_in(X88,c_Message_Osynth(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1194]) ).

fof(c_0_4132,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,X89,tc_Message_Omsg)
      | c_in(X88,c_Message_Oanalz(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1195]) ).

fof(c_0_4133,plain,
    ! [X88,X89] :
      ( ~ c_in(X88,X89,tc_Message_Omsg)
      | c_in(X88,c_Message_Oparts(X89),tc_Message_Omsg) ),
    inference(fof_simplification,[status(thm)],[c_0_1196]) ).

fof(c_0_4134,axiom,
    ! [X22,X17] : c_Binomial_Obinomial(c_Suc(X22),c_Suc(X17)) = c_plus(c_Binomial_Obinomial(X22,X17),c_Binomial_Obinomial(X22,c_Suc(X17)),tc_nat),
    c_0_1197 ).

fof(c_0_4135,plain,
    ! [X93] :
      ( ~ c_in(c_Message_OinvKey(X93),c_Message_OsymKeys,tc_nat)
      | c_in(X93,c_Message_OsymKeys,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1198]) ).

fof(c_0_4136,plain,
    ! [X49] :
      ( ~ c_less(c_0,c_IntDef_Onat(X49),tc_nat)
      | c_less(c_0,X49,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1199]) ).

fof(c_0_4137,plain,
    ! [X22] :
      ( ~ c_less(c_0,c_IntDef_Oint(X22),tc_IntDef_Oint)
      | c_less(c_0,X22,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1200]) ).

fof(c_0_4138,axiom,
    ! [X1,X2] :
      ( c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_1201 ).

fof(c_0_4139,axiom,
    ! [X1,X2] :
      ( c_Parity_Oeven(X1,tc_nat)
      | c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat) ),
    c_0_1202 ).

fof(c_0_4140,axiom,
    ! [X1,X2] :
      ( c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_1203 ).

fof(c_0_4141,plain,
    ! [X41,X2,X4] :
      ( ~ c_in(X2,c_Datatype_Oo2s(X41,X4),X4)
      | X41 = c_Datatype_Ooption_OSome(X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1204]) ).

fof(c_0_4142,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X19,c_uminus(X28,X4),X4) = c_plus(X19,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1205]) ).

fof(c_0_4143,plain,
    ! [X1,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_0 != c_Numeral_Onumber__of(X1,X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1206]) ).

fof(c_0_4144,axiom,
    ! [X51,X4] :
      ( c_in(c_Main_Oconcat__eq__Nil__conv__1(X51,X4),c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Oconcat(X51,X4) = c_List_Olist_ONil ),
    c_0_1207 ).

fof(c_0_4145,axiom,
    ! [X51,X4] :
      ( c_in(c_Main_ONil__eq__concat__conv__1(X51,X4),c_List_Oset(X51,tc_List_Olist(X4)),tc_List_Olist(X4))
      | c_List_Olist_ONil = c_List_Oconcat(X51,X4) ),
    c_0_1208 ).

fof(c_0_4146,plain,
    ! [X93] :
      ( ~ c_in(X93,c_Message_OsymKeys,tc_nat)
      | c_in(c_Message_OinvKey(X93),c_Message_OsymKeys,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1209]) ).

fof(c_0_4147,plain,
    ! [X49] :
      ( ~ c_less(c_0,X49,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Onat(X49),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1210]) ).

fof(c_0_4148,plain,
    ! [X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_less(c_0,c_IntDef_Oint(X22),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1211]) ).

fof(c_0_4149,plain,
    ! [X12,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,c_Numeral_Onumber__of(X12,tc_nat),X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1212]) ).

fof(c_0_4150,plain,
    ! [X1,X22] :
      ( ~ c_less(X1,X22,tc_nat)
      | c_Divides_Oop_Amod(X1,X22,tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1213]) ).

fof(c_0_4151,plain,
    ! [X84] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X84,tc_nat),tc_nat) = c_Suc(c_0) ),
    inference(fof_simplification,[status(thm)],[c_0_1214]) ).

fof(c_0_4152,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1215]) ).

fof(c_0_4153,plain,
    ! [X84,X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X84,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_Numeral_Onumber__of(X84,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1216]) ).

fof(c_0_4154,plain,
    ! [X48] :
      ( ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)),tc_IntDef_Oint)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1217]) ).

fof(c_0_4155,plain,
    ! [X22,X16] :
      ( ~ c_lessequals(X16,X22,tc_nat)
      | c_minus(X16,X22,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1218]) ).

fof(c_0_4156,axiom,
    ! [X22,X16] :
      ( c_minus(X16,X22,tc_nat) != c_0
      | c_lessequals(X16,X22,tc_nat) ),
    c_0_1219 ).

fof(c_0_4157,plain,
    ! [X22,X16] :
      ( ~ c_less(X16,X22,tc_nat)
      | c_div(X16,X22,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1220]) ).

fof(c_0_4158,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1221]) ).

fof(c_0_4159,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1222]) ).

fof(c_0_4160,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X1,tc_nat)
      | c_Parity_Oeven(c_times(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1223]) ).

fof(c_0_4161,plain,
    ! [X1,X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_times(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1224]) ).

fof(c_0_4162,plain,
    ! [X4] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X4)),tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_1225]) ).

fof(c_0_4163,axiom,
    ! [X26,X24,X4] :
      ( X26 = c_List_Olist_ONil
      | c_List_Olast(c_append(X24,X26,X4),X4) = c_List_Olast(X26,X4) ),
    c_0_1226 ).

fof(c_0_4164,axiom,
    ! [X24,X2,X4] :
      ( X24 = c_List_Olist_ONil
      | c_List_Olast(c_List_Olist_OCons(X2,X24,X4),X4) = c_List_Olast(X24,X4) ),
    c_0_1227 ).

fof(c_0_4165,axiom,
    ! [X26,X24,X4] :
      ( X24 = c_List_Olist_ONil
      | c_List_Ohd(c_append(X24,X26,X4),X4) = c_List_Ohd(X24,X4) ),
    c_0_1228 ).

fof(c_0_4166,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Omeet(X19,c_uminus(X19,X4),X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1229]) ).

fof(c_0_4167,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Ojoin(X19,c_uminus(X19,X4),X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1230]) ).

fof(c_0_4168,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Otl(X24,X4),tc_List_Olist(X4)) = c_minus(c_Nat_Osize(X24,tc_List_Olist(X4)),c_1,tc_nat),
    c_0_1231 ).

fof(c_0_4169,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Obutlast(X24,X4),tc_List_Olist(X4)) = c_minus(c_Nat_Osize(X24,tc_List_Olist(X4)),c_1,tc_nat),
    c_0_1232 ).

fof(c_0_4170,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_plus(c_1,c_1,X4) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1233]) ).

fof(c_0_4171,axiom,
    ! [X6,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X6,X4),X4,X4) = c_Relation_ORange(X6,X4,X4),
    c_0_1234 ).

fof(c_0_4172,axiom,
    ! [X6,X4] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X6,X4),X4,X4) = c_Relation_ODomain(X6,X4,X4),
    c_0_1235 ).

fof(c_0_4173,axiom,
    ! [X24,X22,X4] : c_List_Oset(c_List_Orotate(X22,X24,X4),X4) = c_List_Oset(X24,X4),
    c_0_1236 ).

fof(c_0_4174,axiom,
    ! [X24,X2,X4] : c_List_Oitrev(X24,X2,X4) = c_append(c_List_Orev(X24,X4),X2,X4),
    c_0_1237 ).

fof(c_0_4175,plain,
    ! [X22] :
      ( ~ c_less(c_0,X22,tc_nat)
      | c_div(X22,X22,tc_nat) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1238]) ).

fof(c_0_4176,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(X2,X4) != c_0
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X2,c_Numeral_Obin__minus(c_Numeral_OPls)),X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1239]) ).

fof(c_0_4177,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Event_Oknows(c_Message_Oagent_OSpy,X103),tc_Message_Omsg),
    c_0_1240 ).

fof(c_0_4178,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_lessequals(c_HOL_Oabs(X19,X4),c_0,X4)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1241]) ).

fof(c_0_4179,plain,
    ! [X12,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_HOL_Oinverse(c_Numeral_Onumber__of(X12,X3),X3) = c_divide(c_1,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1242]) ).

fof(c_0_4180,plain,
    ! [X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_NatArith_Oof__nat(X16,X4),c_0,X4)
      | X16 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1243]) ).

fof(c_0_4181,axiom,
    ! [X2,X4] : c_in(X2,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X2,X4),X4),X4),
    c_0_1244 ).

fof(c_0_4182,axiom,
    ! [X22,X27,X4] : c_List_Osublist(X27,c_SetInterval_OlessThan(X22,tc_nat),X4) = c_List_Otake(X22,X27,X4),
    c_0_1245 ).

fof(c_0_4183,axiom,
    ! [X24,X4] : c_List_Olast(c_append(X24,c_List_Olist_ONil,X4),X4) = c_List_Olast(X24,X4),
    c_0_1246 ).

fof(c_0_4184,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_less(c_HOL_Oabs(X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1247]) ).

fof(c_0_4185,plain,
    ! [X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_NatArith_Oof__nat(X16,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1248]) ).

fof(c_0_4186,plain,
    ! [X88,X93] : ~ c_in(c_Message_Omsg_OCrypt(X93,X88),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(fof_simplification,[status(thm)],[c_0_1249]) ).

fof(c_0_4187,axiom,
    ! [X49,X12] : c_plus(X49,c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X49,X12,tc_IntDef_Oint),
    c_0_1250 ).

fof(c_0_4188,axiom,
    ! [X1,X2,X4] : c_Nat_Osize(c_List_Oreplicate(X1,X2,X4),tc_List_Olist(X4)) = X1,
    c_0_1251 ).

fof(c_0_4189,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_less(c_0,c_HOL_Oabs(c_0,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1252]) ).

fof(c_0_4190,plain,
    ! [X1,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_Finite__Set_OMin(c_insert(X1,c_emptyset,X4),X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1253]) ).

fof(c_0_4191,plain,
    ! [X1,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_Finite__Set_OMax(c_insert(X1,c_emptyset,X4),X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1254]) ).

fof(c_0_4192,axiom,
    ! [X12,X48] : c_Numeral_Obin__mult(c_Numeral_OBit(X48,c_Numeral_Obit_OB1),X12) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X48,X12),c_Numeral_Obit_OB0),X12),
    c_0_1255 ).

fof(c_0_4193,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) != c_0
      | c_0 = c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1256]) ).

fof(c_0_4194,plain,
    ! [X12,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_Ring__and__Field_Odivision__by__zero(X3)
      | ~ class_Ring__and__Field_Ofield(X3)
      | c_Numeral_Onumber__of(X12,X3) != c_0
      | c_divide(X28,c_Numeral_Onumber__of(X12,X3),X3) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1257]) ).

fof(c_0_4195,axiom,
    ! [X9,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X9),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1258 ).

fof(c_0_4196,axiom,
    ! [X9,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X9),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1259 ).

fof(c_0_4197,axiom,
    ! [X93,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X93),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1260 ).

fof(c_0_4198,axiom,
    ! [X88,X89] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X88),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1261 ).

fof(c_0_4199,axiom,
    ! [X89,X14] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X14),X89,tc_Message_Omsg)) = c_Message_OkeysFor(X89),
    c_0_1262 ).

fof(c_0_4200,axiom,
    ! [X1,X22,X4] :
      ( X22 = c_0
      | c_List_Olast(c_List_Oreplicate(X22,X1,X4),X4) = X1 ),
    c_0_1263 ).

fof(c_0_4201,plain,
    ! [X1,X60] :
      ( ~ c_less(X1,X60,tc_nat)
      | c_List_Ohd(c_List_Oupt(X1,X60),tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1264]) ).

fof(c_0_4202,axiom,
    ! [X1,X22,X4] :
      ( X22 = c_0
      | c_List_Ohd(c_List_Oreplicate(X22,X1,X4),X4) = X1 ),
    c_0_1265 ).

fof(c_0_4203,plain,
    ! [X28,X14] : ~ c_in(c_Public_OpublicKey(X28,X14),c_Message_OsymKeys,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_1266]) ).

fof(c_0_4204,plain,
    ! [X9,X13] : ~ c_in(c_Message_Omsg_ONonce(X9),c_Message_Oparts(c_Event_OinitState(X13)),tc_Message_Omsg),
    inference(fof_simplification,[status(thm)],[c_0_1267]) ).

fof(c_0_4205,axiom,
    ! [X1,X2,X42] : c_List_Otl(c_List_Olist_OCons(X2,X1,X42),X42) = X1,
    c_0_1268 ).

fof(c_0_4206,axiom,
    ! [X1,X24,X4] : c_List_Ohd(c_List_Olist_OCons(X1,X24,X4),X4) = X1,
    c_0_1269 ).

fof(c_0_4207,plain,
    ! [X48] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X48,tc_nat),tc_nat)
      | c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1270]) ).

fof(c_0_4208,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_0,X4) = c_divide(X28,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1271]) ).

fof(c_0_4209,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,X19,X4) = c_divide(c_0,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1272]) ).

fof(c_0_4210,plain,
    ! [X48,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) = c_Numeral_Onumber__of(X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1273]) ).

fof(c_0_4211,plain,
    ! [X48,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_Numeral_Onumber__of(X48,X3) = c_uminus(c_uminus(c_Numeral_Onumber__of(X48,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1274]) ).

fof(c_0_4212,plain,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_emptyset != c_Union(X14,X4)
      | X25 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1275]) ).

fof(c_0_4213,plain,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_Union(X14,X4) != c_emptyset
      | X25 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1276]) ).

fof(c_0_4214,plain,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_UNIV != c_Inter(X14,X4)
      | X25 = c_UNIV ),
    inference(fof_simplification,[status(thm)],[c_0_1277]) ).

fof(c_0_4215,plain,
    ! [X25,X14,X4] :
      ( ~ c_in(X25,X14,tc_set(X4))
      | c_Inter(X14,X4) != c_UNIV
      | X25 = c_UNIV ),
    inference(fof_simplification,[status(thm)],[c_0_1278]) ).

fof(c_0_4216,axiom,
    ! [X98,X104,X105] : c_Nat_Osize(c_Event_Oevent_OSays(X105,X104,X98),tc_Event_Oevent) = c_0,
    c_0_1279 ).

fof(c_0_4217,axiom,
    ! [X24,X4] :
      ( c_Nat_Osize(c_List_Oremdups(X24,X4),tc_List_Olist(X4)) != c_Nat_Osize(X24,tc_List_Olist(X4))
      | c_List_Oremdups(X24,X4) = X24 ),
    c_0_1280 ).

fof(c_0_4218,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_lessequals(X19,c_0,X4)
      | c_HOL_Oabs(X19,X4) = c_uminus(X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1281]) ).

fof(c_0_4219,axiom,
    ! [X6,X4] : c_union(c_Transitive__Closure_Otrancl(X6,X4),c_Relation_OId,tc_prod(X4,X4)) = c_Transitive__Closure_Ortrancl(X6,X4),
    c_0_1282 ).

fof(c_0_4220,axiom,
    ! [X1,X4] : c_Set_Ocontents(c_insert(X1,c_emptyset,X4),X4) = X1,
    c_0_1283 ).

fof(c_0_4221,axiom,
    ! [X2,X4] : c_List_Olast(c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) = X2,
    c_0_1284 ).

fof(c_0_4222,plain,
    ! [X49] :
      ( ~ c_less(c_HOL_Oabs(X49,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
      | X49 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1285]) ).

fof(c_0_4223,axiom,
    ! [X22,X16] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X22)),tc_IntDef_Oint),c_IntDef_Oint(X16),tc_IntDef_Oint),
    c_0_1286 ).

fof(c_0_4224,axiom,
    ! [X22,X16] : c_minus(c_Suc(X16),c_Suc(X22),tc_nat) = c_minus(X16,X22,tc_nat),
    c_0_1287 ).

fof(c_0_4225,axiom,
    ! [X2,X42] : c_List_Obutlast(c_List_Olist_OCons(X2,c_List_Olist_ONil,X42),X42) = c_List_Olist_ONil,
    c_0_1288 ).

fof(c_0_4226,plain,
    ! [X14,X4] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_Finite__Set_Ocard(X14,X4) != c_0
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1289]) ).

fof(c_0_4227,axiom,
    ! [X103,X28,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Event_Oused(X103),tc_Message_Omsg),
    c_0_1290 ).

fof(c_0_4228,axiom,
    ! [X28,X13,X14] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X28,X14)),c_Event_OinitState(X13),tc_Message_Omsg),
    c_0_1291 ).

fof(c_0_4229,axiom,
    ! [X91,X98] : c_Nat_Osize(c_Message_Omsg_OCrypt(X91,X98),tc_Message_Omsg) = c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    c_0_1292 ).

fof(c_0_4230,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Power_Orecpower(X4)
      | c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X2,X4) = c_Numeral_Onumber__of(c_Numeral_OMin,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1293]) ).

fof(c_0_4231,plain,
    ! [X2,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_uminus(c_1,X4),X2,X4) = c_uminus(c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1294]) ).

fof(c_0_4232,plain,
    ! [X19,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | c_SetInterval_OatLeastAtMost(X19,X19,X4) = c_insert(X19,c_emptyset,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1295]) ).

fof(c_0_4233,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(X19,c_0,X4) = c_times(X28,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1296]) ).

fof(c_0_4234,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_times(c_0,X19,X4) = c_times(c_0,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1297]) ).

fof(c_0_4235,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X2,c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) = c_uminus(X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1298]) ).

fof(c_0_4236,plain,
    ! [X2,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Power_Orecpower(X4)
      | ~ c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X2,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1299]) ).

fof(c_0_4237,plain,
    ! [X2,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | ~ c_Parity_Oeven(X2,tc_nat)
      | c_Nat_Opower(c_uminus(c_1,X4),X2,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1300]) ).

fof(c_0_4238,axiom,
    ! [X1,X4] : c_Nat_Opower(X1,c_1,tc_set(tc_prod(X4,X4))) = X1,
    c_0_1301 ).

fof(c_0_4239,axiom,
    ! [X86,X42] : c_Nat_Opower(X86,c_0,tc_set(tc_prod(X42,X42))) = c_Relation_OId,
    c_0_1302 ).

fof(c_0_4240,axiom,
    ! [X16] : c_SetInterval_OatLeastLessThan(X16,c_Suc(X16),tc_nat) = c_insert(X16,c_emptyset,tc_nat),
    c_0_1303 ).

fof(c_0_4241,axiom,
    ! [X12,X48] : c_Numeral_Obin__add(c_Numeral_OBit(X48,c_Numeral_Obit_OB1),c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X48,c_Numeral_Obin__succ(X12)),c_Numeral_Obit_OB0),
    c_0_1304 ).

fof(c_0_4242,axiom,
    ! [X1,X4] :
      ( X1 = c_List_Olist_ONil
      | c_List_Olist_OCons(c_List_Ohd(X1,X4),c_List_Otl(X1,X4),X4) = X1 ),
    c_0_1305 ).

fof(c_0_4243,axiom,
    ! [X61,X4] :
      ( c_in(c_List_Olast(X61,X4),c_List_Oset(X61,X4),X4)
      | X61 = c_List_Olist_ONil ),
    c_0_1306 ).

fof(c_0_4244,axiom,
    ! [X24,X4] :
      ( c_in(c_List_Ohd(X24,X4),c_List_Oset(X24,X4),X4)
      | X24 = c_List_Olist_ONil ),
    c_0_1307 ).

fof(c_0_4245,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OSays(X105,X104,X98),
    c_0_1308 ).

fof(c_0_4246,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_ONotes(X95,X97),
    c_0_1309 ).

fof(c_0_4247,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OSays(X105,X104,X98),
    c_0_1310 ).

fof(c_0_4248,axiom,
    ! [X97,X98,X95,X104,X105] : c_Event_Oevent_OSays(X105,X104,X98) != c_Event_Oevent_OGets(X95,X97),
    c_0_1311 ).

fof(c_0_4249,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,X1,X4)
      | c_OrderedGroup_Opprt(X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1312]) ).

fof(c_0_4250,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X1,c_0,X4)
      | c_OrderedGroup_Onprt(X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1313]) ).

fof(c_0_4251,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | ~ c_lessequals(c_0,X1,X4)
      | c_HOL_Oabs(X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1314]) ).

fof(c_0_4252,plain,
    ! [X16,X42] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X42)
      | c_NatArith_Oof__nat(c_Suc(X16),X42) = c_plus(c_NatArith_Oof__nat(X16,X42),c_1,X42) ),
    inference(fof_simplification,[status(thm)],[c_0_1315]) ).

fof(c_0_4253,plain,
    ! [X2,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(X2,c_0,X4)
      | c_OrderedGroup_Opprt(X2,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1316]) ).

fof(c_0_4254,plain,
    ! [X2,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | ~ c_lessequals(c_0,X2,X4)
      | c_OrderedGroup_Onprt(X2,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1317]) ).

fof(c_0_4255,plain,
    ! [X4] :
      ( ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X4))
      | c_Finite__Set_Ocard(c_emptyset,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1318]) ).

fof(c_0_4256,plain,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Numeral_Onumber__of(X12,tc_nat) != c_0
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1319]) ).

fof(c_0_4257,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,X28,X4) != c_0
      | X28 = c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1320]) ).

fof(c_0_4258,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_1 != c_divide(X19,X28,X4)
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1321]) ).

fof(c_0_4259,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_1 != c_divide(X28,X19,X4)
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1322]) ).

fof(c_0_4260,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(X28,X19,X4) != c_1
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1323]) ).

fof(c_0_4261,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,X28,X4) != c_1
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1324]) ).

fof(c_0_4262,axiom,
    ! [X1,X12,X48] : c_Numeral_Obin__add(c_Numeral_OBit(X48,c_Numeral_Obit_OB0),c_Numeral_OBit(X12,X1)) = c_Numeral_OBit(c_Numeral_Obin__add(X48,X12),X1),
    c_0_1325 ).

fof(c_0_4263,axiom,
    ! [X22,X16] : c_times(X16,c_0,tc_nat) = c_times(X22,c_0,tc_nat),
    c_0_1326 ).

fof(c_0_4264,axiom,
    ! [X22,X16] : c_times(c_0,X16,tc_nat) = c_times(c_0,X22,tc_nat),
    c_0_1327 ).

fof(c_0_4265,plain,
    ! [X22,X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_Nat_Opower(X19,X22,X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1328]) ).

fof(c_0_4266,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_Oempty__Union__conv__1(X14,X4),X14,tc_set(X4))
      | c_emptyset = c_Union(X14,X4) ),
    c_0_1329 ).

fof(c_0_4267,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_OUnion__empty__conv__1(X14,X4),X14,tc_set(X4))
      | c_Union(X14,X4) = c_emptyset ),
    c_0_1330 ).

fof(c_0_4268,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_OInter__UNIV__conv__2__1(X14,X4),X14,tc_set(X4))
      | c_UNIV = c_Inter(X14,X4) ),
    c_0_1331 ).

fof(c_0_4269,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_OInter__UNIV__conv__1__1(X14,X4),X14,tc_set(X4))
      | c_Inter(X14,X4) = c_UNIV ),
    c_0_1332 ).

fof(c_0_4270,axiom,
    ! [X48,X16] :
      ( c_IntDef_Oint(X16) != c_Numeral_Onumber__of(X48,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_1333 ).

fof(c_0_4271,plain,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X48,tc_nat),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1334]) ).

fof(c_0_4272,plain,
    ! [X48,X19,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(X19,X3) != c_Numeral_Onumber__of(X48,X3)
      | c_uminus(c_Numeral_Onumber__of(X48,X3),X3) = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_1335]) ).

fof(c_0_4273,plain,
    ! [X48,X28,X3] :
      ( ~ class_Numeral_Onumber(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_Numeral_Onumber__of(X48,X3) != c_uminus(X28,X3)
      | X28 = c_uminus(c_Numeral_Onumber__of(X48,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1336]) ).

fof(c_0_4274,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_0 != c_divide(c_1,X19,X4)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1337]) ).

fof(c_0_4275,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(c_1,X19,X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1338]) ).

fof(c_0_4276,plain,
    ! [X49,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(X49,c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) = c_uminus(X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1339]) ).

fof(c_0_4277,plain,
    ! [X49,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X49,X4) = c_uminus(X49,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1340]) ).

fof(c_0_4278,axiom,
    ! [X12,X48] : c_Numeral_Obin__add(c_Numeral_OBit(X48,c_Numeral_Obit_OB1),c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X48,X12),c_Numeral_Obit_OB1),
    c_0_1341 ).

fof(c_0_4279,plain,
    ! [X60,X44] :
      ( ~ c_lessequals(X60,X44,tc_nat)
      | c_List_Oupt(X44,X60) = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_1342]) ).

fof(c_0_4280,plain,
    ! [X9] : ~ c_in(c_Message_Omsg_ONonce(X9),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(fof_simplification,[status(thm)],[c_0_1343]) ).

fof(c_0_4281,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_1 != c_divide(X28,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1344]) ).

fof(c_0_4282,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(X28,c_0,X4) != c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1345]) ).

fof(c_0_4283,plain,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_times(X19,X7,X4) != X7
      | X7 = c_0
      | X19 = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1346]) ).

fof(c_0_4284,plain,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 != c_times(X28,X7,X4)
      | X7 = c_0
      | X28 = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1347]) ).

fof(c_0_4285,plain,
    ! [X7,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_times(X7,X19,X4) != X7
      | X7 = c_0
      | X19 = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1348]) ).

fof(c_0_4286,plain,
    ! [X7,X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 != c_times(X7,X28,X4)
      | X7 = c_0
      | X28 = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1349]) ).

fof(c_0_4287,axiom,
    ! [X103,X14] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_Oknows(X14,X103),tc_Message_Omsg),
    c_0_1350 ).

fof(c_0_4288,axiom,
    ! [X98] : c_Nat_Osize(c_Message_Omsg_OHash(X98),tc_Message_Omsg) = c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    c_0_1351 ).

fof(c_0_4289,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | c_times(X19,X28,X4) != c_0
      | X28 = c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1352]) ).

fof(c_0_4290,plain,
    ! [X12,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X12,tc_nat),X4) = c_0
      | c_Numeral_Onumber__of(X12,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1353]) ).

fof(c_0_4291,axiom,
    ! [X60,X44] : c_Nat_Osize(c_List_Oupt(X44,X60),tc_List_Olist(tc_nat)) = c_minus(X60,X44,tc_nat),
    c_0_1354 ).

fof(c_0_4292,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X19,X28,X4) != c_0
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1355]) ).

fof(c_0_4293,plain,
    ! [X14,X4] :
      ( ~ c_lessequals(X14,c_emptyset,tc_set(X4))
      | X14 = c_emptyset ),
    inference(fof_simplification,[status(thm)],[c_0_1356]) ).

fof(c_0_4294,axiom,
    ! [X14,X4] : c_Relation_Oconverse(c_Relation_Odiag(X14,X4),X4,X4) = c_Relation_Odiag(X14,X4),
    c_0_1357 ).

fof(c_0_4295,axiom,
    ! [X22,X16] : c_lessequals(c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint),c_IntDef_Oint(X16),tc_IntDef_Oint),
    c_0_1358 ).

fof(c_0_4296,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_uminus(X19,X4),X4) = c_uminus(c_HOL_Oinverse(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1359]) ).

fof(c_0_4297,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_HOL_Oabs(c_HOL_Oinverse(X19,X4),X4) = c_HOL_Oinverse(c_HOL_Oabs(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1360]) ).

fof(c_0_4298,plain,
    ! [X48,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X48,tc_nat),X4) = c_Numeral_Onumber__of(X48,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1361]) ).

fof(c_0_4299,plain,
    ! [X14,X4] : ~ c_less(X14,c_emptyset,tc_set(X4)),
    inference(fof_simplification,[status(thm)],[c_0_1362]) ).

fof(c_0_4300,plain,
    ! [X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | ~ c_less(X2,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1363]) ).

fof(c_0_4301,axiom,
    ! [X14,X4] : c_inter(X14,c_uminus(X14,tc_set(X4)),X4) = c_emptyset,
    c_0_1364 ).

fof(c_0_4302,axiom,
    ! [X14,X4] : c_inter(c_uminus(X14,tc_set(X4)),X14,X4) = c_emptyset,
    c_0_1365 ).

fof(c_0_4303,axiom,
    ! [X2,X42] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X2,X42),X42) = c_insert(X2,c_emptyset,X42),
    c_0_1366 ).

fof(c_0_4304,plain,
    ! [X49] :
      ( ~ c_lessequals(c_0,X49,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X49)) = X49 ),
    inference(fof_simplification,[status(thm)],[c_0_1367]) ).

fof(c_0_4305,plain,
    ! [X22] :
      ( ~ c_lessequals(c_IntDef_Oint(X22),c_0,tc_IntDef_Oint)
      | X22 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1368]) ).

fof(c_0_4306,plain,
    ! [X16] :
      ( ~ c_Divides_Oop_Advd(X16,c_Suc(c_0),tc_nat)
      | X16 = c_Suc(c_0) ),
    inference(fof_simplification,[status(thm)],[c_0_1369]) ).

fof(c_0_4307,axiom,
    ! [X48] :
      ( c_Numeral_Onumber__of(X48,tc_nat) != c_0
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_1370 ).

fof(c_0_4308,axiom,
    ! [X48] :
      ( c_0 != c_Numeral_Onumber__of(X48,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_1371 ).

fof(c_0_4309,axiom,
    ! [X24,X4] :
      ( c_less(c_0,c_Nat_Osize(X24,tc_List_Olist(X4)),tc_nat)
      | X24 = c_List_Olist_ONil ),
    c_0_1372 ).

fof(c_0_4310,plain,
    ! [X17] : ~ c_less(c_IntDef_Oint(X17),c_0,tc_IntDef_Oint),
    inference(fof_simplification,[status(thm)],[c_0_1373]) ).

fof(c_0_4311,axiom,
    ! [X24,X4] :
      ( c_List_Oremdups(X24,X4) != X24
      | c_Nat_Osize(c_List_Oremdups(X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)) ),
    c_0_1374 ).

fof(c_0_4312,plain,
    ! [X22] :
      ( ~ c_less(X22,c_Suc(c_0),tc_nat)
      | X22 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1375]) ).

fof(c_0_4313,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(X19,c_HOL_Oinverse(X19,X4),X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1376]) ).

fof(c_0_4314,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | X19 = c_0
      | c_times(c_HOL_Oinverse(X19,X4),X19,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1377]) ).

fof(c_0_4315,axiom,
    ! [X24,X22,X4] :
      ( c_List_Otake(X22,X24,X4) != c_List_Olist_ONil
      | X22 = c_0
      | X24 = c_List_Olist_ONil ),
    c_0_1378 ).

fof(c_0_4316,axiom,
    ! [X22,X16] :
      ( c_Suc(c_0) != c_times(X16,X22,tc_nat)
      | X22 = c_1 ),
    c_0_1379 ).

fof(c_0_4317,axiom,
    ! [X22,X16] :
      ( c_Suc(c_0) != c_times(X16,X22,tc_nat)
      | X16 = c_1 ),
    c_0_1380 ).

fof(c_0_4318,axiom,
    ! [X22,X16] :
      ( c_times(X16,X22,tc_nat) != c_Suc(c_0)
      | X22 = c_1 ),
    c_0_1381 ).

fof(c_0_4319,axiom,
    ! [X22,X16] :
      ( c_times(X16,X22,tc_nat) != c_Suc(c_0)
      | X16 = c_1 ),
    c_0_1382 ).

fof(c_0_4320,axiom,
    ! [X26,X24,X4] :
      ( X24 != c_append(X24,X26,X4)
      | X26 = c_List_Olist_ONil ),
    c_0_1383 ).

fof(c_0_4321,axiom,
    ! [X26,X24,X4] :
      ( X26 != c_append(X24,X26,X4)
      | X24 = c_List_Olist_ONil ),
    c_0_1384 ).

fof(c_0_4322,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != X24
      | X26 = c_List_Olist_ONil ),
    c_0_1385 ).

fof(c_0_4323,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != X26
      | X24 = c_List_Olist_ONil ),
    c_0_1386 ).

fof(c_0_4324,plain,
    ! [X88] : ~ c_in(X88,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    inference(fof_simplification,[status(thm)],[c_0_1387]) ).

fof(c_0_4325,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_less(c_1,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1388]) ).

fof(c_0_4326,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_1,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1389]) ).

fof(c_0_4327,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_less(c_0,c_HOL_Oabs(X19,X4),X4)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1390]) ).

fof(c_0_4328,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_plus(X19,c_uminus(X19,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1391]) ).

fof(c_0_4329,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_plus(c_uminus(X19,X4),X19,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1392]) ).

fof(c_0_4330,axiom,
    ! [X13,X14,X4] :
      ( c_union(X14,X13,X4) != c_emptyset
      | X13 = c_emptyset ),
    c_0_1393 ).

fof(c_0_4331,axiom,
    ! [X13,X14,X4] :
      ( c_union(X14,X13,X4) != c_emptyset
      | X14 = c_emptyset ),
    c_0_1394 ).

fof(c_0_4332,axiom,
    ! [X13,X14,X4] :
      ( c_inter(X14,X13,X4) != c_UNIV
      | X13 = c_UNIV ),
    c_0_1395 ).

fof(c_0_4333,axiom,
    ! [X13,X14,X4] :
      ( c_inter(X14,X13,X4) != c_UNIV
      | X14 = c_UNIV ),
    c_0_1396 ).

fof(c_0_4334,axiom,
    ! [X24,X22,X4] :
      ( c_List_Orotate(X22,X24,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    c_0_1397 ).

fof(c_0_4335,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != c_List_Olist_ONil
      | X26 = c_List_Olist_ONil ),
    c_0_1398 ).

fof(c_0_4336,axiom,
    ! [X26,X24,X4] :
      ( c_append(X24,X26,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    c_0_1399 ).

fof(c_0_4337,axiom,
    ! [X26,X24,X4] :
      ( c_List_Olist_ONil != c_append(X24,X26,X4)
      | X26 = c_List_Olist_ONil ),
    c_0_1400 ).

fof(c_0_4338,axiom,
    ! [X26,X24,X4] :
      ( c_List_Olist_ONil != c_append(X24,X26,X4)
      | X24 = c_List_Olist_ONil ),
    c_0_1401 ).

fof(c_0_4339,axiom,
    ! [X6,X14,X4] :
      ( c_Equiv__Relations_Oquotient(X14,X6,X4) != c_emptyset
      | X14 = c_emptyset ),
    c_0_1402 ).

fof(c_0_4340,axiom,
    ! [X6,X14,X4] :
      ( c_emptyset != c_Equiv__Relations_Oquotient(X14,X6,X4)
      | X14 = c_emptyset ),
    c_0_1403 ).

fof(c_0_4341,axiom,
    ! [X2,X82,X4] : c_List_Olist_OCons(X2,X82,X4) != X82,
    c_0_1404 ).

fof(c_0_4342,axiom,
    ! [X24,X2,X4] : X24 != c_List_Olist_OCons(X2,X24,X4),
    c_0_1405 ).

fof(c_0_4343,axiom,
    ! [X22,X16] :
      ( c_times(X16,X22,tc_nat) != c_0
      | X22 = c_0
      | X16 = c_0 ),
    c_0_1406 ).

fof(c_0_4344,plain,
    ! [X1] :
      ( ~ c_in(X1,c_Message_OsymKeys,tc_nat)
      | c_Message_OinvKey(X1) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1407]) ).

fof(c_0_4345,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_lessequals(c_0,c_OrderedGroup_Opprt(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1408]) ).

fof(c_0_4346,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_lessequals(c_OrderedGroup_Onprt(X19,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1409]) ).

fof(c_0_4347,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_lessequals(c_0,c_HOL_Oabs(X19,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1410]) ).

fof(c_0_4348,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_0,c_NatArith_Oof__nat(X22,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1411]) ).

fof(c_0_4349,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_in(c_NatArith_Oof__nat(X22,X4),c_IntDef_ONats,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1412]) ).

fof(c_0_4350,axiom,
    ! [X19,X14,X4] : c_insert(X19,X14,X4) != c_emptyset,
    c_0_1413 ).

fof(c_0_4351,axiom,
    ! [X19,X14,X4] : c_emptyset != c_insert(X19,X14,X4),
    c_0_1414 ).

fof(c_0_4352,axiom,
    ! [X64,X43,X4] : c_List_Olist_OCons(X43,X64,X4) != c_List_Olist_ONil,
    c_0_1415 ).

fof(c_0_4353,axiom,
    ! [X64,X43,X4] : c_List_Olist_ONil != c_List_Olist_OCons(X43,X64,X4),
    c_0_1416 ).

fof(c_0_4354,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(fof_simplification,[status(thm)],[c_0_1417]) ).

fof(c_0_4355,axiom,
    ! [X2,X88] : c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X2)),X2) = c_Message_OHPair(X88,X2),
    c_0_1418 ).

fof(c_0_4356,axiom,
    ! [X2,X88] : c_Message_OHPair(X88,X2) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X2)),X2),
    c_0_1419 ).

fof(c_0_4357,plain,
    ! [X49] :
      ( ~ c_lessequals(X49,c_0,tc_IntDef_Oint)
      | c_IntDef_Onat(X49) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1420]) ).

fof(c_0_4358,axiom,
    ! [X22,X16] :
      ( c_plus(X16,X22,tc_nat) != c_0
      | X22 = c_0 ),
    c_0_1421 ).

fof(c_0_4359,axiom,
    ! [X22,X16] :
      ( c_plus(X16,X22,tc_nat) != c_0
      | X16 = c_0 ),
    c_0_1422 ).

fof(c_0_4360,axiom,
    ! [X19] : c_div(X19,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X19,tc_IntDef_Oint),
    c_0_1423 ).

fof(c_0_4361,axiom,
    ! [X14,X4] : c_in(c_List_Olist_ONil,c_List_Olists(X14,X4),tc_List_Olist(X4)),
    c_0_1424 ).

fof(c_0_4362,axiom,
    ! [X24,X4] : c_in(c_List_Oset(X24,X4),c_Finite__Set_OFinites,tc_set(X4)),
    c_0_1425 ).

fof(c_0_4363,plain,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_uminus(X49,tc_IntDef_Oint),X4) = c_uminus(c_IntDef_Oof__int(X49,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1426]) ).

fof(c_0_4364,plain,
    ! [X7,X4] : ~ c_in(X7,c_emptyset,X4),
    inference(fof_simplification,[status(thm)],[c_0_1427]) ).

fof(c_0_4365,plain,
    ! [X2,X42] : ~ c_List_Oop_Amem(X2,c_List_Olist_ONil,X42),
    inference(fof_simplification,[status(thm)],[c_0_1428]) ).

fof(c_0_4366,plain,
    ! [X22] : ~ c_less(X22,X22,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_1429]) ).

fof(c_0_4367,plain,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1430]) ).

fof(c_0_4368,plain,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X48,tc_nat)) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1431]) ).

fof(c_0_4369,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Omeet(c_0,c_uminus(c_0,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1432]) ).

fof(c_0_4370,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_LOrder_Ojoin(c_0,c_uminus(c_0,X4),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1433]) ).

fof(c_0_4371,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_lessequals(c_HOL_Oabs(c_0,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1434]) ).

fof(c_0_4372,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_NatArith_Oof__nat(c_0,X4),c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1435]) ).

fof(c_0_4373,plain,
    ! [X22] :
      ( ~ c_less(X22,c_1,tc_nat)
      | X22 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1436]) ).

fof(c_0_4374,plain,
    ! [X44] :
      ( ~ c_lessequals(X44,c_0,tc_nat)
      | X44 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1437]) ).

fof(c_0_4375,plain,
    ! [X16] :
      ( ~ c_Divides_Oop_Advd(c_0,X16,tc_IntDef_Oint)
      | X16 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1438]) ).

fof(c_0_4376,plain,
    ! [X16] :
      ( ~ c_Divides_Oop_Advd(c_0,X16,tc_nat)
      | X16 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1439]) ).

fof(c_0_4377,axiom,
    ! [X14,X4] :
      ( c_in(c_Main_Oall__not__in__conv__1(X14,X4),X14,X4)
      | X14 = c_emptyset ),
    c_0_1440 ).

fof(c_0_4378,axiom,
    ! [X1,X4] : c_Relation_ORange(c_Relation_Odiag(X1,X4),X4,X4) = X1,
    c_0_1441 ).

fof(c_0_4379,axiom,
    ! [X1,X4] : c_Relation_ODomain(c_Relation_Odiag(X1,X4),X4,X4) = X1,
    c_0_1442 ).

fof(c_0_4380,axiom,
    ! [X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X48,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X48),tc_nat) ),
    c_0_1443 ).

fof(c_0_4381,plain,
    ! [X22] : ~ c_less(X22,c_0,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_1444]) ).

fof(c_0_4382,axiom,
    ! [X86,X4] : c_Relation_ORange(c_Transitive__Closure_Ortrancl(X86,X4),X4,X4) = c_UNIV,
    c_0_1445 ).

fof(c_0_4383,axiom,
    ! [X86,X4] : c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X86,X4),X4,X4) = c_UNIV,
    c_0_1446 ).

fof(c_0_4384,axiom,
    ! [X17] : c_in(c_SetInterval_OlessThan(X17,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1447 ).

fof(c_0_4385,axiom,
    ! [X17] : c_in(c_SetInterval_OatMost(X17,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1448 ).

fof(c_0_4386,plain,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    inference(fof_simplification,[status(thm)],[c_0_1449]) ).

fof(c_0_4387,plain,
    ~ c_less(c_0,c_0,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_1450]) ).

fof(c_0_4388,plain,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(c_List_Orev(X24,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1451]) ).

fof(c_0_4389,plain,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(c_List_Orotate1(X24,X4),X4)
      | c_List_Odistinct(X24,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1452]) ).

fof(c_0_4390,axiom,
    ! [X103,X14] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_Oused(X103),tc_Message_Omsg),
    c_0_1453 ).

fof(c_0_4391,axiom,
    ! [X14] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X14)),c_Event_OinitState(X14),tc_Message_Omsg),
    c_0_1454 ).

fof(c_0_4392,axiom,
    ! [X60,X44] :
      ( c_List_Oupt(X44,X60) != c_List_Olist_ONil
      | c_lessequals(X60,X44,tc_nat)
      | X60 = c_0 ),
    c_0_1455 ).

fof(c_0_4393,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_Omsg_OMPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X109 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)) ),
    c_0_1456 ).

fof(c_0_4394,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X88,X87) != c_Message_Omsg_OMPair(X109,X108)
      | X109 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X88,X87)) ),
    c_0_1457 ).

fof(c_0_4395,axiom,
    ! [X89] : c_Message_Oparts(c_Message_Osynth(X89)) = c_union(c_Message_Oparts(X89),c_Message_Osynth(X89),tc_Message_Omsg),
    c_0_1458 ).

fof(c_0_4396,axiom,
    ! [X89] : c_Message_Oanalz(c_Message_Osynth(X89)) = c_union(c_Message_Oanalz(X89),c_Message_Osynth(X89),tc_Message_Omsg),
    c_0_1459 ).

fof(c_0_4397,axiom,
    ! [X12,X48] : c_Numeral_Obin__mult(c_Numeral_OBit(X48,c_Numeral_Obit_OB0),X12) = c_Numeral_OBit(c_Numeral_Obin__mult(X48,X12),c_Numeral_Obit_OB0),
    c_0_1460 ).

fof(c_0_4398,axiom,
    ! [X48] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_Numeral_Onumber__of(X48,tc_nat)) = c_Numeral_Onumber__of(X48,tc_IntDef_Oint) ),
    c_0_1461 ).

fof(c_0_4399,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(c_0,X19,X4) = c_uminus(X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1462]) ).

fof(c_0_4400,axiom,
    ! [X60,X44] :
      ( c_lessequals(X44,X60,tc_nat)
      | c_List_Oupt(X44,c_Suc(X60)) = c_List_Olist_ONil ),
    c_0_1463 ).

fof(c_0_4401,axiom,
    ! [X14,X4] :
      ( c_in(X14,c_Finite__Set_OFinites,tc_set(X4))
      | c_Finite__Set_Ocard(X14,X4) = c_0 ),
    c_0_1464 ).

fof(c_0_4402,axiom,
    ! [X19] : c_Divides_Oop_Amod(X19,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0,
    c_0_1465 ).

fof(c_0_4403,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1466]) ).

fof(c_0_4404,axiom,
    ! [X22] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X22)),tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_1467 ).

fof(c_0_4405,axiom,
    c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
    c_0_1468 ).

fof(c_0_4406,plain,
    ! [X2,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | X2 = c_0
      | c_1 = c_divide(X2,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1469]) ).

fof(c_0_4407,plain,
    ! [X2,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | X2 = c_0
      | c_divide(X2,X2,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1470]) ).

fof(c_0_4408,axiom,
    ! [X4] : c_Pow(c_emptyset,X4) = c_insert(c_emptyset,c_emptyset,tc_set(X4)),
    c_0_1471 ).

fof(c_0_4409,axiom,
    ! [X42] : c_List_Olistset(c_List_Olist_ONil,X42) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X42)),
    c_0_1472 ).

fof(c_0_4410,axiom,
    ! [X7,X28,X112,X14] : c_Public_OpublicKey(X7,X112) != c_Message_OinvKey(c_Public_OpublicKey(X28,X14)),
    c_0_1473 ).

fof(c_0_4411,axiom,
    ! [X7,X28,X112,X14] : c_Message_OinvKey(c_Public_OpublicKey(X28,X14)) != c_Public_OpublicKey(X7,X112),
    c_0_1474 ).

fof(c_0_4412,plain,
    ! [X2] :
      ( ~ c_Parity_Oeven(c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1475]) ).

fof(c_0_4413,plain,
    ! [X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1476]) ).

fof(c_0_4414,plain,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X48,tc_nat) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1477]) ).

fof(c_0_4415,plain,
    ! [X48] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X48,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1478]) ).

fof(c_0_4416,plain,
    ! [X48] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X48,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X48,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1479]) ).

fof(c_0_4417,plain,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X6,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_1480]) ).

fof(c_0_4418,plain,
    ! [X6,X4] :
      ( ~ c_Wellfounded__Recursion_Owf(X6,X4)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X6,X4),tc_List_Olist(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_1481]) ).

fof(c_0_4419,axiom,
    ! [X16] : c_IntDef_Oint(c_Suc(X16)) = c_plus(c_1,c_IntDef_Oint(X16),tc_IntDef_Oint),
    c_0_1482 ).

fof(c_0_4420,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X19,c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1483]) ).

fof(c_0_4421,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,X28,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1484]) ).

fof(c_0_4422,plain,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OlessThan(X17,X4),tc_set(X4)) = c_SetInterval_OatLeast(X17,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1485]) ).

fof(c_0_4423,plain,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OgreaterThan(X17,X4),tc_set(X4)) = c_SetInterval_OatMost(X17,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1486]) ).

fof(c_0_4424,plain,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OatMost(X17,X4),tc_set(X4)) = c_SetInterval_OgreaterThan(X17,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1487]) ).

fof(c_0_4425,plain,
    ! [X17,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_uminus(c_SetInterval_OatLeast(X17,X4),tc_set(X4)) = c_SetInterval_OlessThan(X17,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1488]) ).

fof(c_0_4426,plain,
    ! [X12,X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_uminus(c_Numeral_Onumber__of(X12,X4),X4) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X12),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1489]) ).

fof(c_0_4427,plain,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_0,c_Suc(X22),X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1490]) ).

fof(c_0_4428,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Orotate1(X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    c_0_1491 ).

fof(c_0_4429,axiom,
    ! [X24,X4] : c_Nat_Osize(c_List_Orev(X24,X4),tc_List_Olist(X4)) = c_Nat_Osize(X24,tc_List_Olist(X4)),
    c_0_1492 ).

fof(c_0_4430,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_0 = c_divide(c_1,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1493]) ).

fof(c_0_4431,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Oordered__field(X4)
      | c_divide(c_1,c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1494]) ).

fof(c_0_4432,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(c_0,c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1495]) ).

fof(c_0_4433,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1496]) ).

fof(c_0_4434,axiom,
    ! [X13,X14,X4] :
      ( c_uminus(X14,tc_set(X4)) != c_uminus(X13,tc_set(X4))
      | X14 = X13 ),
    c_0_1497 ).

fof(c_0_4435,axiom,
    ! [X22,X89] : c_in(c_Message_Omsg_ONumber(X22),c_Message_Osynth(X89),tc_Message_Omsg),
    c_0_1498 ).

fof(c_0_4436,axiom,
    ! [X89,X14] : c_in(c_Message_Omsg_OAgent(X14),c_Message_Osynth(X89),tc_Message_Omsg),
    c_0_1499 ).

fof(c_0_4437,plain,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Orev(X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1500]) ).

fof(c_0_4438,plain,
    ! [X24,X4] :
      ( ~ c_List_Odistinct(X24,X4)
      | c_List_Odistinct(c_List_Orotate1(X24,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1501]) ).

fof(c_0_4439,plain,
    ! [X1,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omax(X1,X1,X3) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1502]) ).

fof(c_0_4440,plain,
    ! [X1,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Omin(X1,X1,X3) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1503]) ).

fof(c_0_4441,plain,
    ! [X1,X4] :
      ( ~ class_LOrder_Omeet__semilorder(X4)
      | c_LOrder_Omeet(X1,X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1504]) ).

fof(c_0_4442,plain,
    ! [X1,X4] :
      ( ~ class_LOrder_Ojoin__semilorder(X4)
      | c_LOrder_Ojoin(X1,X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1505]) ).

fof(c_0_4443,axiom,
    ! [X49] :
      ( c_lessequals(c_0,X49,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X49)) = c_0 ),
    c_0_1506 ).

fof(c_0_4444,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X19,X19,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1507]) ).

fof(c_0_4445,plain,
    ! [X2,X4] :
      ( ~ class_Orderings_Oorder(X4)
      | c_lessequals(X2,X2,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1508]) ).

fof(c_0_4446,plain,
    ! [X7,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 = c_times(c_1,X7,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1509]) ).

fof(c_0_4447,plain,
    ! [X7,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | X7 = c_times(X7,c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1510]) ).

fof(c_0_4448,plain,
    ! [X1,X4] :
      ( ~ class_Ring__and__Field_Ofield(X4)
      | c_divide(X1,c_1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1511]) ).

fof(c_0_4449,plain,
    ! [X1,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(X1,c_1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1512]) ).

fof(c_0_4450,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X4)
      | c_times(X1,c_1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1513]) ).

fof(c_0_4451,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X4)
      | c_times(c_1,X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1514]) ).

fof(c_0_4452,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_minus(X1,c_0,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1515]) ).

fof(c_0_4453,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
      | c_plus(c_0,X1,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1516]) ).

fof(c_0_4454,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
      | c_plus(X1,c_0,X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1517]) ).

fof(c_0_4455,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_uminus(X19,X4),X4) = c_HOL_Oabs(X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1518]) ).

fof(c_0_4456,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_HOL_Oabs(X19,X4),X4) = c_HOL_Oabs(X19,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1519]) ).

fof(c_0_4457,axiom,
    ! [X14,X4] : c_minus(X14,X14,tc_set(X4)) = c_emptyset,
    c_0_1520 ).

fof(c_0_4458,axiom,
    c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
    c_0_1521 ).

fof(c_0_4459,plain,
    ! [X28,X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(X19,X4) != c_HOL_Oinverse(X28,X4)
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1522]) ).

fof(c_0_4460,axiom,
    ! [X14,X4] : c_lessequals(X14,X14,tc_set(X4)),
    c_0_1523 ).

fof(c_0_4461,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X4)
      | c_times(X19,c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1524]) ).

fof(c_0_4462,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X4)
      | c_times(c_0,X19,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1525]) ).

fof(c_0_4463,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 = c_times(X28,c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1526]) ).

fof(c_0_4464,plain,
    ! [X28,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 = c_times(c_0,X28,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1527]) ).

fof(c_0_4465,plain,
    ! [X19,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(X19,c_0,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1528]) ).

fof(c_0_4466,plain,
    ! [X22,X4] :
      ( ~ class_Power_Orecpower(X4)
      | c_Nat_Opower(c_1,X22,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1529]) ).

fof(c_0_4467,axiom,
    ! [X1,X4] : c_minus(X1,c_emptyset,tc_set(X4)) = X1,
    c_0_1530 ).

fof(c_0_4468,axiom,
    ! [X14,X4] : c_lessequals(X14,c_UNIV,tc_set(X4)),
    c_0_1531 ).

fof(c_0_4469,axiom,
    ! [X14,X4] : c_minus(c_emptyset,X14,tc_set(X4)) = c_emptyset,
    c_0_1532 ).

fof(c_0_4470,axiom,
    ! [X1,X4] : c_uminus(c_uminus(X1,tc_set(X4)),tc_set(X4)) = X1,
    c_0_1533 ).

fof(c_0_4471,axiom,
    ! [X14,X4] : c_minus(X14,c_UNIV,tc_set(X4)) = c_emptyset,
    c_0_1534 ).

fof(c_0_4472,axiom,
    c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
    c_0_1535 ).

fof(c_0_4473,axiom,
    ! [X14,X4] : c_lessequals(c_emptyset,X14,tc_set(X4)),
    c_0_1536 ).

fof(c_0_4474,axiom,
    ! [X22] : c_less(X22,c_Suc(X22),tc_nat),
    c_0_1537 ).

fof(c_0_4475,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_0,c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1538]) ).

fof(c_0_4476,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_less(c_0,c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1539]) ).

fof(c_0_4477,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_in(c_1,c_IntDef_ONats,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1540]) ).

fof(c_0_4478,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_in(c_0,c_IntDef_ONats,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1541]) ).

fof(c_0_4479,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_in(c_1,c_IntDef_OInts,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1542]) ).

fof(c_0_4480,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_in(c_0,c_IntDef_OInts,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1543]) ).

fof(c_0_4481,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_NatArith_Oof__nat(X22,tc_IntDef_Oint),X4) = c_NatArith_Oof__nat(X22,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1544]) ).

fof(c_0_4482,axiom,
    ! [X88] : c_in(c_Public_OshrK(X88),c_Message_OsymKeys,tc_nat),
    c_0_1545 ).

fof(c_0_4483,axiom,
    ! [X4] : c_lessequals(c_emptyset,c_emptyset,tc_set(X4)),
    c_0_1546 ).

fof(c_0_4484,axiom,
    ! [X12] : c_Numeral_Obin__minus(c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X12)),c_Numeral_Obit_OB1),
    c_0_1547 ).

fof(c_0_4485,axiom,
    ! [X22] : c_lessequals(c_0,c_IntDef_Oint(X22),tc_IntDef_Oint),
    c_0_1548 ).

fof(c_0_4486,axiom,
    ! [X22] : c_less(c_0,c_Suc(X22),tc_nat),
    c_0_1549 ).

fof(c_0_4487,axiom,
    ! [X4] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X4)),
    c_0_1550 ).

fof(c_0_4488,axiom,
    ! [X1] : c_div(X1,c_Suc(c_0),tc_nat) = X1,
    c_0_1551 ).

fof(c_0_4489,axiom,
    ! [X16] : c_Divides_Oop_Amod(X16,c_Suc(c_0),tc_nat) = c_0,
    c_0_1552 ).

fof(c_0_4490,axiom,
    ! [X17] : c_Divides_Oop_Advd(c_Suc(c_0),X17,tc_nat),
    c_0_1553 ).

fof(c_0_4491,plain,
    ! [X2] :
      ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
      | c_Parity_Oeven(c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_1554]) ).

fof(c_0_4492,axiom,
    ! [X1,X4] : c_union(X1,X1,X4) = X1,
    c_0_1555 ).

fof(c_0_4493,axiom,
    ! [X1,X4] : c_inter(X1,X1,X4) = X1,
    c_0_1556 ).

fof(c_0_4494,plain,
    ! [X1,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_HOL_Oinverse(X1,X4),X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1557]) ).

fof(c_0_4495,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    c_0_1558 ).

fof(c_0_4496,axiom,
    ! [X19] :
      ( X19 = c_0
      | c_div(X19,X19,tc_IntDef_Oint) = c_1 ),
    c_0_1559 ).

fof(c_0_4497,axiom,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    c_0_1560 ).

fof(c_0_4498,axiom,
    ! [X48,X16] :
      ( c_IntDef_Oint(X16) != c_Numeral_Onumber__of(X48,tc_IntDef_Oint)
      | X16 = c_IntDef_Onat(c_Numeral_Onumber__of(X48,tc_IntDef_Oint)) ),
    c_0_1561 ).

fof(c_0_4499,axiom,
    ! [X6,X4] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X6,X4),X4) = c_Transitive__Closure_Ortrancl(X6,X4),
    c_0_1562 ).

fof(c_0_4500,axiom,
    ! [X1,X4] : c_union(X1,c_emptyset,X4) = X1,
    c_0_1563 ).

fof(c_0_4501,axiom,
    ! [X1,X4] : c_union(c_emptyset,X1,X4) = X1,
    c_0_1564 ).

fof(c_0_4502,axiom,
    ! [X1,X4] : c_inter(X1,c_UNIV,X4) = X1,
    c_0_1565 ).

fof(c_0_4503,axiom,
    ! [X1,X4] : c_inter(c_UNIV,X1,X4) = X1,
    c_0_1566 ).

fof(c_0_4504,axiom,
    ! [X24,X4] : c_List_Oset(c_List_Orotate1(X24,X4),X4) = c_List_Oset(X24,X4),
    c_0_1567 ).

fof(c_0_4505,axiom,
    ! [X24,X4] : c_List_Oset(c_List_Orev(X24,X4),X4) = c_List_Oset(X24,X4),
    c_0_1568 ).

fof(c_0_4506,axiom,
    ! [X24,X4] : c_List_Oset(c_List_Oremdups(X24,X4),X4) = c_List_Oset(X24,X4),
    c_0_1569 ).

fof(c_0_4507,axiom,
    ! [X24,X4] : X24 = c_append(X24,c_List_Olist_ONil,X4),
    c_0_1570 ).

fof(c_0_4508,axiom,
    ! [X26,X4] : X26 = c_append(c_List_Olist_ONil,X26,X4),
    c_0_1571 ).

fof(c_0_4509,axiom,
    ! [X1,X42] : c_List_Oitrev(c_List_Olist_ONil,X1,X42) = X1,
    c_0_1572 ).

fof(c_0_4510,axiom,
    ! [X1,X4] : c_List_Odrop(c_0,X1,X4) = X1,
    c_0_1573 ).

fof(c_0_4511,axiom,
    ! [X24,X4] : c_append(X24,c_List_Olist_ONil,X4) = X24,
    c_0_1574 ).

fof(c_0_4512,axiom,
    ! [X26,X4] : c_append(c_List_Olist_ONil,X26,X4) = X26,
    c_0_1575 ).

fof(c_0_4513,axiom,
    ! [X1,X4] : c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X4) = X1,
    c_0_1576 ).

fof(c_0_4514,axiom,
    ! [X1,X4] : c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X4) = X1,
    c_0_1577 ).

fof(c_0_4515,axiom,
    ! [X28,X33,X14] : c_Message_OinvKey(c_Public_OpublicKey(X28,X33)) != c_Public_OshrK(X14),
    c_0_1578 ).

fof(c_0_4516,axiom,
    ! [X28,X33,X14] : c_Public_OshrK(X14) != c_Message_OinvKey(c_Public_OpublicKey(X28,X33)),
    c_0_1579 ).

fof(c_0_4517,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OlessThan(X2,X4) != c_SetInterval_OlessThan(X1,X4)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1580]) ).

fof(c_0_4518,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OgreaterThan(X2,X4) != c_SetInterval_OgreaterThan(X1,X4)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1581]) ).

fof(c_0_4519,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OatMost(X2,X4) != c_SetInterval_OatMost(X1,X4)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1582]) ).

fof(c_0_4520,plain,
    ! [X1,X2,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | c_SetInterval_OatLeast(X2,X4) != c_SetInterval_OatLeast(X1,X4)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1583]) ).

fof(c_0_4521,plain,
    ! [X28,X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(X19,X4) != c_uminus(X28,X4)
      | X19 = X28 ),
    inference(fof_simplification,[status(thm)],[c_0_1584]) ).

fof(c_0_4522,plain,
    ! [X22,X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_NatArith_Oof__nat(X16,X4) != c_NatArith_Oof__nat(X22,X4)
      | X16 = X22 ),
    inference(fof_simplification,[status(thm)],[c_0_1585]) ).

fof(c_0_4523,plain,
    ! [X49,X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oof__int(X12,X4) != c_IntDef_Oof__int(X49,X4)
      | X12 = X49 ),
    inference(fof_simplification,[status(thm)],[c_0_1586]) ).

fof(c_0_4524,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X4) = c_Numeral_Onumber__of(c_Numeral_OMin,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1587]) ).

fof(c_0_4525,axiom,
    ! [X14,X4] : c_union(X14,c_UNIV,X4) = c_UNIV,
    c_0_1588 ).

fof(c_0_4526,axiom,
    ! [X13,X4] : c_union(c_UNIV,X13,X4) = c_UNIV,
    c_0_1589 ).

fof(c_0_4527,axiom,
    ! [X14,X4] : c_inter(X14,c_emptyset,X4) = c_emptyset,
    c_0_1590 ).

fof(c_0_4528,axiom,
    ! [X13,X4] : c_inter(c_emptyset,X13,X4) = c_emptyset,
    c_0_1591 ).

fof(c_0_4529,axiom,
    ! [X4] : c_Relation_Oconverse(c_Relation_OId,X4,X4) = c_Relation_OId,
    c_0_1592 ).

fof(c_0_4530,axiom,
    ! [X3,X4] : c_Relation_ORange(c_emptyset,X3,X4) = c_emptyset,
    c_0_1593 ).

fof(c_0_4531,axiom,
    ! [X4] : c_Relation_ORange(c_Relation_OId,X4,X4) = c_UNIV,
    c_0_1594 ).

fof(c_0_4532,axiom,
    ! [X3,X4] : c_Relation_ODomain(c_emptyset,X4,X3) = c_emptyset,
    c_0_1595 ).

fof(c_0_4533,axiom,
    ! [X4] : c_Relation_ODomain(c_Relation_OId,X4,X4) = c_UNIV,
    c_0_1596 ).

fof(c_0_4534,axiom,
    ! [X22] :
      ( c_less(c_0,X22,tc_nat)
      | X22 = c_0 ),
    c_0_1597 ).

fof(c_0_4535,axiom,
    ! [X16] : c_minus(X16,X16,tc_nat) = c_0,
    c_0_1598 ).

fof(c_0_4536,axiom,
    ! [X22,X4] : c_List_Otake(X22,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    c_0_1599 ).

fof(c_0_4537,axiom,
    ! [X24,X4] : c_List_Otake(c_0,X24,X4) = c_List_Olist_ONil,
    c_0_1600 ).

fof(c_0_4538,axiom,
    ! [X14,X4] : c_List_Osublist(c_List_Olist_ONil,X14,X4) = c_List_Olist_ONil,
    c_0_1601 ).

fof(c_0_4539,axiom,
    ! [X24,X4] : c_List_Osublist(X24,c_emptyset,X4) = c_List_Olist_ONil,
    c_0_1602 ).

fof(c_0_4540,axiom,
    ! [X22,X4] : c_List_Orotate(X22,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    c_0_1603 ).

fof(c_0_4541,axiom,
    ! [X2,X42] : c_List_Oreplicate(c_0,X2,X42) = c_List_Olist_ONil,
    c_0_1604 ).

fof(c_0_4542,axiom,
    ! [X2,X42] : c_List_Oremove1(X2,c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    c_0_1605 ).

fof(c_0_4543,axiom,
    ! [X66,X42] : c_List_Olist__inter(c_List_Olist_ONil,X66,X42) = c_List_Olist_ONil,
    c_0_1606 ).

fof(c_0_4544,axiom,
    ! [X6,X42] : c_List_Olexn(X6,c_0,X42) = c_emptyset,
    c_0_1607 ).

fof(c_0_4545,axiom,
    ! [X22,X42] : c_List_Odrop(X22,c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    c_0_1608 ).

fof(c_0_4546,axiom,
    ! [X19] : c_Divides_Oop_Amod(X19,X19,tc_IntDef_Oint) = c_0,
    c_0_1609 ).

fof(c_0_4547,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,X16,tc_IntDef_Oint),
    c_0_1610 ).

fof(c_0_4548,axiom,
    ! [X6,X4] : c_Equiv__Relations_Oquotient(c_emptyset,X6,X4) = c_emptyset,
    c_0_1611 ).

fof(c_0_4549,axiom,
    ! [X6,X4] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X6,X4),
    c_0_1612 ).

fof(c_0_4550,axiom,
    ! [X22] : c_Divides_Oop_Amod(X22,X22,tc_nat) = c_0,
    c_0_1613 ).

fof(c_0_4551,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,X16,tc_nat),
    c_0_1614 ).

fof(c_0_4552,axiom,
    ! [X2,X4] : c_in(X2,c_UNIV,X4),
    c_0_1615 ).

fof(c_0_4553,axiom,
    ! [X1] : c_minus(X1,c_0,tc_nat) = X1,
    c_0_1616 ).

fof(c_0_4554,axiom,
    ! [X1] : c_plus(c_0,X1,tc_nat) = X1,
    c_0_1617 ).

fof(c_0_4555,axiom,
    c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
    c_0_1618 ).

fof(c_0_4556,axiom,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    c_0_1619 ).

fof(c_0_4557,axiom,
    ! [X1] : c_Orderings_Omax(X1,c_0,tc_nat) = X1,
    c_0_1620 ).

fof(c_0_4558,axiom,
    ! [X1] : c_Orderings_Omax(c_0,X1,tc_nat) = X1,
    c_0_1621 ).

fof(c_0_4559,axiom,
    ! [X1] : c_plus(X1,c_0,tc_nat) = X1,
    c_0_1622 ).

fof(c_0_4560,axiom,
    ! [X1] : c_div(X1,c_1,tc_IntDef_Oint) = X1,
    c_0_1623 ).

fof(c_0_4561,axiom,
    ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
    c_0_1624 ).

fof(c_0_4562,axiom,
    ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1,
    c_0_1625 ).

fof(c_0_4563,axiom,
    ! [X4] : c_union(c_emptyset,c_emptyset,X4) = c_emptyset,
    c_0_1626 ).

fof(c_0_4564,axiom,
    ! [X4] : c_inter(c_UNIV,c_UNIV,X4) = c_UNIV,
    c_0_1627 ).

fof(c_0_4565,axiom,
    ! [X29] : c_Nat_Opower(X29,c_0,tc_nat) = c_1,
    c_0_1628 ).

fof(c_0_4566,axiom,
    ! [X22] : c_times(c_0,X22,tc_nat) = c_0,
    c_0_1629 ).

fof(c_0_4567,axiom,
    ! [X16] : c_times(X16,c_0,tc_nat) = c_0,
    c_0_1630 ).

fof(c_0_4568,axiom,
    ! [X22] : c_Orderings_Omin(X22,c_0,tc_nat) = c_0,
    c_0_1631 ).

fof(c_0_4569,axiom,
    ! [X22] : c_Orderings_Omin(c_0,X22,tc_nat) = c_0,
    c_0_1632 ).

fof(c_0_4570,axiom,
    ! [X22] : c_minus(c_0,X22,tc_nat) = c_0,
    c_0_1633 ).

fof(c_0_4571,axiom,
    ! [X4] : c_append(c_List_Olist_ONil,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    c_0_1634 ).

fof(c_0_4572,axiom,
    ! [X4] : c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X4),
    c_0_1635 ).

fof(c_0_4573,axiom,
    ! [X28] : c_Divides_Oop_Amod(c_0,X28,tc_IntDef_Oint) = c_0,
    c_0_1636 ).

fof(c_0_4574,axiom,
    ! [X19] : c_Divides_Oop_Amod(X19,c_1,tc_IntDef_Oint) = c_0,
    c_0_1637 ).

fof(c_0_4575,axiom,
    ! [X28] : c_div(c_0,X28,tc_IntDef_Oint) = c_0,
    c_0_1638 ).

fof(c_0_4576,axiom,
    ! [X29] : c_Nat_Opower(X29,c_0,tc_IntDef_Oint) = c_1,
    c_0_1639 ).

fof(c_0_4577,axiom,
    ! [X16] : c_Divides_Oop_Amod(c_0,X16,tc_nat) = c_0,
    c_0_1640 ).

fof(c_0_4578,axiom,
    ! [X16] : c_div(c_0,X16,tc_nat) = c_0,
    c_0_1641 ).

fof(c_0_4579,axiom,
    ! [X19] : c_div(X19,c_0,tc_nat) = c_0,
    c_0_1642 ).

fof(c_0_4580,axiom,
    ! [X22] : c_lessequals(c_0,X22,tc_nat),
    c_0_1643 ).

fof(c_0_4581,axiom,
    ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_IntDef_Oint),
    c_0_1644 ).

fof(c_0_4582,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,c_0,tc_IntDef_Oint),
    c_0_1645 ).

fof(c_0_4583,axiom,
    ! [X16] : c_Divides_Oop_Advd(X16,c_0,tc_nat),
    c_0_1646 ).

fof(c_0_4584,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1647]) ).

fof(c_0_4585,plain,
    ! [X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(c_uminus(c_1,X3),X3) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1648]) ).

fof(c_0_4586,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X4),X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1649]) ).

fof(c_0_4587,plain,
    ! [X28,X3] :
      ( ~ class_HOL_Oone(X3)
      | ~ class_OrderedGroup_Oab__group__add(X3)
      | c_uminus(X28,X3) != c_1
      | X28 = c_uminus(c_1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1650]) ).

fof(c_0_4588,axiom,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    c_0_1651 ).

fof(c_0_4589,plain,
    ! [X2] :
      ( ~ c_Parity_Oeven(X2,tc_nat)
      | ~ c_Parity_Oeven(c_Suc(X2),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1652]) ).

fof(c_0_4590,axiom,
    c_less(c_0,c_1,tc_nat),
    c_0_1653 ).

fof(c_0_4591,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    c_0_1654 ).

fof(c_0_4592,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    c_0_1655 ).

fof(c_0_4593,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    c_0_1656 ).

fof(c_0_4594,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    c_0_1657 ).

fof(c_0_4595,axiom,
    ! [X13,X14] : c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,X14)) != c_Public_OshrK(X13),
    c_0_1658 ).

fof(c_0_4596,plain,
    ! [X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_uminus(X1,X4),X4) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_1659]) ).

fof(c_0_4597,axiom,
    ! [X7,X28,X112,X14] :
      ( c_Public_OpublicKey(X28,X14) != c_Public_OpublicKey(X7,X112)
      | X14 = X112 ),
    c_0_1660 ).

fof(c_0_4598,axiom,
    ! [X7,X28,X112,X14] :
      ( c_Public_OpublicKey(X28,X14) != c_Public_OpublicKey(X7,X112)
      | X28 = X7 ),
    c_0_1661 ).

fof(c_0_4599,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_Omsg_OMPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X108 = X87 ),
    c_0_1662 ).

fof(c_0_4600,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X88,X87) != c_Message_Omsg_OMPair(X109,X108)
      | X108 = X87 ),
    c_0_1663 ).

fof(c_0_4601,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X108 = X87 ),
    c_0_1664 ).

fof(c_0_4602,axiom,
    ! [X108,X87,X109,X88] :
      ( c_Message_OHPair(X109,X108) != c_Message_OHPair(X88,X87)
      | X109 = X88 ),
    c_0_1665 ).

fof(c_0_4603,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_ONotes(X96,X98) != c_Event_Oevent_ONotes(X95,X97)
      | X98 = X97 ),
    c_0_1666 ).

fof(c_0_4604,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_ONotes(X96,X98) != c_Event_Oevent_ONotes(X95,X97)
      | X96 = X95 ),
    c_0_1667 ).

fof(c_0_4605,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_OGets(X96,X98) != c_Event_Oevent_OGets(X95,X97)
      | X98 = X97 ),
    c_0_1668 ).

fof(c_0_4606,axiom,
    ! [X97,X98,X95,X96] :
      ( c_Event_Oevent_OGets(X96,X98) != c_Event_Oevent_OGets(X95,X97)
      | X96 = X95 ),
    c_0_1669 ).

fof(c_0_4607,axiom,
    ! [X90,X91,X97,X98] :
      ( c_Message_Omsg_OCrypt(X91,X98) != c_Message_Omsg_OCrypt(X90,X97)
      | X98 = X97 ),
    c_0_1670 ).

fof(c_0_4608,axiom,
    ! [X90,X91,X97,X98] :
      ( c_Message_Omsg_OCrypt(X91,X98) != c_Message_Omsg_OCrypt(X90,X97)
      | X91 = X90 ),
    c_0_1671 ).

fof(c_0_4609,axiom,
    ! [X99,X100,X101,X102] :
      ( c_Message_Omsg_OMPair(X102,X100) != c_Message_Omsg_OMPair(X101,X99)
      | X100 = X99 ),
    c_0_1672 ).

fof(c_0_4610,axiom,
    ! [X99,X100,X101,X102] :
      ( c_Message_Omsg_OMPair(X102,X100) != c_Message_Omsg_OMPair(X101,X99)
      | X102 = X101 ),
    c_0_1673 ).

fof(c_0_4611,axiom,
    ! [X26,X24,X4] :
      ( c_List_Orev(X24,X4) != c_List_Orev(X26,X4)
      | X24 = X26 ),
    c_0_1674 ).

fof(c_0_4612,axiom,
    ! [X55,X56,X57,X58] :
      ( c_List_Ochar_OChar(X58,X56) != c_List_Ochar_OChar(X57,X55)
      | X56 = X55 ),
    c_0_1675 ).

fof(c_0_4613,axiom,
    ! [X55,X56,X57,X58] :
      ( c_List_Ochar_OChar(X58,X56) != c_List_Ochar_OChar(X57,X55)
      | X58 = X57 ),
    c_0_1676 ).

fof(c_0_4614,axiom,
    ! [X43,X19,X4] :
      ( c_Datatype_Ooption_OSome(X19,X4) != c_Datatype_Ooption_OSome(X43,X4)
      | X19 = X43 ),
    c_0_1677 ).

fof(c_0_4615,axiom,
    ! [X19,X4] : c_Nat_Osize(c_Datatype_Ooption_OSome(X19,X4),tc_Datatype_Ooption(X4)) = c_0,
    c_0_1678 ).

fof(c_0_4616,axiom,
    ! [X12] : c_Numeral_Obin__succ(c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X12),c_Numeral_Obit_OB0),
    c_0_1679 ).

fof(c_0_4617,axiom,
    ! [X12] : c_Numeral_Obin__pred(c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X12),c_Numeral_Obit_OB1),
    c_0_1680 ).

fof(c_0_4618,axiom,
    ! [X12] : c_Numeral_Obin__minus(c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X12),c_Numeral_Obit_OB0),
    c_0_1681 ).

fof(c_0_4619,plain,
    ! [X39,X38] :
      ( class_Finite__Set_Ofinite(tc_sum(X39,X38))
      | ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X39) ),
    inference(fof_simplification,[status(thm)],[c_0_1682]) ).

fof(c_0_4620,plain,
    ! [X39,X38] :
      ( class_Finite__Set_Ofinite(tc_prod(X39,X38))
      | ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X39) ),
    inference(fof_simplification,[status(thm)],[c_0_1683]) ).

fof(c_0_4621,plain,
    ! [X39,X38] :
      ( class_Finite__Set_Ofinite(tc_fun(X39,X38))
      | ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X39) ),
    inference(fof_simplification,[status(thm)],[c_0_1684]) ).

fof(c_0_4622,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1685]) ).

fof(c_0_4623,axiom,
    ! [X87,X109,X88,X93] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OCrypt(X93,X109),
    c_0_1686 ).

fof(c_0_4624,axiom,
    ! [X87,X109,X88,X93] : c_Message_Omsg_OCrypt(X93,X109) != c_Message_OHPair(X88,X87),
    c_0_1687 ).

fof(c_0_4625,axiom,
    ! [X97,X98,X95,X96] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X96,X98),
    c_0_1688 ).

fof(c_0_4626,axiom,
    ! [X97,X98,X95,X96] : c_Event_Oevent_OGets(X96,X98) != c_Event_Oevent_ONotes(X95,X97),
    c_0_1689 ).

fof(c_0_4627,axiom,
    ! [X2,X4] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X2,X4),X4) ),
    c_0_1690 ).

fof(c_0_4628,axiom,
    ! [X2,X4] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X2,X4),X4) ),
    c_0_1691 ).

fof(c_0_4629,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1692]) ).

fof(c_0_4630,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_IntDef_Oint(X22),X4) = c_NatArith_Oof__nat(X22,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1693]) ).

fof(c_0_4631,axiom,
    ! [X1,X4] : c_Union(c_Pow(X1,X4),X4) = X1,
    c_0_1694 ).

fof(c_0_4632,axiom,
    ! [X1,X4] : c_List_Orev(c_List_Orev(X1,X4),X4) = X1,
    c_0_1695 ).

fof(c_0_4633,axiom,
    ! [X1,X4] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X4),X4) = X1,
    c_0_1696 ).

fof(c_0_4634,axiom,
    ! [X24,X4] : c_List_Odistinct(c_List_Oremdups(X24,X4),X4),
    c_0_1697 ).

fof(c_0_4635,axiom,
    ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) = c_Suc(X15),
    c_0_1698 ).

fof(c_0_4636,axiom,
    ! [X12] : c_Numeral_Obin__succ(c_Numeral_OBit(X12,c_Numeral_Obit_OB0)) = c_Numeral_OBit(X12,c_Numeral_Obit_OB1),
    c_0_1699 ).

fof(c_0_4637,axiom,
    ! [X12] : c_Numeral_Obin__pred(c_Numeral_OBit(X12,c_Numeral_Obit_OB1)) = c_Numeral_OBit(X12,c_Numeral_Obit_OB0),
    c_0_1700 ).

fof(c_0_4638,axiom,
    ! [X12] : c_IntDef_Onat(c_Numeral_Onumber__of(X12,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X12,tc_nat),
    c_0_1701 ).

fof(c_0_4639,axiom,
    ! [X22] : c_IntDef_Onat(c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint)) = c_0,
    c_0_1702 ).

fof(c_0_4640,axiom,
    ! [X98,X96] : c_Nat_Osize(c_Event_Oevent_ONotes(X96,X98),tc_Event_Oevent) = c_0,
    c_0_1703 ).

fof(c_0_4641,axiom,
    ! [X98,X96] : c_Nat_Osize(c_Event_Oevent_OGets(X96,X98),tc_Event_Oevent) = c_0,
    c_0_1704 ).

fof(c_0_4642,axiom,
    ! [X60,X44] : c_List_Odistinct(c_List_Oupt(X44,X60),tc_nat),
    c_0_1705 ).

fof(c_0_4643,axiom,
    ! [X56,X58] : c_Nat_Osize(c_List_Ochar_OChar(X58,X56),tc_List_Ochar) = c_0,
    c_0_1706 ).

fof(c_0_4644,plain,
    ! [X19,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(X19,X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1707]) ).

fof(c_0_4645,plain,
    ! [X2,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(X2,X4) != c_1
      | X2 = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1708]) ).

fof(c_0_4646,axiom,
    ! [X22,X16] :
      ( c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint) != c_IntDef_Oint(X16)
      | X16 = c_0 ),
    c_0_1709 ).

fof(c_0_4647,axiom,
    ! [X22,X16] :
      ( c_uminus(c_IntDef_Oint(X22),tc_IntDef_Oint) != c_IntDef_Oint(X16)
      | X22 = c_0 ),
    c_0_1710 ).

fof(c_0_4648,axiom,
    ! [X14,X4] :
      ( c_Main_Oempty__Union__conv__1(X14,X4) != c_emptyset
      | c_emptyset = c_Union(X14,X4) ),
    c_0_1711 ).

fof(c_0_4649,axiom,
    ! [X14,X4] :
      ( c_Main_OUnion__empty__conv__1(X14,X4) != c_emptyset
      | c_Union(X14,X4) = c_emptyset ),
    c_0_1712 ).

fof(c_0_4650,axiom,
    ! [X14,X4] :
      ( c_Main_OInter__UNIV__conv__2__1(X14,X4) != c_UNIV
      | c_UNIV = c_Inter(X14,X4) ),
    c_0_1713 ).

fof(c_0_4651,axiom,
    ! [X14,X4] :
      ( c_Main_OInter__UNIV__conv__1__1(X14,X4) != c_UNIV
      | c_Inter(X14,X4) = c_UNIV ),
    c_0_1714 ).

fof(c_0_4652,axiom,
    ! [X51,X4] :
      ( c_Main_Oconcat__eq__Nil__conv__1(X51,X4) != c_List_Olist_ONil
      | c_List_Oconcat(X51,X4) = c_List_Olist_ONil ),
    c_0_1715 ).

fof(c_0_4653,axiom,
    ! [X51,X4] :
      ( c_Main_ONil__eq__concat__conv__1(X51,X4) != c_List_Olist_ONil
      | c_List_Olist_ONil = c_List_Oconcat(X51,X4) ),
    c_0_1716 ).

fof(c_0_4654,axiom,
    ! [X1] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
    c_0_1717 ).

fof(c_0_4655,axiom,
    ! [X24,X4] :
      ( c_Nat_Osize(X24,tc_List_Olist(X4)) != c_0
      | X24 = c_List_Olist_ONil ),
    c_0_1718 ).

fof(c_0_4656,axiom,
    c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1,
    c_0_1719 ).

fof(c_0_4657,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_uminus(c_1,X4) = c_Numeral_Onumber__of(c_Numeral_OMin,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1720]) ).

fof(c_0_4658,axiom,
    ! [X2] :
      ( c_Parity_Oeven(X2,tc_nat)
      | c_Parity_Oeven(c_Suc(X2),tc_nat) ),
    c_0_1721 ).

fof(c_0_4659,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(X19,X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1722]) ).

fof(c_0_4660,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_0 != c_uminus(X19,X4)
      | c_0 = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_1723]) ).

fof(c_0_4661,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(X19,X4) != c_0
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1724]) ).

fof(c_0_4662,plain,
    ! [X19,X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_0 != c_HOL_Oabs(X19,X4)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1725]) ).

fof(c_0_4663,plain,
    ! [X16,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_NatArith_Oof__nat(X16,X4) != c_0
      | X16 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1726]) ).

fof(c_0_4664,plain,
    ! [X22,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_0 != c_NatArith_Oof__nat(X22,X4)
      | c_0 = X22 ),
    inference(fof_simplification,[status(thm)],[c_0_1727]) ).

fof(c_0_4665,plain,
    ! [X12,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oof__int(X12,X4) != c_0
      | X12 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1728]) ).

fof(c_0_4666,plain,
    ! [X49,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 != c_IntDef_Oof__int(X49,X4)
      | c_0 = X49 ),
    inference(fof_simplification,[status(thm)],[c_0_1729]) ).

fof(c_0_4667,axiom,
    ! [X39,X38] : class_Nat_Opower(tc_fun(X39,X38)),
    c_0_1730 ).

fof(c_0_4668,plain,
    ! [X22] : ~ c_IntDef_Oneg(c_IntDef_Oint(X22),tc_IntDef_Oint),
    inference(fof_simplification,[status(thm)],[c_0_1731]) ).

fof(c_0_4669,axiom,
    ! [X28,X33,X14] : c_Public_OpublicKey(X28,X33) != c_Public_OshrK(X14),
    c_0_1732 ).

fof(c_0_4670,axiom,
    ! [X28,X33,X14] : c_Public_OshrK(X14) != c_Public_OpublicKey(X28,X33),
    c_0_1733 ).

fof(c_0_4671,axiom,
    ! [X87,X88,X9] : c_Message_OHPair(X88,X87) != c_Message_Omsg_ONumber(X9),
    c_0_1734 ).

fof(c_0_4672,axiom,
    ! [X87,X88,X9] : c_Message_OHPair(X88,X87) != c_Message_Omsg_ONonce(X9),
    c_0_1735 ).

fof(c_0_4673,axiom,
    ! [X87,X88,X93] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OKey(X93),
    c_0_1736 ).

fof(c_0_4674,axiom,
    ! [X110,X87,X88] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OHash(X110),
    c_0_1737 ).

fof(c_0_4675,axiom,
    ! [X87,X88,X14] : c_Message_OHPair(X88,X87) != c_Message_Omsg_OAgent(X14),
    c_0_1738 ).

fof(c_0_4676,axiom,
    ! [X110,X87,X88] : c_Message_Omsg_OHash(X110) != c_Message_OHPair(X88,X87),
    c_0_1739 ).

fof(c_0_4677,axiom,
    ! [X87,X88,X93] : c_Message_Omsg_OKey(X93) != c_Message_OHPair(X88,X87),
    c_0_1740 ).

fof(c_0_4678,axiom,
    ! [X87,X88,X9] : c_Message_Omsg_ONumber(X9) != c_Message_OHPair(X88,X87),
    c_0_1741 ).

fof(c_0_4679,axiom,
    ! [X87,X88,X9] : c_Message_Omsg_ONonce(X9) != c_Message_OHPair(X88,X87),
    c_0_1742 ).

fof(c_0_4680,axiom,
    ! [X87,X88,X14] : c_Message_Omsg_OAgent(X14) != c_Message_OHPair(X88,X87),
    c_0_1743 ).

fof(c_0_4681,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1744]) ).

fof(c_0_4682,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | ~ c_IntDef_Oneg(c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1745]) ).

fof(c_0_4683,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | ~ c_IntDef_Oiszero(c_1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1746]) ).

fof(c_0_4684,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1747]) ).

fof(c_0_4685,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
      | ~ class_Ring__and__Field_Ofield(X4)
      | c_HOL_Oinverse(c_1,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1748]) ).

fof(c_0_4686,axiom,
    ! [X22] : c_Binomial_Obinomial(c_Suc(X22),X22) = c_Suc(X22),
    c_0_1749 ).

fof(c_0_4687,axiom,
    ! [X24,X4] :
      ( c_List_Oset(X24,X4) != c_emptyset
      | X24 = c_List_Olist_ONil ),
    c_0_1750 ).

fof(c_0_4688,axiom,
    ! [X24,X4] :
      ( c_emptyset != c_List_Oset(X24,X4)
      | X24 = c_List_Olist_ONil ),
    c_0_1751 ).

fof(c_0_4689,axiom,
    ! [X24,X4] :
      ( c_List_Orotate1(X24,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    c_0_1752 ).

fof(c_0_4690,axiom,
    ! [X24,X4] :
      ( c_List_Orev(X24,X4) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    c_0_1753 ).

fof(c_0_4691,axiom,
    ! [X2,X4] :
      ( c_List_Olist_ONil != c_List_Oremdups(X2,X4)
      | X2 = c_List_Olist_ONil ),
    c_0_1754 ).

fof(c_0_4692,axiom,
    ! [X2,X4] :
      ( c_List_Oremdups(X2,X4) != c_List_Olist_ONil
      | X2 = c_List_Olist_ONil ),
    c_0_1755 ).

fof(c_0_4693,axiom,
    ! [X24,X4] :
      ( c_List_Olist_ONil != c_List_Orev(X24,X4)
      | X24 = c_List_Olist_ONil ),
    c_0_1756 ).

fof(c_0_4694,axiom,
    ! [X41,X4] :
      ( c_Datatype_Oo2s(X41,X4) != c_emptyset
      | X41 = c_Datatype_Ooption_ONone ),
    c_0_1757 ).

fof(c_0_4695,axiom,
    ! [X33] : c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X33))) = c_emptyset,
    c_0_1758 ).

fof(c_0_4696,axiom,
    ! [X16] : c_HOL_Oabs(c_IntDef_Oint(X16),tc_IntDef_Oint) = c_IntDef_Oint(X16),
    c_0_1759 ).

fof(c_0_4697,axiom,
    ! [X43,X4] : c_Datatype_Ooption_OSome(X43,X4) != c_Datatype_Ooption_ONone,
    c_0_1760 ).

fof(c_0_4698,axiom,
    ! [X43,X4] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X43,X4),
    c_0_1761 ).

fof(c_0_4699,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_HOL_Oabs(c_1,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1762]) ).

fof(c_0_4700,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_OrderedGroup_Opprt(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1763]) ).

fof(c_0_4701,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X4)
      | c_OrderedGroup_Onprt(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1764]) ).

fof(c_0_4702,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1765]) ).

fof(c_0_4703,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X4)
      | c_0 = c_uminus(c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1766]) ).

fof(c_0_4704,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_HOL_Oabs(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1767]) ).

fof(c_0_4705,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X4)
      | c_0 = c_HOL_Oabs(c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1768]) ).

fof(c_0_4706,plain,
    ! [X4] :
      ( ~ class_Numeral_Onumber__ring(X4)
      | c_Numeral_Onumber__of(c_Numeral_OPls,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1769]) ).

fof(c_0_4707,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_NatArith_Oof__nat(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1770]) ).

fof(c_0_4708,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X4)
      | c_NatArith_Oof__nat(c_1,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1771]) ).

fof(c_0_4709,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_0 = c_NatArith_Oof__nat(c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1772]) ).

fof(c_0_4710,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_IntDef_Oof__int(c_0,X4) = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_1773]) ).

fof(c_0_4711,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
      | c_IntDef_Oof__int(c_1,X4) = c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_1774]) ).

fof(c_0_4712,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X4)
      | c_0 = c_IntDef_Oof__int(c_0,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_1775]) ).

fof(c_0_4713,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Omsg_OKey(X91),tc_Message_Omsg) = c_0,
    c_0_1776 ).

fof(c_0_4714,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Omsg_ONonce(X91),tc_Message_Omsg) = c_0,
    c_0_1777 ).

fof(c_0_4715,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Omsg_ONumber(X91),tc_Message_Omsg) = c_0,
    c_0_1778 ).

fof(c_0_4716,axiom,
    ! [X96] : c_Nat_Osize(c_Message_Omsg_OAgent(X96),tc_Message_Omsg) = c_0,
    c_0_1779 ).

fof(c_0_4717,axiom,
    ! [X91] : c_Nat_Osize(c_Message_Oagent_OFriend(X91),tc_Message_Oagent) = c_0,
    c_0_1780 ).

fof(c_0_4718,axiom,
    ! [X4] : c_uminus(c_emptyset,tc_set(X4)) = c_UNIV,
    c_0_1781 ).

fof(c_0_4719,axiom,
    ! [X4] : c_uminus(c_UNIV,tc_set(X4)) = c_emptyset,
    c_0_1782 ).

fof(c_0_4720,axiom,
    ! [X4] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X4)) = c_0,
    c_0_1783 ).

fof(c_0_4721,axiom,
    ! [X4] : c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X4)) = c_0,
    c_0_1784 ).

fof(c_0_4722,axiom,
    ! [X17] : c_Binomial_Obinomial(c_0,c_Suc(X17)) = c_0,
    c_0_1785 ).

fof(c_0_4723,axiom,
    c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
    c_0_1786 ).

fof(c_0_4724,axiom,
    ! [X1] : c_Binomial_Obinomial(X1,c_Suc(c_0)) = X1,
    c_0_1787 ).

fof(c_0_4725,plain,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    inference(fof_simplification,[status(thm)],[c_0_1788]) ).

fof(c_0_4726,plain,
    ! [X38] :
      ( class_Finite__Set_Ofinite(tc_set(X38))
      | ~ class_Finite__Set_Ofinite(X38) ),
    inference(fof_simplification,[status(thm)],[c_0_1789]) ).

fof(c_0_4727,plain,
    ! [X38] :
      ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X38))
      | ~ class_Finite__Set_Ofinite(X38) ),
    inference(fof_simplification,[status(thm)],[c_0_1790]) ).

fof(c_0_4728,axiom,
    ! [X14] : c_Event_Oknows(X14,c_List_Olist_ONil) = c_Event_OinitState(X14),
    c_0_1791 ).

fof(c_0_4729,axiom,
    ! [X12] : c_Numeral_Obin__mult(c_Numeral_OMin,X12) = c_Numeral_Obin__minus(X12),
    c_0_1792 ).

fof(c_0_4730,axiom,
    ! [X12] : c_Numeral_Obin__add(X12,c_Numeral_OMin) = c_Numeral_Obin__pred(X12),
    c_0_1793 ).

fof(c_0_4731,axiom,
    ! [X12] : c_Numeral_Obin__add(c_Numeral_OMin,X12) = c_Numeral_Obin__pred(X12),
    c_0_1794 ).

fof(c_0_4732,axiom,
    ! [X1,X2] :
      ( c_Public_OshrK(X2) != c_Public_OshrK(X1)
      | X2 = X1 ),
    c_0_1795 ).

fof(c_0_4733,axiom,
    ! [X97,X98] :
      ( c_Message_Omsg_OHash(X98) != c_Message_Omsg_OHash(X97)
      | X98 = X97 ),
    c_0_1796 ).

fof(c_0_4734,axiom,
    ! [X90,X91] :
      ( c_Message_Omsg_OKey(X91) != c_Message_Omsg_OKey(X90)
      | X91 = X90 ),
    c_0_1797 ).

fof(c_0_4735,axiom,
    ! [X90,X91] :
      ( c_Message_Omsg_ONonce(X91) != c_Message_Omsg_ONonce(X90)
      | X91 = X90 ),
    c_0_1798 ).

fof(c_0_4736,axiom,
    ! [X90,X91] :
      ( c_Message_Omsg_ONumber(X91) != c_Message_Omsg_ONumber(X90)
      | X91 = X90 ),
    c_0_1799 ).

fof(c_0_4737,axiom,
    ! [X95,X96] :
      ( c_Message_Omsg_OAgent(X96) != c_Message_Omsg_OAgent(X95)
      | X96 = X95 ),
    c_0_1800 ).

fof(c_0_4738,axiom,
    ! [X92,X93] :
      ( c_Message_OinvKey(X93) != c_Message_OinvKey(X92)
      | X93 = X92 ),
    c_0_1801 ).

fof(c_0_4739,axiom,
    ! [X90,X91] :
      ( c_Message_Oagent_OFriend(X91) != c_Message_Oagent_OFriend(X90)
      | X91 = X90 ),
    c_0_1802 ).

fof(c_0_4740,axiom,
    ! [X22,X16] :
      ( c_Suc(X16) != c_Suc(X22)
      | X16 = X22 ),
    c_0_1803 ).

fof(c_0_4741,axiom,
    ! [X22,X16] :
      ( c_IntDef_Oint(X16) != c_IntDef_Oint(X22)
      | X16 = X22 ),
    c_0_1804 ).

fof(c_0_4742,axiom,
    ! [X1,X4] : c_Fun_Oid(X1,X4) = X1,
    c_0_1805 ).

fof(c_0_4743,axiom,
    ! [X14] : c_Message_OinvKey(c_Public_OshrK(X14)) = c_Public_OshrK(X14),
    c_0_1806 ).

fof(c_0_4744,axiom,
    ! [X89] : c_Message_Oparts(c_Message_Oparts(X89)) = c_Message_Oparts(X89),
    c_0_1807 ).

fof(c_0_4745,axiom,
    ! [X89] : c_Message_Oparts(c_Message_Oanalz(X89)) = c_Message_Oparts(X89),
    c_0_1808 ).

fof(c_0_4746,axiom,
    ! [X89] : c_Message_Oanalz(c_Message_Oparts(X89)) = c_Message_Oparts(X89),
    c_0_1809 ).

fof(c_0_4747,axiom,
    ! [X89] : c_Message_Oanalz(c_Message_Oanalz(X89)) = c_Message_Oanalz(X89),
    c_0_1810 ).

fof(c_0_4748,axiom,
    ! [X22] : c_Binomial_Obinomial(X22,X22) = c_1,
    c_0_1811 ).

fof(c_0_4749,axiom,
    c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    c_0_1812 ).

fof(c_0_4750,axiom,
    c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
    c_0_1813 ).

fof(c_0_4751,axiom,
    c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    c_0_1814 ).

fof(c_0_4752,axiom,
    ! [X1] : c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1,
    c_0_1815 ).

fof(c_0_4753,axiom,
    ! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1,
    c_0_1816 ).

fof(c_0_4754,axiom,
    ! [X1] : c_NatArith_Oof__nat(X1,tc_nat) = X1,
    c_0_1817 ).

fof(c_0_4755,axiom,
    ! [X4] : c_Transitive__Closure_Otrancl(c_emptyset,X4) = c_emptyset,
    c_0_1818 ).

fof(c_0_4756,axiom,
    ! [X4] : c_Transitive__Closure_Ortrancl(c_emptyset,X4) = c_Relation_OId,
    c_0_1819 ).

fof(c_0_4757,axiom,
    ! [X4] : c_Union(c_emptyset,X4) = c_emptyset,
    c_0_1820 ).

fof(c_0_4758,axiom,
    ! [X4] : c_Union(c_UNIV,X4) = c_UNIV,
    c_0_1821 ).

fof(c_0_4759,axiom,
    ! [X4] : c_Pow(c_UNIV,X4) = c_UNIV,
    c_0_1822 ).

fof(c_0_4760,axiom,
    ! [X4] : c_Inter(c_emptyset,X4) = c_UNIV,
    c_0_1823 ).

fof(c_0_4761,axiom,
    ! [X4] : c_Inter(c_UNIV,X4) = c_emptyset,
    c_0_1824 ).

fof(c_0_4762,axiom,
    ! [X4] : c_Relation_Odiag(c_emptyset,X4) = c_emptyset,
    c_0_1825 ).

fof(c_0_4763,axiom,
    ! [X12] : c_Numeral_Obin__mult(c_Numeral_OPls,X12) = c_Numeral_OPls,
    c_0_1826 ).

fof(c_0_4764,axiom,
    ! [X44] : c_List_Oupt(X44,c_0) = c_List_Olist_ONil,
    c_0_1827 ).

fof(c_0_4765,axiom,
    ! [X42] : c_List_Otl(c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    c_0_1828 ).

fof(c_0_4766,axiom,
    ! [X4] : c_List_Oset(c_List_Olist_ONil,X4) = c_emptyset,
    c_0_1829 ).

fof(c_0_4767,axiom,
    ! [X4] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X4),
    c_0_1830 ).

fof(c_0_4768,axiom,
    ! [X4] : c_List_Orotate1(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    c_0_1831 ).

fof(c_0_4769,axiom,
    ! [X4] : c_List_Orev(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    c_0_1832 ).

fof(c_0_4770,axiom,
    ! [X4] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X4),
    c_0_1833 ).

fof(c_0_4771,axiom,
    ! [X4] : c_List_Oremdups(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    c_0_1834 ).

fof(c_0_4772,axiom,
    ! [X42] : c_List_Onull(c_List_Olist_ONil,X42),
    c_0_1835 ).

fof(c_0_4773,axiom,
    ! [X4] : c_List_Olists(c_UNIV,X4) = c_UNIV,
    c_0_1836 ).

fof(c_0_4774,axiom,
    ! [X42] : c_List_Odistinct(c_List_Olist_ONil,X42),
    c_0_1837 ).

fof(c_0_4775,axiom,
    ! [X42] : c_List_Oconcat(c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    c_0_1838 ).

fof(c_0_4776,axiom,
    ! [X42] : c_List_Obutlast(c_List_Olist_ONil,X42) = c_List_Olist_ONil,
    c_0_1839 ).

fof(c_0_4777,axiom,
    ! [X4] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X4),
    c_0_1840 ).

fof(c_0_4778,axiom,
    ! [X4] : c_Finite__Set_Ocard(c_emptyset,X4) = c_0,
    c_0_1841 ).

fof(c_0_4779,axiom,
    ! [X4] : c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X4) = c_emptyset,
    c_0_1842 ).

fof(c_0_4780,axiom,
    ! [X22] : c_Binomial_Obinomial(X22,c_0) = c_1,
    c_0_1843 ).

fof(c_0_4781,axiom,
    ! [X4] : c_Wellfounded__Recursion_Owf(c_emptyset,X4),
    c_0_1844 ).

fof(c_0_4782,plain,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1845]) ).

fof(c_0_4783,plain,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1846]) ).

fof(c_0_4784,plain,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1847]) ).

fof(c_0_4785,plain,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1848]) ).

fof(c_0_4786,plain,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1849]) ).

fof(c_0_4787,plain,
    ! [X40] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1850]) ).

fof(c_0_4788,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1851]) ).

fof(c_0_4789,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1852]) ).

fof(c_0_4790,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1853]) ).

fof(c_0_4791,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1854]) ).

fof(c_0_4792,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1855]) ).

fof(c_0_4793,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1856]) ).

fof(c_0_4794,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1857]) ).

fof(c_0_4795,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1858]) ).

fof(c_0_4796,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1859]) ).

fof(c_0_4797,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1860]) ).

fof(c_0_4798,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1861]) ).

fof(c_0_4799,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1862]) ).

fof(c_0_4800,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1863]) ).

fof(c_0_4801,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1864]) ).

fof(c_0_4802,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1865]) ).

fof(c_0_4803,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1866]) ).

fof(c_0_4804,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1867]) ).

fof(c_0_4805,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1868]) ).

fof(c_0_4806,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1869]) ).

fof(c_0_4807,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1870]) ).

fof(c_0_4808,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1871]) ).

fof(c_0_4809,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1872]) ).

fof(c_0_4810,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1873]) ).

fof(c_0_4811,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1874]) ).

fof(c_0_4812,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1875]) ).

fof(c_0_4813,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1876]) ).

fof(c_0_4814,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1877]) ).

fof(c_0_4815,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1878]) ).

fof(c_0_4816,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1879]) ).

fof(c_0_4817,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1880]) ).

fof(c_0_4818,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1881]) ).

fof(c_0_4819,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1882]) ).

fof(c_0_4820,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1883]) ).

fof(c_0_4821,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1884]) ).

fof(c_0_4822,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1885]) ).

fof(c_0_4823,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1886]) ).

fof(c_0_4824,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1887]) ).

fof(c_0_4825,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1888]) ).

fof(c_0_4826,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1889]) ).

fof(c_0_4827,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1890]) ).

fof(c_0_4828,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1891]) ).

fof(c_0_4829,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1892]) ).

fof(c_0_4830,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1893]) ).

fof(c_0_4831,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1894]) ).

fof(c_0_4832,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1895]) ).

fof(c_0_4833,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1896]) ).

fof(c_0_4834,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring__0(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1897]) ).

fof(c_0_4835,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1898]) ).

fof(c_0_4836,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1899]) ).

fof(c_0_4837,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1900]) ).

fof(c_0_4838,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1901]) ).

fof(c_0_4839,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Osemiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1902]) ).

fof(c_0_4840,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1903]) ).

fof(c_0_4841,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1904]) ).

fof(c_0_4842,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1905]) ).

fof(c_0_4843,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1906]) ).

fof(c_0_4844,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1907]) ).

fof(c_0_4845,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1908]) ).

fof(c_0_4846,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1909]) ).

fof(c_0_4847,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1910]) ).

fof(c_0_4848,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1911]) ).

fof(c_0_4849,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1912]) ).

fof(c_0_4850,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1913]) ).

fof(c_0_4851,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1914]) ).

fof(c_0_4852,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1915]) ).

fof(c_0_4853,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1916]) ).

fof(c_0_4854,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1917]) ).

fof(c_0_4855,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1918]) ).

fof(c_0_4856,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1919]) ).

fof(c_0_4857,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1920]) ).

fof(c_0_4858,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1921]) ).

fof(c_0_4859,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring__1(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1922]) ).

fof(c_0_4860,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1923]) ).

fof(c_0_4861,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1924]) ).

fof(c_0_4862,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1925]) ).

fof(c_0_4863,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1926]) ).

fof(c_0_4864,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1927]) ).

fof(c_0_4865,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1928]) ).

fof(c_0_4866,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1929]) ).

fof(c_0_4867,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1930]) ).

fof(c_0_4868,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1931]) ).

fof(c_0_4869,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1932]) ).

fof(c_0_4870,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1933]) ).

fof(c_0_4871,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1934]) ).

fof(c_0_4872,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1935]) ).

fof(c_0_4873,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1936]) ).

fof(c_0_4874,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1937]) ).

fof(c_0_4875,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1938]) ).

fof(c_0_4876,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1939]) ).

fof(c_0_4877,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1940]) ).

fof(c_0_4878,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1941]) ).

fof(c_0_4879,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1942]) ).

fof(c_0_4880,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1943]) ).

fof(c_0_4881,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1944]) ).

fof(c_0_4882,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1945]) ).

fof(c_0_4883,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1946]) ).

fof(c_0_4884,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1947]) ).

fof(c_0_4885,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1948]) ).

fof(c_0_4886,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1949]) ).

fof(c_0_4887,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1950]) ).

fof(c_0_4888,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1951]) ).

fof(c_0_4889,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1952]) ).

fof(c_0_4890,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1953]) ).

fof(c_0_4891,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1954]) ).

fof(c_0_4892,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1955]) ).

fof(c_0_4893,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1956]) ).

fof(c_0_4894,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1957]) ).

fof(c_0_4895,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1958]) ).

fof(c_0_4896,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1959]) ).

fof(c_0_4897,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1960]) ).

fof(c_0_4898,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1961]) ).

fof(c_0_4899,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1962]) ).

fof(c_0_4900,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1963]) ).

fof(c_0_4901,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1964]) ).

fof(c_0_4902,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1965]) ).

fof(c_0_4903,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1966]) ).

fof(c_0_4904,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1967]) ).

fof(c_0_4905,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1968]) ).

fof(c_0_4906,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1969]) ).

fof(c_0_4907,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1970]) ).

fof(c_0_4908,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1971]) ).

fof(c_0_4909,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1972]) ).

fof(c_0_4910,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1973]) ).

fof(c_0_4911,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1974]) ).

fof(c_0_4912,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1975]) ).

fof(c_0_4913,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1976]) ).

fof(c_0_4914,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1977]) ).

fof(c_0_4915,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1978]) ).

fof(c_0_4916,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1979]) ).

fof(c_0_4917,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1980]) ).

fof(c_0_4918,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1981]) ).

fof(c_0_4919,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1982]) ).

fof(c_0_4920,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1983]) ).

fof(c_0_4921,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1984]) ).

fof(c_0_4922,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1985]) ).

fof(c_0_4923,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1986]) ).

fof(c_0_4924,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1987]) ).

fof(c_0_4925,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1988]) ).

fof(c_0_4926,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1989]) ).

fof(c_0_4927,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1990]) ).

fof(c_0_4928,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1991]) ).

fof(c_0_4929,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1992]) ).

fof(c_0_4930,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1993]) ).

fof(c_0_4931,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1994]) ).

fof(c_0_4932,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1995]) ).

fof(c_0_4933,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1996]) ).

fof(c_0_4934,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1997]) ).

fof(c_0_4935,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1998]) ).

fof(c_0_4936,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_1999]) ).

fof(c_0_4937,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2000]) ).

fof(c_0_4938,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2001]) ).

fof(c_0_4939,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2002]) ).

fof(c_0_4940,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2003]) ).

fof(c_0_4941,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2004]) ).

fof(c_0_4942,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2005]) ).

fof(c_0_4943,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2006]) ).

fof(c_0_4944,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2007]) ).

fof(c_0_4945,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2008]) ).

fof(c_0_4946,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2009]) ).

fof(c_0_4947,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2010]) ).

fof(c_0_4948,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2011]) ).

fof(c_0_4949,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2012]) ).

fof(c_0_4950,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2013]) ).

fof(c_0_4951,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2014]) ).

fof(c_0_4952,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2015]) ).

fof(c_0_4953,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2016]) ).

fof(c_0_4954,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2017]) ).

fof(c_0_4955,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2018]) ).

fof(c_0_4956,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2019]) ).

fof(c_0_4957,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2020]) ).

fof(c_0_4958,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2021]) ).

fof(c_0_4959,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2022]) ).

fof(c_0_4960,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2023]) ).

fof(c_0_4961,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2024]) ).

fof(c_0_4962,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2025]) ).

fof(c_0_4963,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2026]) ).

fof(c_0_4964,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2027]) ).

fof(c_0_4965,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2028]) ).

fof(c_0_4966,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2029]) ).

fof(c_0_4967,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2030]) ).

fof(c_0_4968,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2031]) ).

fof(c_0_4969,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2032]) ).

fof(c_0_4970,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2033]) ).

fof(c_0_4971,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2034]) ).

fof(c_0_4972,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2035]) ).

fof(c_0_4973,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2036]) ).

fof(c_0_4974,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2037]) ).

fof(c_0_4975,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2038]) ).

fof(c_0_4976,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2039]) ).

fof(c_0_4977,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2040]) ).

fof(c_0_4978,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2041]) ).

fof(c_0_4979,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2042]) ).

fof(c_0_4980,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2043]) ).

fof(c_0_4981,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2044]) ).

fof(c_0_4982,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2045]) ).

fof(c_0_4983,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2046]) ).

fof(c_0_4984,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2047]) ).

fof(c_0_4985,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2048]) ).

fof(c_0_4986,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2049]) ).

fof(c_0_4987,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2050]) ).

fof(c_0_4988,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2051]) ).

fof(c_0_4989,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2052]) ).

fof(c_0_4990,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2053]) ).

fof(c_0_4991,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2054]) ).

fof(c_0_4992,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2055]) ).

fof(c_0_4993,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2056]) ).

fof(c_0_4994,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2057]) ).

fof(c_0_4995,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2058]) ).

fof(c_0_4996,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2059]) ).

fof(c_0_4997,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2060]) ).

fof(c_0_4998,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2061]) ).

fof(c_0_4999,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2062]) ).

fof(c_0_5000,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2063]) ).

fof(c_0_5001,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2064]) ).

fof(c_0_5002,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2065]) ).

fof(c_0_5003,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2066]) ).

fof(c_0_5004,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2067]) ).

fof(c_0_5005,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2068]) ).

fof(c_0_5006,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2069]) ).

fof(c_0_5007,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2070]) ).

fof(c_0_5008,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2071]) ).

fof(c_0_5009,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2072]) ).

fof(c_0_5010,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2073]) ).

fof(c_0_5011,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2074]) ).

fof(c_0_5012,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2075]) ).

fof(c_0_5013,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2076]) ).

fof(c_0_5014,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2077]) ).

fof(c_0_5015,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2078]) ).

fof(c_0_5016,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2079]) ).

fof(c_0_5017,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2080]) ).

fof(c_0_5018,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2081]) ).

fof(c_0_5019,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2082]) ).

fof(c_0_5020,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2083]) ).

fof(c_0_5021,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2084]) ).

fof(c_0_5022,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2085]) ).

fof(c_0_5023,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2086]) ).

fof(c_0_5024,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2087]) ).

fof(c_0_5025,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2088]) ).

fof(c_0_5026,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2089]) ).

fof(c_0_5027,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2090]) ).

fof(c_0_5028,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2091]) ).

fof(c_0_5029,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2092]) ).

fof(c_0_5030,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2093]) ).

fof(c_0_5031,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2094]) ).

fof(c_0_5032,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2095]) ).

fof(c_0_5033,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2096]) ).

fof(c_0_5034,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2097]) ).

fof(c_0_5035,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2098]) ).

fof(c_0_5036,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2099]) ).

fof(c_0_5037,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2100]) ).

fof(c_0_5038,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2101]) ).

fof(c_0_5039,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2102]) ).

fof(c_0_5040,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2103]) ).

fof(c_0_5041,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2104]) ).

fof(c_0_5042,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2105]) ).

fof(c_0_5043,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2106]) ).

fof(c_0_5044,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2107]) ).

fof(c_0_5045,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2108]) ).

fof(c_0_5046,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2109]) ).

fof(c_0_5047,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2110]) ).

fof(c_0_5048,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2111]) ).

fof(c_0_5049,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2112]) ).

fof(c_0_5050,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2113]) ).

fof(c_0_5051,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2114]) ).

fof(c_0_5052,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2115]) ).

fof(c_0_5053,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2116]) ).

fof(c_0_5054,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2117]) ).

fof(c_0_5055,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2118]) ).

fof(c_0_5056,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2119]) ).

fof(c_0_5057,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2120]) ).

fof(c_0_5058,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2121]) ).

fof(c_0_5059,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2122]) ).

fof(c_0_5060,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2123]) ).

fof(c_0_5061,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2124]) ).

fof(c_0_5062,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Olordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2125]) ).

fof(c_0_5063,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2126]) ).

fof(c_0_5064,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2127]) ).

fof(c_0_5065,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2128]) ).

fof(c_0_5066,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oaxclass__abs__if(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2129]) ).

fof(c_0_5067,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2130]) ).

fof(c_0_5068,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2131]) ).

fof(c_0_5069,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2132]) ).

fof(c_0_5070,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2133]) ).

fof(c_0_5071,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2134]) ).

fof(c_0_5072,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2135]) ).

fof(c_0_5073,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2136]) ).

fof(c_0_5074,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2137]) ).

fof(c_0_5075,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2138]) ).

fof(c_0_5076,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2139]) ).

fof(c_0_5077,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2140]) ).

fof(c_0_5078,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2141]) ).

fof(c_0_5079,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2142]) ).

fof(c_0_5080,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2143]) ).

fof(c_0_5081,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2144]) ).

fof(c_0_5082,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2145]) ).

fof(c_0_5083,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2146]) ).

fof(c_0_5084,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2147]) ).

fof(c_0_5085,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2148]) ).

fof(c_0_5086,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2149]) ).

fof(c_0_5087,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2150]) ).

fof(c_0_5088,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2151]) ).

fof(c_0_5089,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2152]) ).

fof(c_0_5090,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2153]) ).

fof(c_0_5091,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2154]) ).

fof(c_0_5092,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oidom(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2155]) ).

fof(c_0_5093,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2156]) ).

fof(c_0_5094,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__semidom(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2157]) ).

fof(c_0_5095,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2158]) ).

fof(c_0_5096,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2159]) ).

fof(c_0_5097,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2160]) ).

fof(c_0_5098,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2161]) ).

fof(c_0_5099,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2162]) ).

fof(c_0_5100,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2163]) ).

fof(c_0_5101,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2164]) ).

fof(c_0_5102,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Olordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2165]) ).

fof(c_0_5103,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__ring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2166]) ).

fof(c_0_5104,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oaxclass__abs__if(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2167]) ).

fof(c_0_5105,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2168]) ).

fof(c_0_5106,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2169]) ).

fof(c_0_5107,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2170]) ).

fof(c_0_5108,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2171]) ).

fof(c_0_5109,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2172]) ).

fof(c_0_5110,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2173]) ).

fof(c_0_5111,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2174]) ).

fof(c_0_5112,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2175]) ).

fof(c_0_5113,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2176]) ).

fof(c_0_5114,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2177]) ).

fof(c_0_5115,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2178]) ).

fof(c_0_5116,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2179]) ).

fof(c_0_5117,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2180]) ).

fof(c_0_5118,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2181]) ).

fof(c_0_5119,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2182]) ).

fof(c_0_5120,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2183]) ).

fof(c_0_5121,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2184]) ).

fof(c_0_5122,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2185]) ).

fof(c_0_5123,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2186]) ).

fof(c_0_5124,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2187]) ).

fof(c_0_5125,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2188]) ).

fof(c_0_5126,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2189]) ).

fof(c_0_5127,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2190]) ).

fof(c_0_5128,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2191]) ).

fof(c_0_5129,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2192]) ).

fof(c_0_5130,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2193]) ).

fof(c_0_5131,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2194]) ).

fof(c_0_5132,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2195]) ).

fof(c_0_5133,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2196]) ).

fof(c_0_5134,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2197]) ).

fof(c_0_5135,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2198]) ).

fof(c_0_5136,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2199]) ).

fof(c_0_5137,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2200]) ).

fof(c_0_5138,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2201]) ).

fof(c_0_5139,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2202]) ).

fof(c_0_5140,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2203]) ).

fof(c_0_5141,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2204]) ).

fof(c_0_5142,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2205]) ).

fof(c_0_5143,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2206]) ).

fof(c_0_5144,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2207]) ).

fof(c_0_5145,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__idom(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2208]) ).

fof(c_0_5146,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2209]) ).

fof(c_0_5147,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2210]) ).

fof(c_0_5148,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2211]) ).

fof(c_0_5149,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__semidom(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2212]) ).

fof(c_0_5150,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2213]) ).

fof(c_0_5151,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2214]) ).

fof(c_0_5152,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2215]) ).

fof(c_0_5153,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2216]) ).

fof(c_0_5154,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2217]) ).

fof(c_0_5155,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2218]) ).

fof(c_0_5156,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2219]) ).

fof(c_0_5157,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2220]) ).

fof(c_0_5158,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2221]) ).

fof(c_0_5159,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2222]) ).

fof(c_0_5160,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2223]) ).

fof(c_0_5161,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2224]) ).

fof(c_0_5162,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2225]) ).

fof(c_0_5163,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2226]) ).

fof(c_0_5164,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2227]) ).

fof(c_0_5165,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2228]) ).

fof(c_0_5166,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2229]) ).

fof(c_0_5167,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2230]) ).

fof(c_0_5168,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Olordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2231]) ).

fof(c_0_5169,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oaxclass__abs__if(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2232]) ).

fof(c_0_5170,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2233]) ).

fof(c_0_5171,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2234]) ).

fof(c_0_5172,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2235]) ).

fof(c_0_5173,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2236]) ).

fof(c_0_5174,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__ring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2237]) ).

fof(c_0_5175,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2238]) ).

fof(c_0_5176,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2239]) ).

fof(c_0_5177,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2240]) ).

fof(c_0_5178,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oordered__idom(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2241]) ).

fof(c_0_5179,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2242]) ).

fof(c_0_5180,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2243]) ).

fof(c_0_5181,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2244]) ).

fof(c_0_5182,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2245]) ).

fof(c_0_5183,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2246]) ).

fof(c_0_5184,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2247]) ).

fof(c_0_5185,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2248]) ).

fof(c_0_5186,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2249]) ).

fof(c_0_5187,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2250]) ).

fof(c_0_5188,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2251]) ).

fof(c_0_5189,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2252]) ).

fof(c_0_5190,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2253]) ).

fof(c_0_5191,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2254]) ).

fof(c_0_5192,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2255]) ).

fof(c_0_5193,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2256]) ).

fof(c_0_5194,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oidom(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2257]) ).

fof(c_0_5195,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2258]) ).

fof(c_0_5196,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2259]) ).

fof(c_0_5197,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2260]) ).

fof(c_0_5198,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2261]) ).

fof(c_0_5199,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2262]) ).

fof(c_0_5200,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2263]) ).

fof(c_0_5201,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2264]) ).

fof(c_0_5202,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2265]) ).

fof(c_0_5203,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2266]) ).

fof(c_0_5204,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2267]) ).

fof(c_0_5205,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_HOL_Oinverse(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2268]) ).

fof(c_0_5206,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__field(X40)
      | class_Ring__and__Field_Ofield(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2269]) ).

fof(c_0_5207,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2270]) ).

fof(c_0_5208,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2271]) ).

fof(c_0_5209,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2272]) ).

fof(c_0_5210,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2273]) ).

fof(c_0_5211,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2274]) ).

fof(c_0_5212,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2275]) ).

fof(c_0_5213,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2276]) ).

fof(c_0_5214,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2277]) ).

fof(c_0_5215,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2278]) ).

fof(c_0_5216,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2279]) ).

fof(c_0_5217,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2280]) ).

fof(c_0_5218,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2281]) ).

fof(c_0_5219,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Oordered__semiring__strict(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2282]) ).

fof(c_0_5220,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2283]) ).

fof(c_0_5221,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2284]) ).

fof(c_0_5222,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2285]) ).

fof(c_0_5223,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2286]) ).

fof(c_0_5224,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2287]) ).

fof(c_0_5225,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2288]) ).

fof(c_0_5226,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2289]) ).

fof(c_0_5227,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2290]) ).

fof(c_0_5228,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2291]) ).

fof(c_0_5229,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2292]) ).

fof(c_0_5230,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2293]) ).

fof(c_0_5231,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2294]) ).

fof(c_0_5232,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2295]) ).

fof(c_0_5233,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2296]) ).

fof(c_0_5234,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2297]) ).

fof(c_0_5235,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2298]) ).

fof(c_0_5236,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2299]) ).

fof(c_0_5237,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2300]) ).

fof(c_0_5238,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Opordered__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2301]) ).

fof(c_0_5239,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Opordered__cancel__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2302]) ).

fof(c_0_5240,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2303]) ).

fof(c_0_5241,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2304]) ).

fof(c_0_5242,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2305]) ).

fof(c_0_5243,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group__join(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2306]) ).

fof(c_0_5244,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2307]) ).

fof(c_0_5245,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group__meet(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2308]) ).

fof(c_0_5246,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2309]) ).

fof(c_0_5247,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2310]) ).

fof(c_0_5248,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2311]) ).

fof(c_0_5249,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2312]) ).

fof(c_0_5250,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Olordered__ab__group__abs(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2313]) ).

fof(c_0_5251,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2314]) ).

fof(c_0_5252,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2315]) ).

fof(c_0_5253,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2316]) ).

fof(c_0_5254,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2317]) ).

fof(c_0_5255,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2318]) ).

fof(c_0_5256,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2319]) ).

fof(c_0_5257,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2320]) ).

fof(c_0_5258,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2321]) ).

fof(c_0_5259,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2322]) ).

fof(c_0_5260,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2323]) ).

fof(c_0_5261,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2324]) ).

fof(c_0_5262,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2325]) ).

fof(c_0_5263,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2326]) ).

fof(c_0_5264,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2327]) ).

fof(c_0_5265,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2328]) ).

fof(c_0_5266,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2329]) ).

fof(c_0_5267,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Olordered__ring(X40)
      | class_Ring__and__Field_Opordered__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2330]) ).

fof(c_0_5268,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2331]) ).

fof(c_0_5269,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2332]) ).

fof(c_0_5270,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2333]) ).

fof(c_0_5271,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2334]) ).

fof(c_0_5272,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2335]) ).

fof(c_0_5273,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2336]) ).

fof(c_0_5274,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2337]) ).

fof(c_0_5275,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2338]) ).

fof(c_0_5276,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2339]) ).

fof(c_0_5277,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2340]) ).

fof(c_0_5278,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2341]) ).

fof(c_0_5279,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2342]) ).

fof(c_0_5280,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2343]) ).

fof(c_0_5281,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2344]) ).

fof(c_0_5282,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2345]) ).

fof(c_0_5283,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2346]) ).

fof(c_0_5284,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2347]) ).

fof(c_0_5285,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2348]) ).

fof(c_0_5286,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2349]) ).

fof(c_0_5287,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2350]) ).

fof(c_0_5288,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2351]) ).

fof(c_0_5289,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2352]) ).

fof(c_0_5290,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2353]) ).

fof(c_0_5291,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2354]) ).

fof(c_0_5292,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2355]) ).

fof(c_0_5293,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2356]) ).

fof(c_0_5294,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2357]) ).

fof(c_0_5295,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2358]) ).

fof(c_0_5296,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2359]) ).

fof(c_0_5297,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2360]) ).

fof(c_0_5298,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2361]) ).

fof(c_0_5299,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2362]) ).

fof(c_0_5300,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2363]) ).

fof(c_0_5301,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2364]) ).

fof(c_0_5302,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2365]) ).

fof(c_0_5303,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2366]) ).

fof(c_0_5304,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2367]) ).

fof(c_0_5305,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2368]) ).

fof(c_0_5306,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oidom(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2369]) ).

fof(c_0_5307,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Oinverse(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2370]) ).

fof(c_0_5308,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2371]) ).

fof(c_0_5309,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2372]) ).

fof(c_0_5310,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2373]) ).

fof(c_0_5311,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2374]) ).

fof(c_0_5312,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2375]) ).

fof(c_0_5313,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2376]) ).

fof(c_0_5314,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2377]) ).

fof(c_0_5315,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2378]) ).

fof(c_0_5316,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2379]) ).

fof(c_0_5317,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2380]) ).

fof(c_0_5318,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2381]) ).

fof(c_0_5319,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2382]) ).

fof(c_0_5320,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2383]) ).

fof(c_0_5321,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2384]) ).

fof(c_0_5322,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2385]) ).

fof(c_0_5323,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2386]) ).

fof(c_0_5324,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2387]) ).

fof(c_0_5325,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2388]) ).

fof(c_0_5326,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2389]) ).

fof(c_0_5327,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2390]) ).

fof(c_0_5328,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2391]) ).

fof(c_0_5329,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2392]) ).

fof(c_0_5330,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2393]) ).

fof(c_0_5331,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ofield(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2394]) ).

fof(c_0_5332,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X40)
      | class_HOL_Oinverse(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2395]) ).

fof(c_0_5333,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2396]) ).

fof(c_0_5334,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2397]) ).

fof(c_0_5335,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2398]) ).

fof(c_0_5336,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2399]) ).

fof(c_0_5337,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2400]) ).

fof(c_0_5338,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2401]) ).

fof(c_0_5339,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2402]) ).

fof(c_0_5340,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2403]) ).

fof(c_0_5341,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2404]) ).

fof(c_0_5342,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2405]) ).

fof(c_0_5343,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2406]) ).

fof(c_0_5344,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2407]) ).

fof(c_0_5345,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2408]) ).

fof(c_0_5346,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2409]) ).

fof(c_0_5347,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2410]) ).

fof(c_0_5348,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2411]) ).

fof(c_0_5349,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2412]) ).

fof(c_0_5350,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2413]) ).

fof(c_0_5351,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2414]) ).

fof(c_0_5352,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2415]) ).

fof(c_0_5353,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2416]) ).

fof(c_0_5354,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2417]) ).

fof(c_0_5355,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2418]) ).

fof(c_0_5356,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2419]) ).

fof(c_0_5357,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2420]) ).

fof(c_0_5358,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2421]) ).

fof(c_0_5359,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2422]) ).

fof(c_0_5360,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2423]) ).

fof(c_0_5361,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2424]) ).

fof(c_0_5362,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2425]) ).

fof(c_0_5363,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2426]) ).

fof(c_0_5364,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2427]) ).

fof(c_0_5365,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2428]) ).

fof(c_0_5366,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2429]) ).

fof(c_0_5367,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2430]) ).

fof(c_0_5368,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2431]) ).

fof(c_0_5369,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2432]) ).

fof(c_0_5370,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2433]) ).

fof(c_0_5371,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2434]) ).

fof(c_0_5372,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2435]) ).

fof(c_0_5373,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2436]) ).

fof(c_0_5374,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2437]) ).

fof(c_0_5375,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2438]) ).

fof(c_0_5376,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2439]) ).

fof(c_0_5377,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2440]) ).

fof(c_0_5378,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2441]) ).

fof(c_0_5379,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2442]) ).

fof(c_0_5380,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2443]) ).

fof(c_0_5381,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2444]) ).

fof(c_0_5382,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2445]) ).

fof(c_0_5383,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2446]) ).

fof(c_0_5384,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2447]) ).

fof(c_0_5385,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2448]) ).

fof(c_0_5386,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2449]) ).

fof(c_0_5387,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2450]) ).

fof(c_0_5388,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2451]) ).

fof(c_0_5389,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2452]) ).

fof(c_0_5390,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2453]) ).

fof(c_0_5391,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2454]) ).

fof(c_0_5392,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2455]) ).

fof(c_0_5393,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2456]) ).

fof(c_0_5394,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2457]) ).

fof(c_0_5395,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2458]) ).

fof(c_0_5396,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2459]) ).

fof(c_0_5397,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2460]) ).

fof(c_0_5398,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2461]) ).

fof(c_0_5399,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2462]) ).

fof(c_0_5400,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2463]) ).

fof(c_0_5401,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2464]) ).

fof(c_0_5402,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2465]) ).

fof(c_0_5403,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2466]) ).

fof(c_0_5404,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2467]) ).

fof(c_0_5405,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2468]) ).

fof(c_0_5406,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2469]) ).

fof(c_0_5407,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2470]) ).

fof(c_0_5408,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2471]) ).

fof(c_0_5409,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2472]) ).

fof(c_0_5410,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2473]) ).

fof(c_0_5411,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2474]) ).

fof(c_0_5412,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2475]) ).

fof(c_0_5413,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2476]) ).

fof(c_0_5414,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2477]) ).

fof(c_0_5415,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2478]) ).

fof(c_0_5416,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2479]) ).

fof(c_0_5417,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2480]) ).

fof(c_0_5418,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2481]) ).

fof(c_0_5419,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2482]) ).

fof(c_0_5420,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2483]) ).

fof(c_0_5421,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2484]) ).

fof(c_0_5422,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2485]) ).

fof(c_0_5423,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2486]) ).

fof(c_0_5424,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2487]) ).

fof(c_0_5425,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2488]) ).

fof(c_0_5426,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2489]) ).

fof(c_0_5427,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2490]) ).

fof(c_0_5428,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2491]) ).

fof(c_0_5429,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2492]) ).

fof(c_0_5430,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2493]) ).

fof(c_0_5431,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2494]) ).

fof(c_0_5432,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2495]) ).

fof(c_0_5433,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2496]) ).

fof(c_0_5434,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2497]) ).

fof(c_0_5435,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2498]) ).

fof(c_0_5436,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2499]) ).

fof(c_0_5437,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2500]) ).

fof(c_0_5438,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2501]) ).

fof(c_0_5439,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2502]) ).

fof(c_0_5440,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2503]) ).

fof(c_0_5441,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2504]) ).

fof(c_0_5442,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2505]) ).

fof(c_0_5443,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2506]) ).

fof(c_0_5444,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2507]) ).

fof(c_0_5445,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2508]) ).

fof(c_0_5446,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2509]) ).

fof(c_0_5447,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2510]) ).

fof(c_0_5448,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2511]) ).

fof(c_0_5449,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2512]) ).

fof(c_0_5450,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2513]) ).

fof(c_0_5451,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2514]) ).

fof(c_0_5452,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2515]) ).

fof(c_0_5453,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2516]) ).

fof(c_0_5454,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2517]) ).

fof(c_0_5455,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2518]) ).

fof(c_0_5456,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2519]) ).

fof(c_0_5457,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2520]) ).

fof(c_0_5458,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2521]) ).

fof(c_0_5459,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2522]) ).

fof(c_0_5460,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2523]) ).

fof(c_0_5461,plain,
    ! [X40] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2524]) ).

fof(c_0_5462,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2525]) ).

fof(c_0_5463,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2526]) ).

fof(c_0_5464,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2527]) ).

fof(c_0_5465,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2528]) ).

fof(c_0_5466,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2529]) ).

fof(c_0_5467,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2530]) ).

fof(c_0_5468,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2531]) ).

fof(c_0_5469,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2532]) ).

fof(c_0_5470,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2533]) ).

fof(c_0_5471,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2534]) ).

fof(c_0_5472,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2535]) ).

fof(c_0_5473,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2536]) ).

fof(c_0_5474,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2537]) ).

fof(c_0_5475,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2538]) ).

fof(c_0_5476,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2539]) ).

fof(c_0_5477,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2540]) ).

fof(c_0_5478,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2541]) ).

fof(c_0_5479,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2542]) ).

fof(c_0_5480,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2543]) ).

fof(c_0_5481,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2544]) ).

fof(c_0_5482,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2545]) ).

fof(c_0_5483,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2546]) ).

fof(c_0_5484,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2547]) ).

fof(c_0_5485,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2548]) ).

fof(c_0_5486,plain,
    ! [X40] :
      ( ~ class_Power_Orecpower(X40)
      | class_Nat_Opower(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2549]) ).

fof(c_0_5487,plain,
    ! [X40] :
      ( ~ class_Orderings_Oorder(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2550]) ).

fof(c_0_5488,plain,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2551]) ).

fof(c_0_5489,plain,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2552]) ).

fof(c_0_5490,plain,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2553]) ).

fof(c_0_5491,plain,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2554]) ).

fof(c_0_5492,plain,
    ! [X40] :
      ( ~ class_Orderings_Olinorder(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2555]) ).

fof(c_0_5493,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2556]) ).

fof(c_0_5494,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Osemigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2557]) ).

fof(c_0_5495,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2558]) ).

fof(c_0_5496,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2559]) ).

fof(c_0_5497,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2560]) ).

fof(c_0_5498,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2561]) ).

fof(c_0_5499,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2562]) ).

fof(c_0_5500,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2563]) ).

fof(c_0_5501,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2564]) ).

fof(c_0_5502,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2565]) ).

fof(c_0_5503,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2566]) ).

fof(c_0_5504,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2567]) ).

fof(c_0_5505,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2568]) ).

fof(c_0_5506,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2569]) ).

fof(c_0_5507,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2570]) ).

fof(c_0_5508,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2571]) ).

fof(c_0_5509,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2572]) ).

fof(c_0_5510,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2573]) ).

fof(c_0_5511,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2574]) ).

fof(c_0_5512,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2575]) ).

fof(c_0_5513,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2576]) ).

fof(c_0_5514,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2577]) ).

fof(c_0_5515,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2578]) ).

fof(c_0_5516,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2579]) ).

fof(c_0_5517,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2580]) ).

fof(c_0_5518,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2581]) ).

fof(c_0_5519,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2582]) ).

fof(c_0_5520,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2583]) ).

fof(c_0_5521,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2584]) ).

fof(c_0_5522,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2585]) ).

fof(c_0_5523,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2586]) ).

fof(c_0_5524,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2587]) ).

fof(c_0_5525,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2588]) ).

fof(c_0_5526,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2589]) ).

fof(c_0_5527,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2590]) ).

fof(c_0_5528,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2591]) ).

fof(c_0_5529,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2592]) ).

fof(c_0_5530,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2593]) ).

fof(c_0_5531,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Olinorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2594]) ).

fof(c_0_5532,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2595]) ).

fof(c_0_5533,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2596]) ).

fof(c_0_5534,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2597]) ).

fof(c_0_5535,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2598]) ).

fof(c_0_5536,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2599]) ).

fof(c_0_5537,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2600]) ).

fof(c_0_5538,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2601]) ).

fof(c_0_5539,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2602]) ).

fof(c_0_5540,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2603]) ).

fof(c_0_5541,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2604]) ).

fof(c_0_5542,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2605]) ).

fof(c_0_5543,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2606]) ).

fof(c_0_5544,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2607]) ).

fof(c_0_5545,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Omonoid__mult(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2608]) ).

fof(c_0_5546,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Omonoid__mult(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2609]) ).

fof(c_0_5547,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Omonoid__mult(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2610]) ).

fof(c_0_5548,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2611]) ).

fof(c_0_5549,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2612]) ).

fof(c_0_5550,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2613]) ).

fof(c_0_5551,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2614]) ).

fof(c_0_5552,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2615]) ).

fof(c_0_5553,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2616]) ).

fof(c_0_5554,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2617]) ).

fof(c_0_5555,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2618]) ).

fof(c_0_5556,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2619]) ).

fof(c_0_5557,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2620]) ).

fof(c_0_5558,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2621]) ).

fof(c_0_5559,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2622]) ).

fof(c_0_5560,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2623]) ).

fof(c_0_5561,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2624]) ).

fof(c_0_5562,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2625]) ).

fof(c_0_5563,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2626]) ).

fof(c_0_5564,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2627]) ).

fof(c_0_5565,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2628]) ).

fof(c_0_5566,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2629]) ).

fof(c_0_5567,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2630]) ).

fof(c_0_5568,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2631]) ).

fof(c_0_5569,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2632]) ).

fof(c_0_5570,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2633]) ).

fof(c_0_5571,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2634]) ).

fof(c_0_5572,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2635]) ).

fof(c_0_5573,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2636]) ).

fof(c_0_5574,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2637]) ).

fof(c_0_5575,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2638]) ).

fof(c_0_5576,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2639]) ).

fof(c_0_5577,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2640]) ).

fof(c_0_5578,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2641]) ).

fof(c_0_5579,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2642]) ).

fof(c_0_5580,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2643]) ).

fof(c_0_5581,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2644]) ).

fof(c_0_5582,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2645]) ).

fof(c_0_5583,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2646]) ).

fof(c_0_5584,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2647]) ).

fof(c_0_5585,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2648]) ).

fof(c_0_5586,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2649]) ).

fof(c_0_5587,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2650]) ).

fof(c_0_5588,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2651]) ).

fof(c_0_5589,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2652]) ).

fof(c_0_5590,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2653]) ).

fof(c_0_5591,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2654]) ).

fof(c_0_5592,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2655]) ).

fof(c_0_5593,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2656]) ).

fof(c_0_5594,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2657]) ).

fof(c_0_5595,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2658]) ).

fof(c_0_5596,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2659]) ).

fof(c_0_5597,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2660]) ).

fof(c_0_5598,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2661]) ).

fof(c_0_5599,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2662]) ).

fof(c_0_5600,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2663]) ).

fof(c_0_5601,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2664]) ).

fof(c_0_5602,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2665]) ).

fof(c_0_5603,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2666]) ).

fof(c_0_5604,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X40)
      | class_OrderedGroup_Olordered__ab__group(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2667]) ).

fof(c_0_5605,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2668]) ).

fof(c_0_5606,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2669]) ).

fof(c_0_5607,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2670]) ).

fof(c_0_5608,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2671]) ).

fof(c_0_5609,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2672]) ).

fof(c_0_5610,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2673]) ).

fof(c_0_5611,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2674]) ).

fof(c_0_5612,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2675]) ).

fof(c_0_5613,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2676]) ).

fof(c_0_5614,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2677]) ).

fof(c_0_5615,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_LOrder_Olorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2678]) ).

fof(c_0_5616,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2679]) ).

fof(c_0_5617,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2680]) ).

fof(c_0_5618,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2681]) ).

fof(c_0_5619,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2682]) ).

fof(c_0_5620,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2683]) ).

fof(c_0_5621,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2684]) ).

fof(c_0_5622,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X40)
      | class_OrderedGroup_Opordered__ab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2685]) ).

fof(c_0_5623,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2686]) ).

fof(c_0_5624,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2687]) ).

fof(c_0_5625,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2688]) ).

fof(c_0_5626,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2689]) ).

fof(c_0_5627,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2690]) ).

fof(c_0_5628,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2691]) ).

fof(c_0_5629,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2692]) ).

fof(c_0_5630,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2693]) ).

fof(c_0_5631,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2694]) ).

fof(c_0_5632,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2695]) ).

fof(c_0_5633,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2696]) ).

fof(c_0_5634,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2697]) ).

fof(c_0_5635,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2698]) ).

fof(c_0_5636,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2699]) ).

fof(c_0_5637,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2700]) ).

fof(c_0_5638,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2701]) ).

fof(c_0_5639,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2702]) ).

fof(c_0_5640,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2703]) ).

fof(c_0_5641,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2704]) ).

fof(c_0_5642,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2705]) ).

fof(c_0_5643,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2706]) ).

fof(c_0_5644,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2707]) ).

fof(c_0_5645,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2708]) ).

fof(c_0_5646,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2709]) ).

fof(c_0_5647,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2710]) ).

fof(c_0_5648,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2711]) ).

fof(c_0_5649,plain,
    ! [X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2712]) ).

fof(c_0_5650,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2713]) ).

fof(c_0_5651,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Ozero(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2714]) ).

fof(c_0_5652,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2715]) ).

fof(c_0_5653,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2716]) ).

fof(c_0_5654,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Oab__semigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2717]) ).

fof(c_0_5655,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Osemigroup__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2718]) ).

fof(c_0_5656,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Numeral_Onumber(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2719]) ).

fof(c_0_5657,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Otimes(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2720]) ).

fof(c_0_5658,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__ring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2721]) ).

fof(c_0_5659,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2722]) ).

fof(c_0_5660,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Oring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2723]) ).

fof(c_0_5661,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__1__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2724]) ).

fof(c_0_5662,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2725]) ).

fof(c_0_5663,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2726]) ).

fof(c_0_5664,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocomm__monoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2727]) ).

fof(c_0_5665,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Omonoid__mult(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2728]) ).

fof(c_0_5666,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2729]) ).

fof(c_0_5667,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Oone(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2730]) ).

fof(c_0_5668,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Oab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2731]) ).

fof(c_0_5669,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__ring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2732]) ).

fof(c_0_5670,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2733]) ).

fof(c_0_5671,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Oring(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2734]) ).

fof(c_0_5672,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__0__cancel(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2735]) ).

fof(c_0_5673,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Oab__group__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2736]) ).

fof(c_0_5674,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2737]) ).

fof(c_0_5675,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Ocancel__semigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2738]) ).

fof(c_0_5676,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Ominus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2739]) ).

fof(c_0_5677,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Ocomm__semiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2740]) ).

fof(c_0_5678,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_Ring__and__Field_Osemiring__0(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2741]) ).

fof(c_0_5679,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_OrderedGroup_Osemigroup__add(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2742]) ).

fof(c_0_5680,plain,
    ! [X40] :
      ( ~ class_Numeral_Onumber__ring(X40)
      | class_HOL_Oplus(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2743]) ).

fof(c_0_5681,plain,
    ! [X40] :
      ( ~ class_LOrder_Omeet__semilorder(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2744]) ).

fof(c_0_5682,plain,
    ! [X40] :
      ( ~ class_LOrder_Omeet__semilorder(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2745]) ).

fof(c_0_5683,plain,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_LOrder_Ojoin__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2746]) ).

fof(c_0_5684,plain,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2747]) ).

fof(c_0_5685,plain,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2748]) ).

fof(c_0_5686,plain,
    ! [X40] :
      ( ~ class_LOrder_Olorder(X40)
      | class_LOrder_Omeet__semilorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2749]) ).

fof(c_0_5687,plain,
    ! [X40] :
      ( ~ class_LOrder_Ojoin__semilorder(X40)
      | class_Orderings_Oorder(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2750]) ).

fof(c_0_5688,plain,
    ! [X40] :
      ( ~ class_LOrder_Ojoin__semilorder(X40)
      | class_Orderings_Oord(X40) ),
    inference(fof_simplification,[status(thm)],[c_0_2751]) ).

fof(c_0_5689,axiom,
    c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
    c_0_2752 ).

fof(c_0_5690,axiom,
    c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
    c_0_2753 ).

fof(c_0_5691,axiom,
    ! [X1] : c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
    c_0_2754 ).

fof(c_0_5692,axiom,
    c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
    c_0_2755 ).

fof(c_0_5693,axiom,
    c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
    c_0_2756 ).

fof(c_0_5694,axiom,
    c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
    c_0_2757 ).

fof(c_0_5695,axiom,
    c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
    c_0_2758 ).

fof(c_0_5696,axiom,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    c_0_2759 ).

fof(c_0_5697,axiom,
    c_Parity_Oeven(c_0,tc_nat),
    c_0_2760 ).

fof(c_0_5698,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
    c_0_2761 ).

fof(c_0_5699,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
    c_0_2762 ).

fof(c_0_5700,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
    c_0_2763 ).

fof(c_0_5701,axiom,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
    c_0_2764 ).

fof(c_0_5702,axiom,
    c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
    c_0_2765 ).

fof(c_0_5703,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
    c_0_2766 ).

fof(c_0_5704,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
    c_0_2767 ).

fof(c_0_5705,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
    c_0_2768 ).

fof(c_0_5706,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
    c_0_2769 ).

fof(c_0_5707,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
    c_0_2770 ).

fof(c_0_5708,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
    c_0_2771 ).

fof(c_0_5709,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
    c_0_2772 ).

fof(c_0_5710,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
    c_0_2773 ).

fof(c_0_5711,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
    c_0_2774 ).

fof(c_0_5712,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
    c_0_2775 ).

fof(c_0_5713,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
    c_0_2776 ).

fof(c_0_5714,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
    c_0_2777 ).

fof(c_0_5715,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
    c_0_2778 ).

fof(c_0_5716,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
    c_0_2779 ).

fof(c_0_5717,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
    c_0_2780 ).

fof(c_0_5718,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
    c_0_2781 ).

fof(c_0_5719,axiom,
    ! [X1] : c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
    c_0_2782 ).

fof(c_0_5720,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
    c_0_2783 ).

fof(c_0_5721,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
    c_0_2784 ).

fof(c_0_5722,axiom,
    c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
    c_0_2785 ).

fof(c_0_5723,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_2786 ).

fof(c_0_5724,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_2787 ).

fof(c_0_5725,axiom,
    ! [X38] : class_Nat_Opower(tc_set(X38)),
    c_0_2788 ).

fof(c_0_5726,axiom,
    ! [X38] : class_Orderings_Oorder(tc_set(X38)),
    c_0_2789 ).

fof(c_0_5727,axiom,
    ! [X38] : class_Orderings_Oord(tc_set(X38)),
    c_0_2790 ).

fof(c_0_5728,axiom,
    ! [X38] : class_HOL_Ominus(tc_set(X38)),
    c_0_2791 ).

fof(c_0_5729,axiom,
    ! [X22] :
      ( c_IntDef_Oint(X22) != c_0
      | X22 = c_0 ),
    c_0_2792 ).

fof(c_0_5730,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X4)
      | c_1 != c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_2793]) ).

fof(c_0_5731,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X4)
      | c_0 != c_1 ),
    inference(fof_simplification,[status(thm)],[c_0_2794]) ).

fof(c_0_5732,axiom,
    ! [X91] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X91),
    c_0_2795 ).

fof(c_0_5733,axiom,
    ! [X91] : c_Message_Oagent_OFriend(X91) != c_Message_Oagent_OSpy,
    c_0_2796 ).

fof(c_0_5734,axiom,
    ! [X90] : c_Message_Oagent_OFriend(X90) != c_Message_Oagent_OServer,
    c_0_2797 ).

fof(c_0_5735,axiom,
    ! [X90] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X90),
    c_0_2798 ).

fof(c_0_5736,axiom,
    ! [X16] : c_0 != c_Suc(X16),
    c_0_2799 ).

fof(c_0_5737,axiom,
    ! [X16] : c_Suc(X16) != c_0,
    c_0_2800 ).

fof(c_0_5738,axiom,
    c_IntDef_Onat(c_1) = c_Suc(c_0),
    c_0_2801 ).

fof(c_0_5739,axiom,
    c_Message_Oanalz(c_emptyset) = c_emptyset,
    c_0_2802 ).

fof(c_0_5740,axiom,
    c_Message_Oparts(c_emptyset) = c_emptyset,
    c_0_2803 ).

fof(c_0_5741,axiom,
    c_Message_OkeysFor(c_emptyset) = c_emptyset,
    c_0_2804 ).

fof(c_0_5742,axiom,
    c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
    c_0_2805 ).

fof(c_0_5743,axiom,
    c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
    c_0_2806 ).

fof(c_0_5744,axiom,
    c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
    c_0_2807 ).

fof(c_0_5745,axiom,
    c_1 = c_Suc(c_0),
    c_0_2808 ).

fof(c_0_5746,axiom,
    c_IntDef_Onat(c_0) = c_0,
    c_0_2809 ).

fof(c_0_5747,axiom,
    c_IntDef_Oint(c_0) = c_0,
    c_0_2810 ).

fof(c_0_5748,axiom,
    c_IntDef_Oint(c_1) = c_1,
    c_0_2811 ).

fof(c_0_5749,axiom,
    class_HOL_Ominus(tc_nat),
    c_0_2812 ).

fof(c_0_5750,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    c_0_2813 ).

fof(c_0_5751,axiom,
    class_Orderings_Olinorder(tc_nat),
    c_0_2814 ).

fof(c_0_5752,axiom,
    class_LOrder_Olorder(tc_nat),
    c_0_2815 ).

fof(c_0_5753,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    c_0_2816 ).

fof(c_0_5754,axiom,
    class_Parity_Oeven__odd(tc_nat),
    c_0_2817 ).

fof(c_0_5755,axiom,
    class_Numeral_Onumber(tc_nat),
    c_0_2818 ).

fof(c_0_5756,axiom,
    class_Power_Orecpower(tc_nat),
    c_0_2819 ).

fof(c_0_5757,axiom,
    class_Divides_Odiv(tc_nat),
    c_0_2820 ).

fof(c_0_5758,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_2821 ).

fof(c_0_5759,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_2822 ).

fof(c_0_5760,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    c_0_2823 ).

fof(c_0_5761,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    c_0_2824 ).

fof(c_0_5762,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    c_0_2825 ).

fof(c_0_5763,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_2826 ).

fof(c_0_5764,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_2827 ).

fof(c_0_5765,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_2828 ).

fof(c_0_5766,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    c_0_2829 ).

fof(c_0_5767,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_2830 ).

fof(c_0_5768,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_2831 ).

fof(c_0_5769,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_2832 ).

fof(c_0_5770,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    c_0_2833 ).

fof(c_0_5771,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    c_0_2834 ).

fof(c_0_5772,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    c_0_2835 ).

fof(c_0_5773,axiom,
    class_Orderings_Oorder(tc_nat),
    c_0_2836 ).

fof(c_0_5774,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    c_0_2837 ).

fof(c_0_5775,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_2838 ).

fof(c_0_5776,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_2839 ).

fof(c_0_5777,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_2840 ).

fof(c_0_5778,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_2841 ).

fof(c_0_5779,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    c_0_2842 ).

fof(c_0_5780,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    c_0_2843 ).

fof(c_0_5781,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    c_0_2844 ).

fof(c_0_5782,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    c_0_2845 ).

fof(c_0_5783,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_2846 ).

fof(c_0_5784,axiom,
    class_Orderings_Oord(tc_nat),
    c_0_2847 ).

fof(c_0_5785,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_2848 ).

fof(c_0_5786,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_2849 ).

fof(c_0_5787,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_2850 ).

fof(c_0_5788,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    c_0_2851 ).

fof(c_0_5789,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_2852 ).

fof(c_0_5790,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    c_0_2853 ).

fof(c_0_5791,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    c_0_2854 ).

fof(c_0_5792,axiom,
    class_Nat_Opower(tc_nat),
    c_0_2855 ).

fof(c_0_5793,axiom,
    class_HOL_Otimes(tc_nat),
    c_0_2856 ).

fof(c_0_5794,axiom,
    class_HOL_Oplus(tc_nat),
    c_0_2857 ).

fof(c_0_5795,axiom,
    class_HOL_Ozero(tc_nat),
    c_0_2858 ).

fof(c_0_5796,axiom,
    class_HOL_Oone(tc_nat),
    c_0_2859 ).

fof(c_0_5797,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    c_0_2860 ).

fof(c_0_5798,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    c_0_2861 ).

fof(c_0_5799,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    c_0_2862 ).

fof(c_0_5800,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    c_0_2863 ).

fof(c_0_5801,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    c_0_2864 ).

fof(c_0_5802,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    c_0_2865 ).

fof(c_0_5803,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    c_0_2866 ).

fof(c_0_5804,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    c_0_2867 ).

fof(c_0_5805,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    c_0_2868 ).

fof(c_0_5806,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    c_0_2869 ).

fof(c_0_5807,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    c_0_2870 ).

fof(c_0_5808,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    c_0_2871 ).

fof(c_0_5809,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    c_0_2872 ).

fof(c_0_5810,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    c_0_2873 ).

fof(c_0_5811,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    c_0_2874 ).

fof(c_0_5812,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    c_0_2875 ).

fof(c_0_5813,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    c_0_2876 ).

fof(c_0_5814,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    c_0_2877 ).

fof(c_0_5815,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    c_0_2878 ).

fof(c_0_5816,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    c_0_2879 ).

fof(c_0_5817,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    c_0_2880 ).

fof(c_0_5818,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    c_0_2881 ).

fof(c_0_5819,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    c_0_2882 ).

fof(c_0_5820,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    c_0_2883 ).

fof(c_0_5821,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    c_0_2884 ).

fof(c_0_5822,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    c_0_2885 ).

fof(c_0_5823,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    c_0_2886 ).

fof(c_0_5824,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    c_0_2887 ).

fof(c_0_5825,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    c_0_2888 ).

fof(c_0_5826,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    c_0_2889 ).

fof(c_0_5827,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    c_0_2890 ).

fof(c_0_5828,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    c_0_2891 ).

fof(c_0_5829,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    c_0_2892 ).

fof(c_0_5830,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2893 ).

fof(c_0_5831,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    c_0_2894 ).

fof(c_0_5832,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2895 ).

fof(c_0_5833,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2896 ).

fof(c_0_5834,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    c_0_2897 ).

fof(c_0_5835,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    c_0_2898 ).

fof(c_0_5836,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    c_0_2899 ).

fof(c_0_5837,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    c_0_2900 ).

fof(c_0_5838,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    c_0_2901 ).

fof(c_0_5839,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    c_0_2902 ).

fof(c_0_5840,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    c_0_2903 ).

fof(c_0_5841,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    c_0_2904 ).

fof(c_0_5842,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    c_0_2905 ).

fof(c_0_5843,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    c_0_2906 ).

fof(c_0_5844,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    c_0_2907 ).

fof(c_0_5845,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    c_0_2908 ).

fof(c_0_5846,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    c_0_2909 ).

fof(c_0_5847,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    c_0_2910 ).

fof(c_0_5848,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    c_0_2911 ).

fof(c_0_5849,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    c_0_2912 ).

fof(c_0_5850,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    c_0_2913 ).

fof(c_0_5851,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    c_0_2914 ).

fof(c_0_5852,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    c_0_2915 ).

fof(c_0_5853,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    c_0_2916 ).

fof(c_0_5854,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    c_0_2917 ).

fof(c_0_5855,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2918 ).

fof(c_0_5856,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    c_0_2919 ).

fof(c_0_5857,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    c_0_2920 ).

fof(c_0_5858,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    c_0_2921 ).

fof(c_0_5859,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    c_0_2922 ).

fof(c_0_5860,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    c_0_2923 ).

fof(c_0_5861,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    c_0_2924 ).

fof(c_0_5862,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    c_0_2925 ).

fof(c_0_5863,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    c_0_2926 ).

fof(c_0_5864,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    c_0_2927 ).

fof(c_0_5865,axiom,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    c_0_2928 ).

fof(c_0_5866,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    c_0_2929 ).

fof(c_0_5867,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    c_0_2930 ).

fof(c_0_5868,axiom,
    c_UNIV != c_emptyset,
    c_0_2931 ).

fof(c_0_5869,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    c_0_2932 ).

fof(c_0_5870,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    c_0_2933 ).

fof(c_0_5871,axiom,
    c_0 != c_1,
    c_0_2934 ).

fof(c_0_5872,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_2935 ).

fof(c_0_5873,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    c_0_2936 ).

fof(c_0_5874,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X88,X87,X86,X85,X84,X83,X82,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble8,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2937]) ).

fof(c_0_5875,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X88,X87,X86,X85,X84,X82,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble7,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2938]) ).

fof(c_0_5876,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X88,X87,X86,X85,X82,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble6,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2939]) ).

fof(c_0_5877,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X88,X87,X86,X82,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble5,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2940]) ).

fof(c_0_5878,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X88,X87,X82,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble4,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2941]) ).

fof(c_0_5879,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X88,X82,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble3,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2942]) ).

fof(c_0_5880,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X89,X82,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble2,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2943]) ).

fof(c_0_5881,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X82,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble1,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2944]) ).

fof(c_0_5882,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X82,X90,X89,X88,X87,X86,X85,X84,X83,X97,X96,X95,X94,X93,X92,X91,c_List_Onibble_ONibble0,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2945]) ).

fof(c_0_5883,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X82,c_List_Onibble_ONibbleF,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2946]) ).

fof(c_0_5884,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X82,X91,c_List_Onibble_ONibbleE,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2947]) ).

fof(c_0_5885,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X82,X92,X91,c_List_Onibble_ONibbleD,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2948]) ).

fof(c_0_5886,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X82,X93,X92,X91,c_List_Onibble_ONibbleC,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2949]) ).

fof(c_0_5887,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X82,X94,X93,X92,X91,c_List_Onibble_ONibbleB,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2950]) ).

fof(c_0_5888,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__rec(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X82,X95,X94,X93,X92,X91,c_List_Onibble_ONibbleA,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2951]) ).

fof(c_0_5889,plain,
    ! [X81,X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97] : c_List_Onibble_Onibble__rec(X96,X89,X88,X87,X86,X85,X84,X83,X82,X81,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble9,X97) = X81,
    inference(variable_rename,[status(thm)],[c_0_2952]) ).

fof(c_0_5890,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X88,X87,X86,X85,X84,X83,X82,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble8,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2953]) ).

fof(c_0_5891,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X88,X87,X86,X85,X84,X82,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble7,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2954]) ).

fof(c_0_5892,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X88,X87,X86,X85,X82,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble6,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2955]) ).

fof(c_0_5893,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X88,X87,X86,X82,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble5,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2956]) ).

fof(c_0_5894,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X88,X87,X82,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble4,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2957]) ).

fof(c_0_5895,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X88,X82,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble3,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2958]) ).

fof(c_0_5896,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X89,X82,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble2,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2959]) ).

fof(c_0_5897,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X82,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble1,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2960]) ).

fof(c_0_5898,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X82,X90,X89,X88,X87,X86,X85,X84,X83,X97,X96,X95,X94,X93,X92,X91,c_List_Onibble_ONibble0,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2961]) ).

fof(c_0_5899,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X91,X82,c_List_Onibble_ONibbleF,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2962]) ).

fof(c_0_5900,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X92,X82,X91,c_List_Onibble_ONibbleE,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2963]) ).

fof(c_0_5901,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X93,X82,X92,X91,c_List_Onibble_ONibbleD,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2964]) ).

fof(c_0_5902,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X94,X82,X93,X92,X91,c_List_Onibble_ONibbleC,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2965]) ).

fof(c_0_5903,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X95,X82,X94,X93,X92,X91,c_List_Onibble_ONibbleB,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2966]) ).

fof(c_0_5904,plain,
    ! [X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98] : c_List_Onibble_Onibble__case(X97,X90,X89,X88,X87,X86,X85,X84,X83,X96,X82,X95,X94,X93,X92,X91,c_List_Onibble_ONibbleA,X98) = X82,
    inference(variable_rename,[status(thm)],[c_0_2967]) ).

fof(c_0_5905,plain,
    ! [X81,X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97] : c_List_Onibble_Onibble__case(X96,X89,X88,X87,X86,X85,X84,X83,X82,X81,X95,X94,X93,X92,X91,X90,c_List_Onibble_ONibble9,X97) = X81,
    inference(variable_rename,[status(thm)],[c_0_2968]) ).

fof(c_0_5906,plain,
    ! [X33,X34,X35,X36,X37,X38] :
      ( ~ c_in(X33,c_Relation_Orel__comp(X35,X34,X36,X37,X38),tc_prod(X38,X37))
      | c_in(c_Pair(c_Main_Orel__compE__1(X35,X34,X33,X36,X37,X38),c_Main_Orel__compE__2(X35,X34,X33,X36,X37,X38),X38,X36),X34,tc_prod(X38,X36)) ),
    inference(variable_rename,[status(thm)],[c_0_2969]) ).

fof(c_0_5907,plain,
    ! [X33,X34,X35,X36,X37,X38] :
      ( ~ c_in(X33,c_Relation_Orel__comp(X35,X34,X36,X37,X38),tc_prod(X38,X37))
      | c_in(c_Pair(c_Main_Orel__compE__2(X35,X34,X33,X36,X37,X38),c_Main_Orel__compE__3(X35,X34,X33,X36,X37,X38),X36,X37),X35,tc_prod(X36,X37)) ),
    inference(variable_rename,[status(thm)],[c_0_2970]) ).

fof(c_0_5908,plain,
    ! [X33,X34,X35,X36,X37,X38] :
      ( ~ c_in(X33,c_Relation_Orel__comp(X35,X34,X36,X37,X38),tc_prod(X38,X37))
      | X33 = c_Pair(c_Main_Orel__compE__1(X35,X34,X33,X36,X37,X38),c_Main_Orel__compE__3(X35,X34,X33,X36,X37,X38),X38,X37) ),
    inference(variable_rename,[status(thm)],[c_0_2971]) ).

fof(c_0_5909,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ~ c_in(X10,c_Datatype__Universe_Odprod(X9,X8,X12,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11))))
      | X10 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X10,X9,X8,X12,X11),c_Main_OdprodE__2(X10,X9,X8,X12,X11),X12,X11),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X10,X9,X8,X12,X11),c_Main_OdprodE__4(X10,X9,X8,X12,X11),X12,X11),tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11))) ),
    inference(variable_rename,[status(thm)],[c_0_2972]) ).

fof(c_0_5910,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ~ c_in(X10,c_Datatype__Universe_Odprod(X9,X8,X12,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11))))
      | c_in(c_Pair(c_Main_OdprodE__1(X10,X9,X8,X12,X11),c_Main_OdprodE__3(X10,X9,X8,X12,X11),tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11))),X9,tc_prod(tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11)))) ),
    inference(variable_rename,[status(thm)],[c_0_2973]) ).

fof(c_0_5911,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ~ c_in(X10,c_Datatype__Universe_Odprod(X9,X8,X12,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11))))
      | c_in(c_Pair(c_Main_OdprodE__2(X10,X9,X8,X12,X11),c_Main_OdprodE__4(X10,X9,X8,X12,X11),tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X12,X11)),tc_set(tc_Datatype__Universe_Onode(X12,X11)))) ),
    inference(variable_rename,[status(thm)],[c_0_2974]) ).

fof(c_0_5912,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ~ c_in(X13,c_Datatype__Universe_Odsum(X15,X14,X17,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | c_in(c_Pair(c_Main_OdsumE__1(X15,X13,X17,X16),c_Main_OdsumE__2(X15,X13,X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))),X15,tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | c_in(c_Pair(c_Main_OdsumE__3(X14,X13,X17,X16),c_Main_OdsumE__4(X14,X13,X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16)))) ),
    inference(variable_rename,[status(thm)],[c_0_2975]) ).

fof(c_0_5913,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ~ c_in(X13,c_Datatype__Universe_Odsum(X15,X14,X17,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | c_in(c_Pair(c_Main_OdsumE__1(X15,X13,X17,X16),c_Main_OdsumE__2(X15,X13,X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))),X15,tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | X13 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X14,X13,X17,X16),X17,X16),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X14,X13,X17,X16),X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))) ),
    inference(variable_rename,[status(thm)],[c_0_2976]) ).

fof(c_0_5914,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ~ c_in(X13,c_Datatype__Universe_Odsum(X15,X14,X17,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | c_in(c_Pair(c_Main_OdsumE__3(X14,X13,X17,X16),c_Main_OdsumE__4(X14,X13,X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | X13 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X15,X13,X17,X16),X17,X16),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X15,X13,X17,X16),X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))) ),
    inference(variable_rename,[status(thm)],[c_0_2977]) ).

fof(c_0_5915,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(X29,c_List_Olist_OCons(X28,X27,X31),tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X30,X29,X28,X27,X31),X27,tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31))) ),
    inference(variable_rename,[status(thm)],[c_0_2978]) ).

fof(c_0_5916,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X28,X27,X31),X29,tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | c_in(c_Pair(X27,c_Main_Olistrel__Cons1__2(X30,X29,X28,X27,X31),tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31))) ),
    inference(variable_rename,[status(thm)],[c_0_2979]) ).

fof(c_0_5917,plain,
    ! [X12,X13,X14,X15,X16,X17,X18,X19] :
      ( ~ c_in(c_Pair(X15,X14,tc_set(tc_Datatype__Universe_Onode(X19,X18)),tc_set(tc_Datatype__Universe_Onode(X19,X18))),X12,tc_prod(tc_set(tc_Datatype__Universe_Onode(X19,X18)),tc_set(tc_Datatype__Universe_Onode(X19,X18))))
      | ~ c_in(c_Pair(X17,X16,tc_set(tc_Datatype__Universe_Onode(X19,X18)),tc_set(tc_Datatype__Universe_Onode(X19,X18))),X13,tc_prod(tc_set(tc_Datatype__Universe_Onode(X19,X18)),tc_set(tc_Datatype__Universe_Onode(X19,X18))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X17,X15,X19,X18),c_Datatype__Universe_OScons(X16,X14,X19,X18),tc_set(tc_Datatype__Universe_Onode(X19,X18)),tc_set(tc_Datatype__Universe_Onode(X19,X18))),c_Datatype__Universe_Odprod(X13,X12,X19,X18),tc_prod(tc_set(tc_Datatype__Universe_Onode(X19,X18)),tc_set(tc_Datatype__Universe_Onode(X19,X18)))) ),
    inference(variable_rename,[status(thm)],[c_0_2980]) ).

fof(c_0_5918,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(X29,c_List_Olist_OCons(X28,X27,X31),tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X30,X29,X28,X27,X31),X28,X31,X31),X30,tc_prod(X31,X31)) ),
    inference(variable_rename,[status(thm)],[c_0_2981]) ).

fof(c_0_5919,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X28,X27,X31),X29,tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | c_in(c_Pair(X28,c_Main_Olistrel__Cons1__1(X30,X29,X28,X27,X31),X31,X31),X30,tc_prod(X31,X31)) ),
    inference(variable_rename,[status(thm)],[c_0_2982]) ).

fof(c_0_5920,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ~ c_in(X13,c_Datatype__Universe_Odsum(X15,X14,X17,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | X13 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X15,X13,X17,X16),X17,X16),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X15,X13,X17,X16),X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16)))
      | X13 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X14,X13,X17,X16),X17,X16),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X14,X13,X17,X16),X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))) ),
    inference(variable_rename,[status(thm)],[c_0_2983]) ).

fof(c_0_5921,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(X30,c_Relation_OImage(X29,X31,X32,X33),X33)
      | c_in(c_Pair(c_Main_OImageE__1(X31,X30,X29,X32,X33),X30,X32,X33),X29,tc_prod(X32,X33)) ),
    inference(variable_rename,[status(thm)],[c_0_2984]) ).

fof(c_0_5922,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(X29,c_List_Olist_OCons(X28,X27,X31),tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | X29 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X30,X29,X28,X27,X31),c_Main_Olistrel__Cons2__2(X30,X29,X28,X27,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_2985]) ).

fof(c_0_5923,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X28,X27,X31),X29,tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olistrel(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | X29 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X30,X29,X28,X27,X31),c_Main_Olistrel__Cons1__2(X30,X29,X28,X27,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_2986]) ).

fof(c_0_5924,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(X15,c_Datatype__Universe_Ouprod(X17,X16,X19,X18),tc_set(tc_Datatype__Universe_Onode(X19,X18)))
      | X15 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X17,X16,X15,X19,X18),c_Main_OuprodE__2(X17,X16,X15,X19,X18),X19,X18) ),
    inference(variable_rename,[status(thm)],[c_0_2987]) ).

fof(c_0_5925,plain,
    ! [X33,X34,X35,X36,X37,X38,X39,X40] :
      ( ~ c_in(c_Pair(X36,X35,X39,X38),X34,tc_prod(X39,X38))
      | ~ c_in(c_Pair(X37,X36,X40,X39),X33,tc_prod(X40,X39))
      | c_in(c_Pair(X37,X35,X40,X38),c_Relation_Orel__comp(X34,X33,X39,X38,X40),tc_prod(X40,X38)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2988])])]) ).

fof(c_0_5926,plain,
    ! [X49,X50,X51,X52] :
      ( ~ c_in(c_Pair(c_Pair(X50,X49,tc_nat,tc_nat),c_Pair(X52,X51,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_plus(X50,X51,tc_nat) = c_plus(X52,X49,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_2989]) ).

fof(c_0_5927,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(variable_rename,[status(thm)],[c_0_2990]) ).

fof(c_0_5928,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(variable_rename,[status(thm)],[c_0_2991]) ).

fof(c_0_5929,plain,
    ! [X13] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X13,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(variable_rename,[status(thm)],[c_0_2992]) ).

fof(c_0_5930,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ~ c_in(c_Pair(X13,X12,tc_set(tc_Datatype__Universe_Onode(X15,X14)),tc_set(tc_Datatype__Universe_Onode(X15,X14))),X10,tc_prod(tc_set(tc_Datatype__Universe_Onode(X15,X14)),tc_set(tc_Datatype__Universe_Onode(X15,X14))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X13,X15,X14),c_Datatype__Universe_OIn1(X12,X15,X14),tc_set(tc_Datatype__Universe_Onode(X15,X14)),tc_set(tc_Datatype__Universe_Onode(X15,X14))),c_Datatype__Universe_Odsum(X11,X10,X15,X14),tc_prod(tc_set(tc_Datatype__Universe_Onode(X15,X14)),tc_set(tc_Datatype__Universe_Onode(X15,X14)))) ),
    inference(variable_rename,[status(thm)],[c_0_2993]) ).

fof(c_0_5931,plain,
    ! [X12,X13,X14,X15,X16,X17] :
      ( ~ c_in(c_Pair(X15,X14,tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))),X13,tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X15,X17,X16),c_Datatype__Universe_OIn0(X14,X17,X16),tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16))),c_Datatype__Universe_Odsum(X13,X12,X17,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X17,X16)),tc_set(tc_Datatype__Universe_Onode(X17,X16)))) ),
    inference(variable_rename,[status(thm)],[c_0_2994]) ).

fof(c_0_5932,plain,
    ! [X13] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X13,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    inference(variable_rename,[status(thm)],[c_0_2995]) ).

fof(c_0_5933,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(X15,c_Datatype__Universe_Ouprod(X17,X16,X19,X18),tc_set(tc_Datatype__Universe_Onode(X19,X18)))
      | c_in(c_Main_OuprodE__1(X17,X16,X15,X19,X18),X17,tc_set(tc_Datatype__Universe_Onode(X19,X18))) ),
    inference(variable_rename,[status(thm)],[c_0_2996]) ).

fof(c_0_5934,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(X15,c_Datatype__Universe_Ouprod(X17,X16,X19,X18),tc_set(tc_Datatype__Universe_Onode(X19,X18)))
      | c_in(c_Main_OuprodE__2(X17,X16,X15,X19,X18),X16,tc_set(tc_Datatype__Universe_Onode(X19,X18))) ),
    inference(variable_rename,[status(thm)],[c_0_2997]) ).

fof(c_0_5935,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_2998]) ).

fof(c_0_5936,plain,
    ! [X49,X50] :
      ( ~ c_less(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_2999]) ).

fof(c_0_5937,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3000]) ).

fof(c_0_5938,plain,
    ! [X49,X50] :
      ( ~ c_less(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3001]) ).

fof(c_0_5939,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(X30,c_Relation_OImage(X29,X31,X32,X33),X33)
      | c_in(c_Main_OImageE__1(X31,X30,X29,X32,X33),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3002]) ).

fof(c_0_5940,plain,
    ! [X13] :
      ( ~ c_less(c_Numeral_Onumber__of(X13,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3003]) ).

fof(c_0_5941,plain,
    ! [X13] :
      ( ~ c_less(c_Numeral_Onumber__of(X13,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3004]) ).

fof(c_0_5942,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X33,X30,X34),c_List_Olist_OCons(X32,X29,X34),tc_List_Olist(X34),tc_List_Olist(X34)),c_List_Olexord(X31,X34),tc_prod(tc_List_Olist(X34),tc_List_Olist(X34)))
      | c_in(c_Pair(X33,X32,X34,X34),X31,tc_prod(X34,X34))
      | c_in(c_Pair(X30,X29,tc_List_Olist(X34),tc_List_Olist(X34)),c_List_Olexord(X31,X34),tc_prod(tc_List_Olist(X34),tc_List_Olist(X34))) ),
    inference(variable_rename,[status(thm)],[c_0_3005]) ).

fof(c_0_5943,plain,
    ! [X27,X28,X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X30,X29,X32),c_List_Olist_OCons(X28,X27,X32),tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32)))
      | c_in(c_Pair(X30,X28,X32,X32),X31,tc_prod(X32,X32))
      | c_in(c_Pair(X29,X27,tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32))) ),
    inference(variable_rename,[status(thm)],[c_0_3006]) ).

fof(c_0_5944,plain,
    ! [X3,X4] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X4,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(variable_rename,[status(thm)],[c_0_3007]) ).

fof(c_0_5945,plain,
    ! [X49,X50,X51,X52] :
      ( c_plus(X50,X51,tc_nat) != c_plus(X52,X49,tc_nat)
      | c_in(c_Pair(c_Pair(X50,X49,tc_nat,tc_nat),c_Pair(X52,X51,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_3008]) ).

fof(c_0_5946,plain,
    ! [X31,X32,X33,X34] :
      ( ~ c_in(X31,c_Relation_Oconverse(X32,X33,X34),tc_prod(X34,X33))
      | c_in(c_Pair(c_Main_OconverseE__1(X32,X31,X33,X34),c_Main_OconverseE__2(X32,X31,X33,X34),X33,X34),X32,tc_prod(X33,X34)) ),
    inference(variable_rename,[status(thm)],[c_0_3009]) ).

fof(c_0_5947,plain,
    ! [X7,X8,X9,X10] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X7,X8,X10,X10),X9,tc_prod(X10,X10)),X10)
      | ~ c_in(c_Pair(X8,X7,X10,X10),c_Transitive__Closure_Ortrancl(X9,X10),tc_prod(X10,X10)) ),
    inference(variable_rename,[status(thm)],[c_0_3010]) ).

fof(c_0_5948,plain,
    ! [X7,X8,X9,X10] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X7,X8,X10,X10),X9,tc_prod(X10,X10)),X10)
      | ~ c_in(c_Pair(X8,X7,X10,X10),c_Transitive__Closure_Ortrancl(X9,X10),tc_prod(X10,X10)) ),
    inference(variable_rename,[status(thm)],[c_0_3011]) ).

fof(c_0_5949,plain,
    ! [X27,X28,X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X30,X29,X32),c_List_Olist_OCons(X28,X27,X32),tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32)))
      | c_in(c_Pair(X29,X27,tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32)))
      | c_Nat_Osize(X29,tc_List_Olist(X32)) = c_Nat_Osize(X27,tc_List_Olist(X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3012]) ).

fof(c_0_5950,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X33,X30,X34),c_List_Olist_OCons(X32,X29,X34),tc_List_Olist(X34),tc_List_Olist(X34)),c_List_Olexord(X31,X34),tc_prod(tc_List_Olist(X34),tc_List_Olist(X34)))
      | c_in(c_Pair(X33,X32,X34,X34),X31,tc_prod(X34,X34))
      | X33 = X32 ),
    inference(variable_rename,[status(thm)],[c_0_3013]) ).

fof(c_0_5951,plain,
    ! [X27,X28,X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X30,X29,X32),c_List_Olist_OCons(X28,X27,X32),tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32)))
      | c_in(c_Pair(X30,X28,X32,X32),X31,tc_prod(X32,X32))
      | X30 = X28 ),
    inference(variable_rename,[status(thm)],[c_0_3014]) ).

fof(c_0_5952,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Datatype__Universe_Ousum(X18,X17,X20,X19),tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | c_in(c_Main_OusumE__1(X18,X16,X20,X19),X18,tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | c_in(c_Main_OusumE__2(X17,X16,X20,X19),X17,tc_set(tc_Datatype__Universe_Onode(X20,X19))) ),
    inference(variable_rename,[status(thm)],[c_0_3015]) ).

fof(c_0_5953,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Datatype__Universe_Ousum(X18,X17,X20,X19),tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | c_in(c_Main_OusumE__1(X18,X16,X20,X19),X18,tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | X16 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X17,X16,X20,X19),X20,X19) ),
    inference(variable_rename,[status(thm)],[c_0_3016]) ).

fof(c_0_5954,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Datatype__Universe_Ousum(X18,X17,X20,X19),tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | c_in(c_Main_OusumE__2(X17,X16,X20,X19),X17,tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | X16 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X18,X16,X20,X19),X20,X19) ),
    inference(variable_rename,[status(thm)],[c_0_3017]) ).

fof(c_0_5955,plain,
    ! [X64,X65,X66,X67,X68] :
      ( ~ c_in(c_Pair(X65,X64,tc_List_Olist(X68),tc_List_Olist(X68)),c_List_Olexord(X67,X68),tc_prod(tc_List_Olist(X68),tc_List_Olist(X68)))
      | c_in(c_Pair(c_List_Olist_OCons(X66,X65,X68),c_List_Olist_OCons(X66,X64,X68),tc_List_Olist(X68),tc_List_Olist(X68)),c_List_Olexord(X67,X68),tc_prod(tc_List_Olist(X68),tc_List_Olist(X68))) ),
    inference(variable_rename,[status(thm)],[c_0_3018]) ).

fof(c_0_5956,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(c_Pair(X28,X27,tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olex(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31)))
      | c_in(c_Pair(c_List_Olist_OCons(X29,X28,X31),c_List_Olist_OCons(X29,X27,X31),tc_List_Olist(X31),tc_List_Olist(X31)),c_List_Olex(X30,X31),tc_prod(tc_List_Olist(X31),tc_List_Olist(X31))) ),
    inference(variable_rename,[status(thm)],[c_0_3019]) ).

fof(c_0_5957,plain,
    ! [X3,X4] :
      ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X4,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(X4,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_3020]) ).

fof(c_0_5958,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Datatype__Universe_Ousum(X18,X17,X20,X19),tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | X16 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X18,X16,X20,X19),X20,X19)
      | X16 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X17,X16,X20,X19),X20,X19) ),
    inference(variable_rename,[status(thm)],[c_0_3021]) ).

fof(c_0_5959,plain,
    ! [X27,X28,X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(X30,X28,X32,X32),X31,tc_prod(X32,X32))
      | c_Nat_Osize(X29,tc_List_Olist(X32)) != c_Nat_Osize(X27,tc_List_Olist(X32))
      | c_in(c_Pair(c_List_Olist_OCons(X30,X29,X32),c_List_Olist_OCons(X28,X27,X32),tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32))) ),
    inference(variable_rename,[status(thm)],[c_0_3022]) ).

fof(c_0_5960,plain,
    ! [X3,X4] :
      ( ~ c_in(c_Pair(X4,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X4,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_3023]) ).

fof(c_0_5961,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Sum__Type_OPlus(X18,X17,X20,X19),tc_sum(X20,X19))
      | X16 = c_Sum__Type_OInl(c_Main_OPlusE__1(X18,X16,X20,X19),X20,X19)
      | X16 = c_Sum__Type_OInr(c_Main_OPlusE__2(X17,X16,X19,X20),X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_3024]) ).

fof(c_0_5962,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Sum__Type_OPlus(X18,X17,X20,X19),tc_sum(X20,X19))
      | c_in(c_Main_OPlusE__1(X18,X16,X20,X19),X18,X20)
      | X16 = c_Sum__Type_OInr(c_Main_OPlusE__2(X17,X16,X19,X20),X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_3025]) ).

fof(c_0_5963,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Sum__Type_OPlus(X18,X17,X20,X19),tc_sum(X20,X19))
      | c_in(c_Main_OPlusE__2(X17,X16,X19,X20),X17,X19)
      | X16 = c_Sum__Type_OInl(c_Main_OPlusE__1(X18,X16,X20,X19),X20,X19) ),
    inference(variable_rename,[status(thm)],[c_0_3026]) ).

fof(c_0_5964,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X16,c_Sum__Type_OPlus(X18,X17,X20,X19),tc_sum(X20,X19))
      | c_in(c_Main_OPlusE__1(X18,X16,X20,X19),X18,X20)
      | c_in(c_Main_OPlusE__2(X17,X16,X19,X20),X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_3027]) ).

fof(c_0_5965,plain,
    ! [X18,X19,X20,X21,X22] : c_Datatype__Universe_Ontrunc(c_Suc(X18),c_Datatype__Universe_OScons(X20,X19,X22,X21),X22,X21) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X20,X22,X21),c_Datatype__Universe_Ontrunc(X18,X19,X22,X21),X22,X21),
    inference(variable_rename,[status(thm)],[c_0_3028]) ).

fof(c_0_5966,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ c_in(c_Pair(X33,X32,X34,X34),X31,tc_prod(X34,X34))
      | c_in(c_Pair(c_List_Olist_OCons(X33,X30,X34),c_List_Olist_OCons(X32,X29,X34),tc_List_Olist(X34),tc_List_Olist(X34)),c_List_Olexord(X31,X34),tc_prod(tc_List_Olist(X34),tc_List_Olist(X34))) ),
    inference(variable_rename,[status(thm)],[c_0_3029]) ).

fof(c_0_5967,plain,
    ! [X7,X8,X9,X10] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X7,X8,X10,X10),X9,tc_prod(X10,X10)),X10)
      | c_Wellfounded__Recursion_Owf(X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_3030]) ).

fof(c_0_5968,plain,
    ! [X7,X8,X9,X10] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X7,X8,X10,X10),X9,tc_prod(X10,X10)),X10)
      | c_Wellfounded__Recursion_Oacyclic(X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_3031]) ).

fof(c_0_5969,plain,
    ! [X29,X30,X31,X32] :
      ( ~ c_in(X30,c_Relation_ORange(X29,X31,X32),X32)
      | c_in(c_Pair(c_Main_ORangeE__1(X30,X29,X32,X31),X30,X31,X32),X29,tc_prod(X31,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3032]) ).

fof(c_0_5970,plain,
    ! [X20,X21,X22,X23] :
      ( ~ c_in(X21,c_Relation_ODomain(X20,X23,X22),X23)
      | c_in(c_Pair(X21,c_Main_ODomainE__1(X21,X20,X23,X22),X23,X22),X20,tc_prod(X23,X22)) ),
    inference(variable_rename,[status(thm)],[c_0_3033]) ).

fof(c_0_5971,plain,
    ! [X7,X8,X9,X10] :
      ( ~ c_Wellfounded__Recursion_Owf(X9,X10)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X7,X8,X10,X10),X9,tc_prod(X10,X10)),X10)
      | c_in(c_Pair(X8,X7,X10,X10),c_Transitive__Closure_Ortrancl(X9,X10),tc_prod(X10,X10)) ),
    inference(variable_rename,[status(thm)],[c_0_3034]) ).

fof(c_0_5972,plain,
    ! [X7,X8,X9,X10] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X9,X10)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X7,X8,X10,X10),X9,tc_prod(X10,X10)),X10)
      | c_in(c_Pair(X8,X7,X10,X10),c_Transitive__Closure_Ortrancl(X9,X10),tc_prod(X10,X10)) ),
    inference(variable_rename,[status(thm)],[c_0_3035]) ).

fof(c_0_5973,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(X30,c_Relation_OImage(X29,c_insert(X31,c_emptyset,X32),X32,X33),X33)
      | c_in(c_Pair(X31,X30,X32,X33),X29,tc_prod(X32,X33)) ),
    inference(variable_rename,[status(thm)],[c_0_3036]) ).

fof(c_0_5974,plain,
    ! [X27,X28,X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X30,X29,X32),c_List_Olist_OCons(X28,X27,X32),tc_List_Olist(X32),tc_List_Olist(X32)),c_List_Olex(X31,X32),tc_prod(tc_List_Olist(X32),tc_List_Olist(X32)))
      | X30 = X28
      | c_Nat_Osize(X29,tc_List_Olist(X32)) = c_Nat_Osize(X27,tc_List_Olist(X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3037]) ).

fof(c_0_5975,plain,
    ! [X23,X24,X25] :
      ( ~ c_Divides_Oop_Advd(X25,c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X25,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3038]) ).

fof(c_0_5976,plain,
    ! [X23,X24,X25] :
      ( ~ c_Divides_Oop_Advd(X25,c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X25,X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3039]) ).

fof(c_0_5977,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(c_Pair(X31,X30,X32,X33),X29,tc_prod(X32,X33))
      | c_in(X30,c_Relation_OImage(X29,c_insert(X31,c_emptyset,X32),X32,X33),X33) ),
    inference(variable_rename,[status(thm)],[c_0_3040]) ).

fof(c_0_5978,plain,
    ! [X55,X56,X57,X58,X59,X60] :
      ( c_Nat_Osize(X55,tc_List_Olist(X60)) != c_Nat_Osize(X57,tc_List_Olist(X59))
      | c_Nat_Osize(X56,tc_List_Olist(X60)) != c_Nat_Osize(X58,tc_List_Olist(X59))
      | c_List_Ozip(c_append(X56,X55,X60),c_append(X58,X57,X59),X60,X59) = c_append(c_List_Ozip(X56,X58,X60,X59),c_List_Ozip(X55,X57,X60,X59),tc_prod(X60,X59)) ),
    inference(variable_rename,[status(thm)],[c_0_3041]) ).

fof(c_0_5979,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(c_Pair(X31,X30,X33,X32),c_Relation_Oconverse(X29,X32,X33),tc_prod(X33,X32))
      | c_in(c_Pair(X30,X31,X32,X33),X29,tc_prod(X32,X33)) ),
    inference(variable_rename,[status(thm)],[c_0_3042]) ).

fof(c_0_5980,plain,
    ! [X7,X8,X9,X10] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X8,X7,X10,X9),tc_set(tc_Datatype__Universe_Onode(X10,X9)),tc_set(tc_Datatype__Universe_Onode(X10,X9))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X8,tc_set(tc_Datatype__Universe_Onode(X10,X9)),tc_set(tc_Datatype__Universe_Onode(X10,X9))),c_Relation_ODomain(X7,tc_set(tc_Datatype__Universe_Onode(X10,X9)),tc_set(tc_Datatype__Universe_Onode(X10,X9))),X10,X9),
    inference(variable_rename,[status(thm)],[c_0_3043]) ).

fof(c_0_5981,plain,
    ! [X7,X8,X9,X10] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X8,X7,X10,X9),tc_set(tc_Datatype__Universe_Onode(X10,X9)),tc_set(tc_Datatype__Universe_Onode(X10,X9))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X8,tc_set(tc_Datatype__Universe_Onode(X10,X9)),tc_set(tc_Datatype__Universe_Onode(X10,X9))),c_Relation_ODomain(X7,tc_set(tc_Datatype__Universe_Onode(X10,X9)),tc_set(tc_Datatype__Universe_Onode(X10,X9))),X10,X9),
    inference(variable_rename,[status(thm)],[c_0_3044]) ).

fof(c_0_5982,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(c_Pair(X30,X31,X32,X33),X29,tc_prod(X32,X33))
      | c_in(c_Pair(X31,X30,X33,X32),c_Relation_Oconverse(X29,X32,X33),tc_prod(X33,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3045]) ).

fof(c_0_5983,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3046]) ).

fof(c_0_5984,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3047]) ).

fof(c_0_5985,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3048])])]) ).

fof(c_0_5986,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3049]) ).

fof(c_0_5987,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3050])])]) ).

fof(c_0_5988,plain,
    ! [X87,X88,X89] : c_Nat_Opower(X88,c_Suc(X87),tc_set(tc_prod(X89,X89))) = c_Relation_Orel__comp(X88,c_Nat_Opower(X88,X87,tc_set(tc_prod(X89,X89))),X89,X89,X89),
    inference(variable_rename,[status(thm)],[c_0_3051]) ).

fof(c_0_5989,plain,
    ! [X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(X31,X30,X32,X32),c_Transitive__Closure_Otrancl(X29,X32),tc_prod(X32,X32))
      | c_in(c_Pair(X31,X30,X32,X32),c_Transitive__Closure_Ortrancl(X29,X32),tc_prod(X32,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3052]) ).

fof(c_0_5990,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ c_in(X31,X32,X34)
      | ~ c_in(c_Pair(X31,X30,X34,X33),X29,tc_prod(X34,X33))
      | c_in(X30,c_Relation_OImage(X29,X32,X34,X33),X33) ),
    inference(variable_rename,[status(thm)],[c_0_3053]) ).

fof(c_0_5991,plain,
    ! [X31,X32,X33,X34] :
      ( ~ c_in(X31,c_Relation_Oconverse(X32,X33,X34),tc_prod(X34,X33))
      | X31 = c_Pair(c_Main_OconverseE__2(X32,X31,X33,X34),c_Main_OconverseE__1(X32,X31,X33,X34),X34,X33) ),
    inference(variable_rename,[status(thm)],[c_0_3054]) ).

fof(c_0_5992,plain,
    ! [X27,X28,X29,X30,X31,X32] : c_List_Ozip(c_List_Olist_OCons(X30,X29,X32),c_List_Olist_OCons(X28,X27,X31),X32,X31) = c_List_Olist_OCons(c_Pair(X30,X28,X32,X31),c_List_Ozip(X29,X27,X32,X31),tc_prod(X32,X31)),
    inference(variable_rename,[status(thm)],[c_0_3055]) ).

fof(c_0_5993,plain,
    ! [X29,X30,X31,X32] :
      ( ~ c_in(c_Pair(X31,X30,X32,X32),X29,tc_prod(X32,X32))
      | c_in(c_Pair(X31,X30,X32,X32),c_Transitive__Closure_Otrancl(X29,X32),tc_prod(X32,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3056]) ).

fof(c_0_5994,plain,
    ! [X15,X16,X17,X18,X19,X20] :
      ( ~ c_in(X15,X17,tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | ~ c_in(X16,X18,tc_set(tc_Datatype__Universe_Onode(X20,X19)))
      | c_in(c_Datatype__Universe_OScons(X16,X15,X20,X19),c_Datatype__Universe_Ouprod(X18,X17,X20,X19),tc_set(tc_Datatype__Universe_Onode(X20,X19))) ),
    inference(variable_rename,[status(thm)],[c_0_3057]) ).

fof(c_0_5995,plain,
    ! [X13] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3058]) ).

fof(c_0_5996,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ c_in(X29,c_List_Oset(X28,X31),X31)
      | c_Map_Omap__of(c_List_Ozip(X28,X27,X31,X30),X29,X31,X30) != c_Datatype_Ooption_ONone
      | c_Nat_Osize(X28,tc_List_Olist(X31)) != c_Nat_Osize(X27,tc_List_Olist(X30)) ),
    inference(variable_rename,[status(thm)],[c_0_3059]) ).

fof(c_0_5997,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ c_less(X47,c_Nat_Osize(X45,tc_List_Olist(X48)),tc_nat)
      | ~ c_less(X47,c_Nat_Osize(X46,tc_List_Olist(X49)),tc_nat)
      | c_List_Onth(c_List_Ozip(X46,X45,X49,X48),X47,tc_prod(X49,X48)) = c_Pair(c_List_Onth(X46,X47,X49),c_List_Onth(X45,X47,X48),X49,X48) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3060])])]) ).

fof(c_0_5998,plain,
    ! [X13] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3061]) ).

fof(c_0_5999,plain,
    ! [X13] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3062]) ).

fof(c_0_6000,plain,
    ! [X87,X88] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X87,X88),c_Transitive__Closure_Ortrancl(X87,X88),X88,X88,X88) = c_Transitive__Closure_Ortrancl(X87,X88),
    inference(variable_rename,[status(thm)],[c_0_3063]) ).

fof(c_0_6001,plain,
    ! [X5,X6,X7] : c_Relation_Orel__comp(X5,c_Relation_OId,X7,X6,X7) = X5,
    inference(variable_rename,[status(thm)],[c_0_3064]) ).

fof(c_0_6002,plain,
    ! [X5,X6,X7] : c_Relation_Orel__comp(c_Relation_OId,X5,X6,X6,X7) = X5,
    inference(variable_rename,[status(thm)],[c_0_3065]) ).

fof(c_0_6003,plain,
    ! [X23,X24,X25] :
      ( ~ c_Divides_Oop_Advd(X25,X23,tc_nat)
      | ~ c_Divides_Oop_Advd(X25,X24,tc_nat)
      | c_Divides_Oop_Advd(X25,c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3066]) ).

fof(c_0_6004,plain,
    ! [X23,X24] : c_GCD_Ogcd(c_Pair(X24,c_plus(X23,X24,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_3067]) ).

fof(c_0_6005,plain,
    ! [X23,X24] : c_GCD_Ogcd(c_Pair(X24,c_plus(X24,X23,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_3068]) ).

fof(c_0_6006,plain,
    ! [X23,X24] : c_GCD_Ogcd(c_Pair(c_plus(X24,X23,tc_nat),X23,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_3069]) ).

fof(c_0_6007,plain,
    ! [X61,X62,X63,X64,X65,X66] : c_List_Ozip(c_List_Oreplicate(X64,X62,X66),c_List_Oreplicate(X63,X61,X65),X66,X65) = c_List_Oreplicate(c_Orderings_Omin(X64,X63,tc_nat),c_Pair(X62,X61,X66,X65),tc_prod(X66,X65)),
    inference(variable_rename,[status(thm)],[c_0_3070]) ).

fof(c_0_6008,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ c_less(X48,c_Nat_Osize(X46,tc_List_Olist(X49)),tc_nat)
      | c_List_Olist__update(c_List_Olist__update(X46,X48,X47,X49),X48,X45,X49) = c_List_Olist__update(X46,X48,X45,X49) ),
    inference(variable_rename,[status(thm)],[c_0_3071]) ).

fof(c_0_6009,plain,
    ! [X7,X8,X9] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X7,tc_List_Olist(X9),tc_List_Olist(X9)),c_List_Olexord(X8,X9),tc_prod(tc_List_Olist(X9),tc_List_Olist(X9)))
      | X7 = c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X7,X9),c_Main_Olexord__Nil__left__2(X7,X9),X9) ),
    inference(variable_rename,[status(thm)],[c_0_3072]) ).

fof(c_0_6010,plain,
    ! [X49,X50] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3073]) ).

fof(c_0_6011,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(c_Pair(X31,X30,X33,X32),X29,tc_prod(X33,X32))
      | c_in(X30,c_Relation_ORange(X29,X33,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3074]) ).

fof(c_0_6012,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(c_Pair(X31,X30,X33,X32),X29,tc_prod(X33,X32))
      | c_in(X31,c_Relation_ODomain(X29,X33,X32),X33) ),
    inference(variable_rename,[status(thm)],[c_0_3075]) ).

fof(c_0_6013,plain,
    ! [X23,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3076]) ).

fof(c_0_6014,plain,
    ! [X23,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X23,tc_nat,tc_nat)),X24,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3077]) ).

fof(c_0_6015,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3078]) ).

fof(c_0_6016,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3079]) ).

fof(c_0_6017,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3080]) ).

fof(c_0_6018,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3081]) ).

fof(c_0_6019,plain,
    ! [X25,X26,X27] :
      ( ~ c_in(c_Pair(X25,c_List_Olist_ONil,tc_List_Olist(X27),tc_List_Olist(X27)),c_List_Olistrel(X26,X27),tc_prod(tc_List_Olist(X27),tc_List_Olist(X27)))
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3082])])]) ).

fof(c_0_6020,plain,
    ! [X25,X26,X27] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X27),tc_List_Olist(X27)),c_List_Olistrel(X26,X27),tc_prod(tc_List_Olist(X27),tc_List_Olist(X27)))
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3083])])]) ).

fof(c_0_6021,plain,
    ! [X7,X8,X9] : ~ c_in(c_Pair(X7,c_List_Olist_ONil,tc_List_Olist(X9),tc_List_Olist(X9)),c_List_Olexord(X8,X9),tc_prod(tc_List_Olist(X9),tc_List_Olist(X9))),
    inference(variable_rename,[status(thm)],[c_0_3084]) ).

fof(c_0_6022,plain,
    ! [X27,X28,X29] : ~ c_in(c_Pair(c_List_Olist_ONil,X27,tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olex(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29))),
    inference(variable_rename,[status(thm)],[c_0_3085]) ).

fof(c_0_6023,plain,
    ! [X25,X26,X27] : ~ c_in(c_Pair(X25,c_List_Olist_ONil,tc_List_Olist(X27),tc_List_Olist(X27)),c_List_Olex(X26,X27),tc_prod(tc_List_Olist(X27),tc_List_Olist(X27))),
    inference(variable_rename,[status(thm)],[c_0_3086]) ).

fof(c_0_6024,plain,
    ! [X13] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3087]) ).

fof(c_0_6025,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_0,X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3088]) ).

fof(c_0_6026,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X31,c_0,X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3089]) ).

fof(c_0_6027,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_0,X31,X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3090]) ).

fof(c_0_6028,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_lessequals(c_0,X31,X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3091]) ).

fof(c_0_6029,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X25)
      | c_Nat_Opower(c_uminus(X24,X25),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X23,tc_nat),X25) = c_Nat_Opower(X24,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X23,tc_nat),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3092]) ).

fof(c_0_6030,plain,
    ! [X3,X4] :
      ( ~ c_in(c_Pair(X4,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
      | c_less(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3093]) ).

fof(c_0_6031,plain,
    ! [X18,X19,X20,X21] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X18)),c_Datatype__Universe_OIn1(X19,X21,X20),X21,X20) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X18),X19,X21,X20),X21,X20),
    inference(variable_rename,[status(thm)],[c_0_3094]) ).

fof(c_0_6032,plain,
    ! [X18,X19,X20,X21] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X18)),c_Datatype__Universe_OIn0(X19,X21,X20),X21,X20) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X18),X19,X21,X20),X21,X20),
    inference(variable_rename,[status(thm)],[c_0_3095]) ).

fof(c_0_6033,plain,
    ! [X20,X21,X22] :
      ( ~ c_Wellfounded__Recursion_Owf(X20,X22)
      | ~ c_in(c_Pair(X21,X21,X22,X22),X20,tc_prod(X22,X22)) ),
    inference(variable_rename,[status(thm)],[c_0_3096]) ).

fof(c_0_6034,plain,
    ! [X17] :
      ( ~ c_less(c_0,c_Divides_Oop_Amod(X17,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
      | c_Divides_Oop_Amod(X17,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_3097]) ).

fof(c_0_6035,plain,
    ! [X29,X30,X31] :
      ( ~ c_in(c_Pair(X30,X29,X31,X31),c_Relation_OId,tc_prod(X31,X31))
      | X30 = X29 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3098])])]) ).

fof(c_0_6036,plain,
    ! [X29] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X29,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X29,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3099]) ).

fof(c_0_6037,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(X15,X16,tc_set(tc_Datatype__Universe_Onode(X19,X18)))
      | c_in(c_Datatype__Universe_OIn1(X15,X19,X18),c_Datatype__Universe_Ousum(X17,X16,X19,X18),tc_set(tc_Datatype__Universe_Onode(X19,X18))) ),
    inference(variable_rename,[status(thm)],[c_0_3100]) ).

fof(c_0_6038,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(X15,X17,tc_set(tc_Datatype__Universe_Onode(X19,X18)))
      | c_in(c_Datatype__Universe_OIn0(X15,X19,X18),c_Datatype__Universe_Ousum(X17,X16,X19,X18),tc_set(tc_Datatype__Universe_Onode(X19,X18))) ),
    inference(variable_rename,[status(thm)],[c_0_3101]) ).

fof(c_0_6039,plain,
    ! [X90,X91,X92] : c_Message_Oparts(c_insert(c_Message_OHPair(X91,X90),X92,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X91,X90),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Oparts(c_insert(X90,X92,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3102]) ).

fof(c_0_6040,plain,
    ! [X90,X91,X92] : c_Message_Oanalz(c_insert(c_Message_OHPair(X91,X90),X92,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X91,X90),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Oanalz(c_insert(X90,X92,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3103]) ).

fof(c_0_6041,plain,
    ! [X27,X28,X29,X30,X31] :
      ( c_Nat_Osize(X28,tc_List_Olist(X31)) != c_Nat_Osize(X27,tc_List_Olist(X30))
      | c_in(X29,c_List_Oset(X28,X31),X31)
      | c_Map_Omap__of(c_List_Ozip(X28,X27,X31,X30),X29,X31,X30) = c_Datatype_Ooption_ONone ),
    inference(variable_rename,[status(thm)],[c_0_3104]) ).

fof(c_0_6042,plain,
    ! [X90,X91,X92] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X91,X90),X92,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X91,X90),c_Message_Oparts(c_insert(X91,c_insert(X90,X92,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3105]) ).

fof(c_0_6043,plain,
    ! [X90,X91,X92] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X91,X90),X92,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X91,X90),c_Message_Oanalz(c_insert(X91,c_insert(X90,X92,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3106]) ).

fof(c_0_6044,plain,
    ! [X63,X64,X65,X66] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X65,X64,X66),tc_List_Olist(X66),tc_List_Olist(X66)),c_List_Olexord(X63,X66),tc_prod(tc_List_Olist(X66),tc_List_Olist(X66))),
    inference(variable_rename,[status(thm)],[c_0_3107]) ).

fof(c_0_6045,plain,
    ! [X20,X21,X22,X23] :
      ( ~ c_in(c_minus(X22,c_insert(X20,X21,X23),tc_set(X23)),c_Finite__Set_OFinites,tc_set(X23))
      | c_in(c_minus(X22,X21,tc_set(X23)),c_Finite__Set_OFinites,tc_set(X23)) ),
    inference(variable_rename,[status(thm)],[c_0_3108]) ).

fof(c_0_6046,plain,
    ! [X27,X28,X29,X30] : c_List_Otake(X29,c_append(X28,X27,X30),X30) = c_append(c_List_Otake(X29,X28,X30),c_List_Otake(c_minus(X29,c_Nat_Osize(X28,tc_List_Olist(X30)),tc_nat),X27,X30),X30),
    inference(variable_rename,[status(thm)],[c_0_3109]) ).

fof(c_0_6047,plain,
    ! [X27,X28,X29,X30] : c_List_Odrop(X29,c_append(X28,X27,X30),X30) = c_append(c_List_Odrop(X29,X28,X30),c_List_Odrop(c_minus(X29,c_Nat_Osize(X28,tc_List_Olist(X30)),tc_nat),X27,X30),X30),
    inference(variable_rename,[status(thm)],[c_0_3110]) ).

fof(c_0_6048,plain,
    ! [X86,X87,X88,X89,X90,X91] :
      ( c_Pair(X89,X87,X91,X90) != c_Pair(X88,X86,X91,X90)
      | X87 = X86 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3111])])]) ).

fof(c_0_6049,plain,
    ! [X86,X87,X88,X89,X90,X91] :
      ( c_Pair(X89,X87,X91,X90) != c_Pair(X88,X86,X91,X90)
      | X89 = X88 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3112])])]) ).

fof(c_0_6050,plain,
    ! [X12,X13,X14,X15,X16,X17] :
      ( c_Datatype__Universe_OScons(X15,X13,X17,X16) != c_Datatype__Universe_OScons(X14,X12,X17,X16)
      | X13 = X12 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3113])])]) ).

fof(c_0_6051,plain,
    ! [X12,X13,X14,X15,X16,X17] :
      ( c_Datatype__Universe_OScons(X15,X13,X17,X16) != c_Datatype__Universe_OScons(X14,X12,X17,X16)
      | X15 = X14 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3114])])]) ).

fof(c_0_6052,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | ~ c_lessequals(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | c_less(X50,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3115]) ).

fof(c_0_6053,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_less(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3116]) ).

fof(c_0_6054,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | ~ c_lessequals(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | c_less(X50,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3117]) ).

fof(c_0_6055,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_less(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3118]) ).

fof(c_0_6056,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | ~ c_lessequals(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | c_lessequals(X50,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3119]) ).

fof(c_0_6057,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | ~ c_lessequals(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | c_lessequals(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3120]) ).

fof(c_0_6058,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | c_lessequals(X50,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3121]) ).

fof(c_0_6059,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | c_lessequals(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3122]) ).

fof(c_0_6060,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3123]) ).

fof(c_0_6061,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3124]) ).

fof(c_0_6062,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3125]) ).

fof(c_0_6063,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3126]) ).

fof(c_0_6064,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3127]) ).

fof(c_0_6065,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3128]) ).

fof(c_0_6066,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3129]) ).

fof(c_0_6067,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | ~ c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3130]) ).

fof(c_0_6068,plain,
    ! [X17] :
      ( c_Divides_Oop_Amod(X17,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1
      | c_less(c_0,c_Divides_Oop_Amod(X17,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3131]) ).

fof(c_0_6069,plain,
    ! [X27,X28,X29,X30,X31] : c_List_Olist__update(c_append(X29,c_List_Olist_OCons(X30,X27,X31),X31),c_Nat_Osize(X29,tc_List_Olist(X31)),X28,X31) = c_append(X29,c_List_Olist_OCons(X28,X27,X31),X31),
    inference(variable_rename,[status(thm)],[c_0_3132]) ).

fof(c_0_6070,plain,
    ! [X29,X30,X31,X32,X33] :
      ( ~ c_in(X29,X30,X33)
      | c_in(c_Sum__Type_OInr(X29,X33,X32),c_Sum__Type_OPlus(X31,X30,X32,X33),tc_sum(X32,X33)) ),
    inference(variable_rename,[status(thm)],[c_0_3133]) ).

fof(c_0_6071,plain,
    ! [X20,X21,X22,X23,X24] :
      ( ~ c_in(X20,X22,X24)
      | c_in(c_Sum__Type_OInl(X20,X24,X23),c_Sum__Type_OPlus(X22,X21,X24,X23),tc_sum(X24,X23)) ),
    inference(variable_rename,[status(thm)],[c_0_3134]) ).

fof(c_0_6072,plain,
    ! [X51,X52] : c_IntDiv_OnegateSnd(c_Pair(X52,X51,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X52,c_uminus(X51,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3135]) ).

fof(c_0_6073,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_0,X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3136]) ).

fof(c_0_6074,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_0,X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3137]) ).

fof(c_0_6075,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X31,c_0,X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3138]) ).

fof(c_0_6076,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X31,c_0,X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3139]) ).

fof(c_0_6077,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_0,X31,X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3140]) ).

fof(c_0_6078,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,X31,X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3141]) ).

fof(c_0_6079,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_lessequals(c_0,X31,X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3142]) ).

fof(c_0_6080,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(c_0,X31,X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3143]) ).

fof(c_0_6081,plain,
    ! [X29] : c_IntDiv_OposDivAlg(c_Pair(c_0,X29,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3144]) ).

fof(c_0_6082,plain,
    ! [X23,X24] : c_GCD_Ogcd(c_Pair(X23,c_times(X23,X24,tc_nat),tc_nat,tc_nat)) = X23,
    inference(variable_rename,[status(thm)],[c_0_3145]) ).

fof(c_0_6083,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | ~ c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3146]) ).

fof(c_0_6084,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3147]) ).

fof(c_0_6085,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | ~ c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3148]) ).

fof(c_0_6086,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | ~ c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_lessequals(c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3149]) ).

fof(c_0_6087,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3150]) ).

fof(c_0_6088,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | ~ c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32)
      | c_less(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3151]) ).

fof(c_0_6089,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | ~ c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3152]) ).

fof(c_0_6090,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | ~ c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32)
      | c_lessequals(X30,c_times(X31,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3153]) ).

fof(c_0_6091,plain,
    ! [X27,X28,X29,X30] : c_Nat_Osize(c_List_Ozip(X28,X27,X30,X29),tc_List_Olist(tc_prod(X30,X29))) = c_Orderings_Omin(c_Nat_Osize(X28,tc_List_Olist(X30)),c_Nat_Osize(X27,tc_List_Olist(X29)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3154]) ).

fof(c_0_6092,plain,
    ! [X45,X46,X47,X48] :
      ( ~ c_less(X47,c_Nat_Osize(X46,tc_List_Olist(X48)),tc_nat)
      | c_List_Onth(c_List_Olist__update(X46,X47,X45,X48),X47,X48) = X45 ),
    inference(variable_rename,[status(thm)],[c_0_3155]) ).

fof(c_0_6093,plain,
    ! [X20,X21,X22] :
      ( ~ c_in(X20,X21,X22)
      | c_in(c_Pair(X20,X20,X22,X22),c_Relation_Odiag(X21,X22),tc_prod(X22,X22)) ),
    inference(variable_rename,[status(thm)],[c_0_3156]) ).

fof(c_0_6094,plain,
    ! [X20,X21,X22,X23] :
      ( ~ c_in(c_minus(X22,X21,tc_set(X23)),c_Finite__Set_OFinites,tc_set(X23))
      | c_in(c_minus(X22,c_insert(X20,X21,X23),tc_set(X23)),c_Finite__Set_OFinites,tc_set(X23)) ),
    inference(variable_rename,[status(thm)],[c_0_3157]) ).

fof(c_0_6095,plain,
    ! [X49,X50,X51,X52] :
      ( c_List_Otake(c_Numeral_Onumber__of(X51,tc_nat),c_List_Olist_OCons(X50,X49,X52),X52) = c_List_Olist_OCons(X50,c_List_Otake(c_minus(c_Numeral_Onumber__of(X51,tc_nat),c_1,tc_nat),X49,X52),X52)
      | c_Numeral_Onumber__of(X51,tc_nat) = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3158])])]) ).

fof(c_0_6096,plain,
    ! [X3,X4] :
      ( ~ c_less(X4,X3,tc_nat)
      | c_in(c_Pair(X4,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_3159]) ).

fof(c_0_6097,plain,
    ! [X3] :
      ( c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1 ),
    inference(variable_rename,[status(thm)],[c_0_3160]) ).

fof(c_0_6098,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(X15,c_Relation_Odiag(X16,X17),tc_prod(X17,X17))
      | X15 = c_Pair(c_Main_OdiagE__1(X16,X15,X17),c_Main_OdiagE__1(X16,X15,X17),X17,X17) ),
    inference(variable_rename,[status(thm)],[c_0_3161]) ).

fof(c_0_6099,plain,
    ! [X45,X46,X47,X48] :
      ( ~ c_lessequals(c_plus(X46,X47,tc_nat),c_Nat_Osize(X45,tc_List_Olist(X48)),tc_nat)
      | c_List_Onth(c_List_Odrop(X46,X45,X48),X47,X48) = c_List_Onth(X45,c_plus(X46,X47,tc_nat),X48) ),
    inference(variable_rename,[status(thm)],[c_0_3162]) ).

fof(c_0_6100,plain,
    ! [X17] : c_div(c_Suc(c_Suc(X17)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X17,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_3163]) ).

fof(c_0_6101,plain,
    ! [X61,X62,X63,X64,X65] :
      ( X64 = X63
      | c_List_Onth(c_List_Olist__update(X61,X64,X62,X65),X63,X65) = c_List_Onth(X61,X63,X65) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3164])])]) ).

fof(c_0_6102,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_div(c_plus(X24,c_times(X23,X25,tc_nat),tc_nat),X23,tc_nat) = c_plus(X25,c_div(X24,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3165])])]) ).

fof(c_0_6103,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_div(c_plus(X24,c_times(X25,X23,tc_nat),tc_nat),X23,tc_nat) = c_plus(X25,c_div(X24,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3166])])]) ).

fof(c_0_6104,plain,
    ! [X20,X21,X22] : c_in(c_Pair(X21,X21,X22,X22),c_Transitive__Closure_Ortrancl(X20,X22),tc_prod(X22,X22)),
    inference(variable_rename,[status(thm)],[c_0_3167]) ).

fof(c_0_6105,plain,
    ! [X49,X50] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X50))),c_Numeral_Onumber__of(X49,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X50,tc_nat),c_Numeral_Onumber__of(X49,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3168]) ).

fof(c_0_6106,plain,
    ! [X49,X50] : c_div(c_Suc(c_Suc(c_Suc(X50))),c_Numeral_Onumber__of(X49,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X50,tc_nat),c_Numeral_Onumber__of(X49,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3169]) ).

fof(c_0_6107,plain,
    ! [X104,X105,X106,X107] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X107,X106,X105),X104,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X105,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3170]) ).

fof(c_0_6108,plain,
    ! [X38,X39,X40,X41] :
      ( ~ c_Wellfounded__Recursion_Owf(X38,X40)
      | ~ c_Wellfounded__Recursion_Owf(X39,X41)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X39,X38,X41,X40),tc_prod(X41,X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3171])])]) ).

fof(c_0_6109,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_Relation_Otrans(X36,X38)
      | ~ c_Relation_Otrans(X37,X39)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X37,X36,X39,X38),tc_prod(X39,X38)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3172])])]) ).

fof(c_0_6110,plain,
    ! [X94,X95,X96] :
      ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X95)),c_Message_Oanalz(X96),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X95,X94),c_Message_Oanalz(c_insert(X94,X96,tc_Message_Omsg)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3173]) ).

fof(c_0_6111,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Power_Orecpower(X32)
      | ~ class_Ring__and__Field_Oordered__semidom(X32)
      | ~ c_less(c_1,X31,X32)
      | ~ c_less(c_Nat_Opower(X31,X30,X32),c_Nat_Opower(X31,X29,X32),X32)
      | c_less(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3174]) ).

fof(c_0_6112,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Power_Orecpower(X32)
      | ~ class_Ring__and__Field_Oordered__semidom(X32)
      | ~ c_less(c_1,X31,X32)
      | ~ c_lessequals(c_Nat_Opower(X31,X30,X32),c_Nat_Opower(X31,X29,X32),X32)
      | c_lessequals(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3175]) ).

fof(c_0_6113,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Osemiring(X52)
      | c_times(c_Numeral_Onumber__of(X49,X52),c_plus(X51,X50,X52),X52) = c_plus(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3176]) ).

fof(c_0_6114,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oring(X52)
      | c_times(c_Numeral_Onumber__of(X49,X52),c_minus(X51,X50,X52),X52) = c_minus(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3177]) ).

fof(c_0_6115,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Osemiring(X52)
      | c_times(c_plus(X51,X50,X52),c_Numeral_Onumber__of(X49,X52),X52) = c_plus(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3178]) ).

fof(c_0_6116,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oring(X52)
      | c_times(c_minus(X51,X50,X52),c_Numeral_Onumber__of(X49,X52),X52) = c_minus(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3179]) ).

fof(c_0_6117,plain,
    ! [X5,X6] : c_in(c_Pair(X5,X5,X6,X6),c_Relation_OId,tc_prod(X6,X6)),
    inference(variable_rename,[status(thm)],[c_0_3180]) ).

fof(c_0_6118,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X6),X6)
      | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3181]) ).

fof(c_0_6119,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(X31,c_0,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3182]) ).

fof(c_0_6120,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_lessequals(X31,c_0,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3183]) ).

fof(c_0_6121,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32)
      | c_less(c_0,X31,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3184]) ).

fof(c_0_6122,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_lessequals(c_0,X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3185]) ).

fof(c_0_6123,plain,
    ! [X7,X8] :
      ( ~ class_Numeral_Onumber__ring(X8)
      | ~ class_Ring__and__Field_Odivision__by__zero(X8)
      | ~ class_Ring__and__Field_Oordered__field(X8)
      | ~ c_less(c_0,X7,X8)
      | c_less(c_0,c_divide(X7,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X8),X8),X8) ),
    inference(variable_rename,[status(thm)],[c_0_3186]) ).

fof(c_0_6124,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(X50,X51,X52)
      | ~ c_less(X51,X50,X52)
      | c_less(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3187]) ).

fof(c_0_6125,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(X50,X51,X52)
      | ~ c_less(X51,X50,X52)
      | c_less(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3188]) ).

fof(c_0_6126,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_lessequals(X50,X51,X52)
      | ~ c_lessequals(X51,X50,X52)
      | c_lessequals(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3189]) ).

fof(c_0_6127,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_lessequals(X50,X51,X52)
      | ~ c_lessequals(X51,X50,X52)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3190]) ).

fof(c_0_6128,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(X51,X50,X52)
      | c_less(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | c_lessequals(c_Numeral_Onumber__of(X49,X52),c_0,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3191]) ).

fof(c_0_6129,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(X50,X51,X52)
      | c_less(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X49,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3192]) ).

fof(c_0_6130,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(X51,X50,X52)
      | c_less(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | c_lessequals(c_Numeral_Onumber__of(X49,X52),c_0,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3193]) ).

fof(c_0_6131,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_less(X50,X51,X52)
      | c_less(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X49,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3194]) ).

fof(c_0_6132,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_lessequals(X51,X50,X52)
      | c_less(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | c_lessequals(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3195]) ).

fof(c_0_6133,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_lessequals(X50,X51,X52)
      | c_less(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_lessequals(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3196]) ).

fof(c_0_6134,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_lessequals(X51,X50,X52)
      | c_less(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3197]) ).

fof(c_0_6135,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | ~ c_lessequals(X50,X51,X52)
      | c_less(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3198]) ).

fof(c_0_6136,plain,
    ! [X61,X62,X63,X64,X65] :
      ( ~ class_Orderings_Olinorder(X65)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X64,X63,X65),c_SetInterval_OatLeastLessThan(X62,X61,X65),tc_set(X65))
      | c_lessequals(X63,X61,X65)
      | c_lessequals(X63,X64,X65) ),
    inference(variable_rename,[status(thm)],[c_0_3199]) ).

fof(c_0_6137,plain,
    ! [X61,X62,X63,X64,X65] :
      ( ~ class_Orderings_Olinorder(X65)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X64,X63,X65),c_SetInterval_OatLeastLessThan(X62,X61,X65),tc_set(X65))
      | c_lessequals(X62,X64,X65)
      | c_lessequals(X63,X64,X65) ),
    inference(variable_rename,[status(thm)],[c_0_3200]) ).

fof(c_0_6138,plain,
    ! [X20,X21,X22,X23] : c_snd(c_Pair(X21,X20,X22,X23),X22,X23) = X20,
    inference(variable_rename,[status(thm)],[c_0_3201]) ).

fof(c_0_6139,plain,
    ! [X29,X30,X31,X32] : c_fst(c_Pair(X29,X30,X32,X31),X32,X31) = X29,
    inference(variable_rename,[status(thm)],[c_0_3202]) ).

fof(c_0_6140,plain,
    ! [X23,X24] : c_Divides_Oop_Amod(X24,c_Suc(c_Suc(c_Suc(X23))),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X23,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3203]) ).

fof(c_0_6141,plain,
    ! [X23,X24] : c_div(X24,c_Suc(c_Suc(c_Suc(X23))),tc_nat) = c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X23,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3204]) ).

fof(c_0_6142,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | c_less(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_lessequals(c_Numeral_Onumber__of(X49,X52),c_0,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3205]) ).

fof(c_0_6143,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | c_less(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_lessequals(c_Numeral_Onumber__of(X49,X52),c_0,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3206]) ).

fof(c_0_6144,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | c_less(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_less(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | c_lessequals(c_times(X51,c_Numeral_Onumber__of(X49,X52),X52),c_times(X50,c_Numeral_Onumber__of(X49,X52),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3207]) ).

fof(c_0_6145,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber(X52)
      | ~ class_Ring__and__Field_Oordered__ring__strict(X52)
      | c_less(c_0,c_Numeral_Onumber__of(X49,X52),X52)
      | c_less(c_Numeral_Onumber__of(X49,X52),c_0,X52)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X49,X52),X51,X52),c_times(c_Numeral_Onumber__of(X49,X52),X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3208]) ).

fof(c_0_6146,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_0,X25,tc_nat)
      | ~ c_lessequals(c_times(X24,X25,tc_nat),c_times(X23,X25,tc_nat),tc_nat)
      | c_lessequals(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3209]) ).

fof(c_0_6147,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_0,X25,tc_nat)
      | ~ c_lessequals(c_times(X25,X24,tc_nat),c_times(X25,X23,tc_nat),tc_nat)
      | c_lessequals(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3210]) ).

fof(c_0_6148,plain,
    ! [X60,X61,X62,X63] :
      ( ~ c_in(X61,c_List_Oset(c_List_Osublist(X60,X62,X63),X63),X63)
      | c_in(X61,c_List_Oset(X60,X63),X63) ),
    inference(variable_rename,[status(thm)],[c_0_3211]) ).

fof(c_0_6149,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_in(X27,c_List_Oset(c_List_Oremove1(X25,X26,X28),X28),X28)
      | c_in(X27,c_List_Oset(X26,X28),X28) ),
    inference(variable_rename,[status(thm)],[c_0_3212]) ).

fof(c_0_6150,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(X90,c_Message_Oparts(c_union(X92,X91,tc_Message_Omsg)),tc_Message_Omsg)
      | c_in(X90,c_Message_Oparts(X91),tc_Message_Omsg)
      | c_in(X90,c_Message_Oparts(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3213]) ).

fof(c_0_6151,plain,
    ! [X45,X46,X47,X48] : c_Nat_Osize(c_List_Olist__update(X45,X47,X46,X48),tc_List_Olist(X48)) = c_Nat_Osize(X45,tc_List_Olist(X48)),
    inference(variable_rename,[status(thm)],[c_0_3214]) ).

fof(c_0_6152,plain,
    ! [X29,X30,X31,X32] : c_Nat_Osize(c_Pair(X30,X29,X32,X31),tc_prod(X32,X31)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_3215]) ).

fof(c_0_6153,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X6),X6)
      | c_less(c_Numeral_Onumber__of(X5,X6),c_1,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3216]) ).

fof(c_0_6154,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_less(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3217]) ).

fof(c_0_6155,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_lessequals(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3218]) ).

fof(c_0_6156,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_less(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3219]) ).

fof(c_0_6157,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_lessequals(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3220]) ).

fof(c_0_6158,plain,
    ! [X61,X62,X63] :
      ( ~ c_lessequals(X62,X63,tc_nat)
      | c_minus(c_Suc(c_minus(X63,X62,tc_nat)),X61,tc_nat) = c_minus(c_Suc(X63),c_plus(X62,X61,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3221]) ).

fof(c_0_6159,plain,
    ! [X61,X62,X63] :
      ( ~ c_lessequals(X62,X63,tc_nat)
      | c_minus(X61,c_Suc(c_minus(X63,X62,tc_nat)),tc_nat) = c_minus(c_plus(X61,X62,tc_nat),c_Suc(X63),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3222]) ).

fof(c_0_6160,plain,
    ! [X27,X28,X29,X30,X31] :
      ( c_append(X29,c_List_Olist_OCons(X30,c_List_Olist_ONil,X31),X31) != c_append(X27,c_List_Olist_OCons(X28,c_List_Olist_ONil,X31),X31)
      | X30 = X28 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3223])])]) ).

fof(c_0_6161,plain,
    ! [X27,X28,X29,X30,X31] :
      ( c_append(X29,c_List_Olist_OCons(X30,c_List_Olist_ONil,X31),X31) != c_append(X27,c_List_Olist_OCons(X28,c_List_Olist_ONil,X31),X31)
      | X29 = X27 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3224])])]) ).

fof(c_0_6162,plain,
    ! [X45,X46,X47] :
      ( ~ c_less(X46,c_Nat_Osize(X45,tc_List_Olist(X47)),tc_nat)
      | c_List_Olist__update(X45,X46,c_List_Onth(X45,X46,X47),X47) = X45 ),
    inference(variable_rename,[status(thm)],[c_0_3225]) ).

fof(c_0_6163,plain,
    ! [X17] : c_GCD_Ogcd(c_Pair(c_Suc(c_0),X17,tc_nat,tc_nat)) = c_1,
    inference(variable_rename,[status(thm)],[c_0_3226]) ).

fof(c_0_6164,plain,
    ! [X17] : c_GCD_Ogcd(c_Pair(X17,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
    inference(variable_rename,[status(thm)],[c_0_3227]) ).

fof(c_0_6165,plain,
    ! [X49,X50,X51] :
      ( c_lessequals(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | X51 = c_Numeral_Obit_OB0
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X50,X51),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X49,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3228])])]) ).

fof(c_0_6166,plain,
    ! [X2] : c_GCD_Ogcd(c_Pair(X2,X2,tc_nat,tc_nat)) = X2,
    inference(variable_rename,[status(thm)],[c_0_3229]) ).

fof(c_0_6167,plain,
    ! [X2] : c_GCD_Ogcd(c_Pair(c_0,X2,tc_nat,tc_nat)) = X2,
    inference(variable_rename,[status(thm)],[c_0_3230]) ).

fof(c_0_6168,plain,
    ! [X2] : c_GCD_Ogcd(c_Pair(X2,c_0,tc_nat,tc_nat)) = X2,
    inference(variable_rename,[status(thm)],[c_0_3231]) ).

fof(c_0_6169,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_less(c_0,X30,X31)
      | c_less(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3232]) ).

fof(c_0_6170,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_less(X30,c_0,X31)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3233]) ).

fof(c_0_6171,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_lessequals(c_0,X30,X31)
      | c_lessequals(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3234]) ).

fof(c_0_6172,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_lessequals(X30,c_0,X31)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3235]) ).

fof(c_0_6173,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_less(X30,c_0,X31)
      | c_less(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3236]) ).

fof(c_0_6174,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_less(c_0,X30,X31)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3237]) ).

fof(c_0_6175,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_lessequals(X30,c_0,X31)
      | c_lessequals(c_Numeral_Onumber__of(X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3238]) ).

fof(c_0_6176,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_lessequals(c_0,X30,X31)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3239]) ).

fof(c_0_6177,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_less(c_plus(X31,X29,X32),c_plus(X30,X29,X32),X32)
      | c_less(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3240]) ).

fof(c_0_6178,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_less(c_plus(X29,X31,X32),c_plus(X29,X30,X32),X32)
      | c_less(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3241]) ).

fof(c_0_6179,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_lessequals(c_plus(X31,X29,X32),c_plus(X30,X29,X32),X32)
      | c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3242]) ).

fof(c_0_6180,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_lessequals(c_plus(X29,X31,X32),c_plus(X29,X30,X32),X32)
      | c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3243]) ).

fof(c_0_6181,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(X31,c_0,X32)
      | c_less(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3244]) ).

fof(c_0_6182,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(X31,c_0,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_lessequals(X31,c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3245]) ).

fof(c_0_6183,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_less(c_0,X31,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_less(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3246]) ).

fof(c_0_6184,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Numeral_Onumber(X32)
      | ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Oordered__field(X32)
      | ~ c_lessequals(c_0,X31,X32)
      | c_less(c_0,c_Numeral_Onumber__of(X29,X32),X32)
      | c_less(c_Numeral_Onumber__of(X29,X32),c_0,X32)
      | c_lessequals(c_divide(X30,c_Numeral_Onumber__of(X29,X32),X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3247]) ).

fof(c_0_6185,plain,
    ! [X18,X19,X20,X21,X22] : c_Datatype__Universe_OScons(X20,X19,X22,X21) != c_Datatype__Universe_ONumb(X18,X22,X21),
    inference(variable_rename,[status(thm)],[c_0_3248]) ).

fof(c_0_6186,plain,
    ! [X20,X21,X22,X23,X24] : c_Datatype__Universe_OScons(X22,X21,X24,X23) != c_Datatype__Universe_OLeaf(X20,X24,X23),
    inference(variable_rename,[status(thm)],[c_0_3249]) ).

fof(c_0_6187,plain,
    ! [X20,X21,X22,X23,X24] : c_Datatype__Universe_OScons(X22,X21,X24,X23) != c_Datatype__Universe_OAtom(X20,X24,X23),
    inference(variable_rename,[status(thm)],[c_0_3250]) ).

fof(c_0_6188,plain,
    ! [X18,X19,X20,X21,X22] : c_Datatype__Universe_ONumb(X18,X22,X21) != c_Datatype__Universe_OScons(X20,X19,X22,X21),
    inference(variable_rename,[status(thm)],[c_0_3251]) ).

fof(c_0_6189,plain,
    ! [X20,X21,X22,X23,X24] : c_Datatype__Universe_OLeaf(X20,X24,X23) != c_Datatype__Universe_OScons(X22,X21,X24,X23),
    inference(variable_rename,[status(thm)],[c_0_3252]) ).

fof(c_0_6190,plain,
    ! [X20,X21,X22,X23,X24] : c_Datatype__Universe_OAtom(X20,X24,X23) != c_Datatype__Universe_OScons(X22,X21,X24,X23),
    inference(variable_rename,[status(thm)],[c_0_3253]) ).

fof(c_0_6191,plain,
    ! [X27,X28,X29,X30] :
      ( ~ c_in(X27,c_List_Olists(X29,X30),tc_List_Olist(X30))
      | ~ c_in(X28,c_List_Olists(X29,X30),tc_List_Olist(X30))
      | c_in(c_append(X28,X27,X30),c_List_Olists(X29,X30),tc_List_Olist(X30)) ),
    inference(variable_rename,[status(thm)],[c_0_3254]) ).

fof(c_0_6192,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(X90,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Oanalz(X92),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(c_Message_OHPair(X91,X90),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3255]) ).

fof(c_0_6193,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_plus(X25,X24,tc_nat),c_plus(X25,X23,tc_nat),tc_nat)
      | c_less(X24,X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3256])])]) ).

fof(c_0_6194,plain,
    ! [X23,X24,X25] :
      ( ~ c_lessequals(c_plus(X25,X24,tc_nat),c_plus(X25,X23,tc_nat),tc_nat)
      | c_lessequals(X24,X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3257])])]) ).

fof(c_0_6195,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_times(X24,X25,tc_nat),c_times(X23,X25,tc_nat),tc_nat)
      | c_less(X24,X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3258])])]) ).

fof(c_0_6196,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_times(X25,X24,tc_nat),c_times(X25,X23,tc_nat),tc_nat)
      | c_less(X24,X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3259])])]) ).

fof(c_0_6197,plain,
    ! [X50,X51,X52] : X50 = c_Pair(c_Main_Osurj__pair__1(X50,X52,X51),c_Main_Osurj__pair__2(X50,X52,X51),X52,X51),
    inference(variable_rename,[status(thm)],[c_0_3260]) ).

fof(c_0_6198,plain,
    ! [X5,X6,X7] : c_Pair(c_fst(X5,X7,X6),c_snd(X5,X7,X6),X7,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_3261]) ).

fof(c_0_6199,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_times(X24,X25,tc_nat),c_times(X23,X25,tc_nat),tc_nat)
      | c_less(c_0,X25,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3262]) ).

fof(c_0_6200,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(c_times(X25,X24,tc_nat),c_times(X25,X23,tc_nat),tc_nat)
      | c_less(c_0,X25,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3263]) ).

fof(c_0_6201,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_less(X30,c_0,X31)
      | c_less(c_0,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3264]) ).

fof(c_0_6202,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31)
      | c_lessequals(X30,c_0,X31)
      | c_lessequals(c_0,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3265]) ).

fof(c_0_6203,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_less(X30,c_0,X31)
      | c_less(c_0,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3266]) ).

fof(c_0_6204,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31)
      | c_lessequals(X30,c_0,X31)
      | c_lessequals(c_0,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3267]) ).

fof(c_0_6205,plain,
    ! [X7,X8] : c_Relation_OImage(c_List_Olistrel(X7,X8),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X8)),tc_List_Olist(X8),tc_List_Olist(X8)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X8)),
    inference(variable_rename,[status(thm)],[c_0_3268]) ).

fof(c_0_6206,plain,
    ! [X61,X62,X63,X64,X65] :
      ( ~ class_Orderings_Olinorder(X65)
      | ~ c_lessequals(X63,X61,X65)
      | ~ c_lessequals(X62,X64,X65)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X64,X63,X65),c_SetInterval_OatLeastLessThan(X62,X61,X65),tc_set(X65)) ),
    inference(variable_rename,[status(thm)],[c_0_3269]) ).

fof(c_0_6207,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X6),X6)
      | c_Numeral_Onumber__of(X5,X6) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_3270]) ).

fof(c_0_6208,plain,
    ! [X7,X8,X9] :
      ( ~ c_in(c_Relation_Oconverse(X7,X8,X9),c_Finite__Set_OFinites,tc_set(tc_prod(X9,X8)))
      | c_in(X7,c_Finite__Set_OFinites,tc_set(tc_prod(X8,X9))) ),
    inference(variable_rename,[status(thm)],[c_0_3271]) ).

fof(c_0_6209,plain,
    ! [X94,X95,X96] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X95,X94),c_Message_Oparts(c_insert(X94,X96,tc_Message_Omsg)),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3272]) ).

fof(c_0_6210,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Power_Orecpower(X32)
      | ~ class_Ring__and__Field_Oordered__semidom(X32)
      | ~ c_less(X30,X29,tc_nat)
      | ~ c_less(c_1,X31,X32)
      | c_less(c_Nat_Opower(X31,X30,X32),c_Nat_Opower(X31,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3273]) ).

fof(c_0_6211,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Power_Orecpower(X32)
      | ~ class_Ring__and__Field_Oordered__semidom(X32)
      | ~ c_less(c_1,X31,X32)
      | ~ c_lessequals(X30,X29,tc_nat)
      | c_lessequals(c_Nat_Opower(X31,X30,X32),c_Nat_Opower(X31,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3274]) ).

fof(c_0_6212,plain,
    ! [X67,X68,X69,X70] :
      ( ~ c_in(X69,c_List_Oset(X67,X70),X70)
      | c_List_Olist__inter(c_List_Olist_OCons(X69,X68,X70),X67,X70) = c_List_Olist_OCons(X69,c_List_Olist__inter(X68,X67,X70),X70) ),
    inference(variable_rename,[status(thm)],[c_0_3275]) ).

fof(c_0_6213,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X5)),X6),X6)
      | ~ c_lessequals(c_Numeral_Onumber__of(X5,X6),c_1,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3276]) ).

fof(c_0_6214,plain,
    ! [X45,X46,X47] :
      ( ~ c_lessequals(c_plus(X47,X46,tc_nat),X45,tc_nat)
      | c_List_Otake(X46,c_List_Oupt(X47,X45),tc_nat) = c_List_Oupt(X47,c_plus(X47,X46,tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_3277]) ).

fof(c_0_6215,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_less(c_Numeral_Onumber__of(X29,X31),c_0,X31)
      | c_less(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3278]) ).

fof(c_0_6216,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_less(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3279]) ).

fof(c_0_6217,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(X30,c_0,X31)
      | ~ c_lessequals(c_Numeral_Onumber__of(X29,X31),c_0,X31)
      | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3280]) ).

fof(c_0_6218,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_0,X30,X31)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3281]) ).

fof(c_0_6219,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_less(c_Numeral_Onumber__of(X29,X31),c_0,X31)
      | c_less(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3282]) ).

fof(c_0_6220,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_less(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3283]) ).

fof(c_0_6221,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(c_0,X30,X31)
      | ~ c_lessequals(c_Numeral_Onumber__of(X29,X31),c_0,X31)
      | c_lessequals(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3284]) ).

fof(c_0_6222,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_lessequals(X30,c_0,X31)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X29,X31),X31)
      | c_lessequals(c_divide(c_Numeral_Onumber__of(X29,X31),X30,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3285]) ).

fof(c_0_6223,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_less(c_0,X13,X15)
      | c_Numeral_Onumber__of(X14,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3286]) ).

fof(c_0_6224,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | ~ c_less(X15,c_Main_OMin__gr__iff__1(X16,X15,X17),X17)
      | c_less(X15,c_Finite__Set_OMin(X16,X17),X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3287]) ).

fof(c_0_6225,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | ~ c_lessequals(X15,c_Main_OMin__ge__iff__1(X16,X15,X17),X17)
      | c_lessequals(X15,c_Finite__Set_OMin(X16,X17),X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3288]) ).

fof(c_0_6226,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | ~ c_less(c_Main_OMax__less__iff__1(X16,X15,X17),X15,X17)
      | c_less(c_Finite__Set_OMax(X16,X17),X15,X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3289]) ).

fof(c_0_6227,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | ~ c_lessequals(c_Main_OMax__le__iff__1(X16,X15,X17),X15,X17)
      | c_lessequals(c_Finite__Set_OMax(X16,X17),X15,X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3290]) ).

fof(c_0_6228,plain,
    ! [X20,X21,X22] : c_insert(X20,c_minus(X21,c_insert(X20,c_emptyset,X22),tc_set(X22)),X22) = c_insert(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_3291]) ).

fof(c_0_6229,plain,
    ! [X27,X28,X29] : c_List_Orev(c_append(c_List_Orev(X27,X29),c_List_Olist_OCons(X28,c_List_Olist_ONil,X29),X29),X29) = c_List_Olist_OCons(X28,X27,X29),
    inference(variable_rename,[status(thm)],[c_0_3292]) ).

fof(c_0_6230,plain,
    ! [X20,X21,X22,X23] : c_inter(c_insert(X20,X22,X23),c_insert(X20,X21,X23),X23) = c_insert(X20,c_inter(X22,X21,X23),X23),
    inference(variable_rename,[status(thm)],[c_0_3293]) ).

fof(c_0_6231,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X29,X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X28,X29,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_3294]) ).

fof(c_0_6232,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_lessequals(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_lessequals(c_0,X13,X15) ),
    inference(variable_rename,[status(thm)],[c_0_3295]) ).

fof(c_0_6233,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_lessequals(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_lessequals(X13,c_0,X15) ),
    inference(variable_rename,[status(thm)],[c_0_3296]) ).

fof(c_0_6234,plain,
    ! [X104,X105,X106] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X106,X105),X104,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X105,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3297]) ).

fof(c_0_6235,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(X24,X23,tc_nat)
      | ~ c_less(c_0,X25,tc_nat)
      | c_less(c_times(X24,X25,tc_nat),c_times(X23,X25,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3298])])]) ).

fof(c_0_6236,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(X24,X23,tc_nat)
      | ~ c_less(c_0,X25,tc_nat)
      | c_less(c_times(X25,X24,tc_nat),c_times(X25,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3299])])]) ).

fof(c_0_6237,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X29,X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X28,c_plus(X29,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_3300]) ).

fof(c_0_6238,plain,
    ! [X30,X31] :
      ( ~ c_in(X30,c_Relation_OId,tc_prod(X31,X31))
      | X30 = c_Pair(c_Main_OIdE__1(X30,X31),c_Main_OIdE__1(X30,X31),X31,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3301]) ).

fof(c_0_6239,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Olinorder(X48)
      | ~ c_lessequals(X47,X45,X48)
      | c_minus(c_SetInterval_OatLeastLessThan(X47,X46,X48),c_SetInterval_OatLeastLessThan(X47,X45,X48),tc_set(X48)) = c_SetInterval_OatLeastLessThan(X45,X46,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3302]) ).

fof(c_0_6240,plain,
    ! [X17] : c_Divides_Oop_Amod(c_Suc(c_Suc(X17)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X17,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3303]) ).

fof(c_0_6241,plain,
    ! [X23,X24,X25] : c_Divides_Oop_Amod(c_plus(X24,c_times(X23,X25,tc_nat),tc_nat),X23,tc_nat) = c_Divides_Oop_Amod(X24,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3304]) ).

fof(c_0_6242,plain,
    ! [X23,X24,X25] : c_Divides_Oop_Amod(c_plus(X24,c_times(X25,X23,tc_nat),tc_nat),X23,tc_nat) = c_Divides_Oop_Amod(X24,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3305]) ).

fof(c_0_6243,plain,
    ! [X28,X29,X30,X31] :
      ( ~ c_in(X29,X30,X31)
      | ~ c_in(X28,c_List_Olists(X30,X31),tc_List_Olist(X31))
      | c_in(c_List_Olist_OCons(X29,X28,X31),c_List_Olists(X30,X31),tc_List_Olist(X31)) ),
    inference(variable_rename,[status(thm)],[c_0_3306]) ).

fof(c_0_6244,plain,
    ! [X45,X46,X47,X48] : c_Datatype__Universe_Ontrunc(c_Suc(X45),c_Datatype__Universe_ONumb(X46,X48,X47),X48,X47) = c_Datatype__Universe_ONumb(X46,X48,X47),
    inference(variable_rename,[status(thm)],[c_0_3307]) ).

fof(c_0_6245,plain,
    ! [X20,X21,X22,X23] : c_Datatype__Universe_Ontrunc(c_Suc(X20),c_Datatype__Universe_OLeaf(X21,X23,X22),X23,X22) = c_Datatype__Universe_OLeaf(X21,X23,X22),
    inference(variable_rename,[status(thm)],[c_0_3308]) ).

fof(c_0_6246,plain,
    ! [X20,X21,X22,X23] : c_Datatype__Universe_Ontrunc(c_Suc(X20),c_Datatype__Universe_OAtom(X21,X23,X22),X23,X22) = c_Datatype__Universe_OAtom(X21,X23,X22),
    inference(variable_rename,[status(thm)],[c_0_3309]) ).

fof(c_0_6247,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_less(c_Numeral_Onumber__of(X5,X6),c_1,X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3310]) ).

fof(c_0_6248,plain,
    ! [X27,X28,X29,X30] : c_List_Onth(c_append(X29,c_List_Olist_OCons(X28,X27,X30),X30),c_Nat_Osize(X29,tc_List_Olist(X30)),X30) = X28,
    inference(variable_rename,[status(thm)],[c_0_3311]) ).

fof(c_0_6249,plain,
    ! [X49,X50,X51] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X50,X51),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X49,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3312])])]) ).

fof(c_0_6250,plain,
    ! [X104,X105,X106,X107] : c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X107,X106,X105),X104,tc_Event_Oevent)) = c_insert(X105,c_Event_Oknows(c_Message_Oagent_OSpy,X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3313]) ).

fof(c_0_6251,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_less(c_1,c_divide(X29,X30,X31),X31)
      | c_less(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3314]) ).

fof(c_0_6252,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_less(c_1,c_divide(X29,X30,X31),X31)
      | c_less(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3315]) ).

fof(c_0_6253,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_lessequals(c_1,c_divide(X29,X30,X31),X31)
      | c_lessequals(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3316]) ).

fof(c_0_6254,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_lessequals(c_1,c_divide(X29,X30,X31),X31)
      | c_lessequals(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3317]) ).

fof(c_0_6255,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_less(c_divide(X29,X30,X31),c_1,X31)
      | c_less(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3318]) ).

fof(c_0_6256,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_less(c_divide(X29,X30,X31),c_1,X31)
      | c_less(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3319]) ).

fof(c_0_6257,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_lessequals(c_divide(X29,X30,X31),c_1,X31)
      | c_lessequals(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3320]) ).

fof(c_0_6258,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_lessequals(c_divide(X29,X30,X31),c_1,X31)
      | c_lessequals(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3321]) ).

fof(c_0_6259,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Numeral_Onumber__ring(X52)
      | c_plus(c_Numeral_Onumber__of(X50,X52),c_minus(X51,c_Numeral_Onumber__of(X49,X52),X52),X52) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X50,c_Numeral_Obin__minus(X49)),X52),X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3322]) ).

fof(c_0_6260,plain,
    ! [X3] :
      ( c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
      | c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_3323]) ).

fof(c_0_6261,plain,
    ! [X13,X14] :
      ( ~ class_Power_Orecpower(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X13,tc_nat),tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X13,tc_nat),X14),X14)
      | c_Numeral_Onumber__of(X13,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3324]) ).

fof(c_0_6262,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X5)),X6),X6)
      | c_less(c_1,c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3325]) ).

fof(c_0_6263,plain,
    ! [X49,X50,X51,X52] :
      ( c_List_Onth(c_List_Olist_OCons(X50,X49,X52),c_Numeral_Onumber__of(X51,tc_nat),X52) = c_List_Onth(X49,c_minus(c_Numeral_Onumber__of(X51,tc_nat),c_1,tc_nat),X52)
      | c_Numeral_Onumber__of(X51,tc_nat) = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3326])])]) ).

fof(c_0_6264,plain,
    ! [X49,X50,X51,X52] :
      ( c_List_Odrop(c_Numeral_Onumber__of(X51,tc_nat),c_List_Olist_OCons(X50,X49,X52),X52) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X51,tc_nat),c_1,tc_nat),X49,X52)
      | c_Numeral_Onumber__of(X51,tc_nat) = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3327])])]) ).

fof(c_0_6265,plain,
    ! [X13,X14] :
      ( ~ class_Power_Orecpower(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X13,tc_nat),X14),X14)
      | c_less(c_0,c_0,X14)
      | c_Numeral_Onumber__of(X13,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3328]) ).

fof(c_0_6266,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,c_0,X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_less(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31)
      | c_less(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3329]) ).

fof(c_0_6267,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X29,X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_less(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31)
      | c_less(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3330]) ).

fof(c_0_6268,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,c_0,X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_lessequals(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31)
      | c_lessequals(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3331]) ).

fof(c_0_6269,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X29,X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_lessequals(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31)
      | c_lessequals(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3332]) ).

fof(c_0_6270,plain,
    ! [X61,X62,X63] :
      ( ~ c_lessequals(X61,X62,tc_nat)
      | c_minus(X63,c_minus(X62,X61,tc_nat),tc_nat) = c_minus(c_plus(X63,X61,tc_nat),X62,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3333])])]) ).

fof(c_0_6271,plain,
    ! [X61,X62,X63] :
      ( ~ c_lessequals(X61,X62,tc_nat)
      | c_plus(X63,c_minus(X62,X61,tc_nat),tc_nat) = c_minus(c_plus(X63,X62,tc_nat),X61,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3334])])]) ).

fof(c_0_6272,plain,
    ! [X61,X62,X63] :
      ( ~ c_lessequals(X61,X62,tc_nat)
      | c_plus(c_minus(X62,X61,tc_nat),X63,tc_nat) = c_minus(c_plus(X62,X63,tc_nat),X61,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3335])])]) ).

fof(c_0_6273,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15)
      | X13 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3336]) ).

fof(c_0_6274,plain,
    ! [X27,X28,X29,X30] : c_List_Onth(c_append(X28,X27,X30),c_plus(c_Nat_Osize(X28,tc_List_Olist(X30)),X29,tc_nat),X30) = c_List_Onth(X27,X29,X30),
    inference(variable_rename,[status(thm)],[c_0_3337]) ).

fof(c_0_6275,plain,
    ! [X29,X30,X31] :
      ( ~ c_less(c_0,X29,tc_nat)
      | c_div(c_times(X31,X29,tc_nat),c_times(X30,X29,tc_nat),tc_nat) = c_div(X31,X30,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3338])])]) ).

fof(c_0_6276,plain,
    ! [X29,X30,X31] :
      ( ~ c_less(c_0,X29,tc_nat)
      | c_div(c_times(X29,X31,tc_nat),c_times(X29,X30,tc_nat),tc_nat) = c_div(X31,X30,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3339])])]) ).

fof(c_0_6277,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | ~ c_less(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15) ),
    inference(variable_rename,[status(thm)],[c_0_3340]) ).

fof(c_0_6278,plain,
    ! [X7,X8,X9] :
      ( ~ c_in(X7,c_Finite__Set_OFinites,tc_set(tc_prod(X8,X9)))
      | c_in(c_Relation_Oconverse(X7,X8,X9),c_Finite__Set_OFinites,tc_set(tc_prod(X9,X8))) ),
    inference(variable_rename,[status(thm)],[c_0_3341]) ).

fof(c_0_6279,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Oanalz(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3342]) ).

fof(c_0_6280,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_lessequals(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15)
      | c_lessequals(X13,c_0,X15)
      | X13 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3343]) ).

fof(c_0_6281,plain,
    ! [X90,X91] : c_Message_Oanalz(c_union(c_Message_Osynth(X91),X90,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X91,X90,tc_Message_Omsg)),c_Message_Osynth(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3344]) ).

fof(c_0_6282,plain,
    ! [X45,X46,X47,X48] :
      ( ~ c_lessequals(c_Nat_Osize(X45,tc_List_Olist(X48)),X47,tc_nat)
      | c_List_Olist__update(X45,X47,X46,X48) = X45 ),
    inference(variable_rename,[status(thm)],[c_0_3345]) ).

fof(c_0_6283,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_less(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15)
      | c_less(X13,c_0,X15) ),
    inference(variable_rename,[status(thm)],[c_0_3346]) ).

fof(c_0_6284,plain,
    ! [X27,X28,X29,X30] :
      ( ~ c_in(c_append(X28,X27,X30),c_List_Olists(X29,X30),tc_List_Olist(X30))
      | c_in(X27,c_List_Olists(X29,X30),tc_List_Olist(X30)) ),
    inference(variable_rename,[status(thm)],[c_0_3347]) ).

fof(c_0_6285,plain,
    ! [X27,X28,X29,X30] :
      ( ~ c_in(c_append(X28,X27,X30),c_List_Olists(X29,X30),tc_List_Olist(X30))
      | c_in(X28,c_List_Olists(X29,X30),tc_List_Olist(X30)) ),
    inference(variable_rename,[status(thm)],[c_0_3348]) ).

fof(c_0_6286,plain,
    ! [X28,X29,X30,X31] :
      ( ~ c_in(c_List_Olist_OCons(X28,X29,X31),c_List_Olists(X30,X31),tc_List_Olist(X31))
      | c_in(X29,c_List_Olists(X30,X31),tc_List_Olist(X31)) ),
    inference(variable_rename,[status(thm)],[c_0_3349]) ).

fof(c_0_6287,plain,
    ! [X49] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Parity_Oeven(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3350]) ).

fof(c_0_6288,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Oanalz(X92),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3351]) ).

fof(c_0_6289,plain,
    ! [X13,X14] :
      ( ~ c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),tc_nat),tc_nat)
      | c_less(c_0,X13,tc_nat)
      | c_Numeral_Onumber__of(X14,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3352]) ).

fof(c_0_6290,plain,
    ! [X61,X62,X63] :
      ( ~ c_less(c_plus(X63,X61,tc_nat),X62,tc_nat)
      | c_List_Onth(c_List_Oupt(X63,X62),X61,tc_nat) = c_plus(X63,X61,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3353]) ).

fof(c_0_6291,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Numeral_Onumber__ring(X53)
      | c_times(c_Numeral_Onumber__of(X52,X53),c_times(c_Numeral_Onumber__of(X51,X53),X50,X53),X53) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X52,X51),X53),X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3354]) ).

fof(c_0_6292,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Numeral_Onumber__ring(X53)
      | c_plus(c_Numeral_Onumber__of(X52,X53),c_plus(c_Numeral_Onumber__of(X51,X53),X50,X53),X53) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X52,X51),X53),X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3355]) ).

fof(c_0_6293,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Orderings_Olinorder(X29)
      | ~ c_in(X27,X28,X29)
      | ~ c_in(X28,c_Finite__Set_OFinites,tc_set(X29))
      | ~ c_less(X26,c_Finite__Set_OMin(X28,X29),X29)
      | c_less(X26,X27,X29)
      | X28 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3356]) ).

fof(c_0_6294,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Orderings_Olinorder(X29)
      | ~ c_in(X27,X28,X29)
      | ~ c_in(X28,c_Finite__Set_OFinites,tc_set(X29))
      | ~ c_lessequals(X26,c_Finite__Set_OMin(X28,X29),X29)
      | c_lessequals(X26,X27,X29)
      | X28 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3357]) ).

fof(c_0_6295,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Orderings_Olinorder(X29)
      | ~ c_in(X27,X28,X29)
      | ~ c_in(X28,c_Finite__Set_OFinites,tc_set(X29))
      | ~ c_less(c_Finite__Set_OMax(X28,X29),X26,X29)
      | c_less(X27,X26,X29)
      | X28 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3358]) ).

fof(c_0_6296,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Orderings_Olinorder(X29)
      | ~ c_in(X27,X28,X29)
      | ~ c_in(X28,c_Finite__Set_OFinites,tc_set(X29))
      | ~ c_lessequals(c_Finite__Set_OMax(X28,X29),X26,X29)
      | c_lessequals(X27,X26,X29)
      | X28 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3359]) ).

fof(c_0_6297,plain,
    ! [X85,X86] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3360])])]) ).

fof(c_0_6298,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X6),X6)
      | c_lessequals(c_1,c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3361]) ).

fof(c_0_6299,plain,
    ! [X61,X62,X63,X64,X65] :
      ( ~ class_Orderings_Olinorder(X65)
      | ~ c_lessequals(X63,X64,X65)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X64,X63,X65),c_SetInterval_OatLeastLessThan(X62,X61,X65),tc_set(X65)) ),
    inference(variable_rename,[status(thm)],[c_0_3362]) ).

fof(c_0_6300,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,X30,X31)
      | ~ c_less(X29,c_0,X31)
      | ~ c_less(X30,c_0,X31)
      | c_less(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3363]) ).

fof(c_0_6301,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,X30,X31)
      | ~ c_less(c_0,X29,X31)
      | ~ c_less(c_0,X30,X31)
      | c_less(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3364]) ).

fof(c_0_6302,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,c_0,X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_lessequals(X29,X30,X31)
      | c_lessequals(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3365]) ).

fof(c_0_6303,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X29,X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_lessequals(X29,X30,X31)
      | c_lessequals(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3366]) ).

fof(c_0_6304,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X16,c_insert(X15,c_emptyset,X17),tc_set(X17))
      | c_insert(X15,X16,X17) = c_insert(X15,c_emptyset,X17) ),
    inference(variable_rename,[status(thm)],[c_0_3367]) ).

fof(c_0_6305,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X16,c_insert(X15,c_emptyset,X17),tc_set(X17))
      | c_insert(X15,c_emptyset,X17) = c_insert(X15,X16,X17) ),
    inference(variable_rename,[status(thm)],[c_0_3368]) ).

fof(c_0_6306,plain,
    ! [X5,X6,X7] :
      ( ~ class_Numeral_Onumber__ring(X7)
      | ~ class_Ring__and__Field_Oordered__idom(X7)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(X6)),X7),X7)
      | ~ c_lessequals(c_Numeral_Onumber__of(X6,X7),c_Numeral_Onumber__of(X5,X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_3369]) ).

fof(c_0_6307,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,c_union(X17,X16,X18),X18)
      | c_in(X15,X16,X18)
      | c_in(X15,X17,X18) ),
    inference(variable_rename,[status(thm)],[c_0_3370]) ).

fof(c_0_6308,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_less(X31,X30,X32)
      | c_less(c_plus(X31,X29,X32),c_plus(X30,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3371]) ).

fof(c_0_6309,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_less(X31,X30,X32)
      | c_less(c_plus(X29,X31,X32),c_plus(X29,X30,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3372]) ).

fof(c_0_6310,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_lessequals(X31,X30,X32)
      | c_lessequals(c_plus(X31,X29,X32),c_plus(X30,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3373]) ).

fof(c_0_6311,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X32)
      | ~ c_lessequals(X31,X30,X32)
      | c_lessequals(c_plus(X29,X31,X32),c_plus(X29,X30,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3374]) ).

fof(c_0_6312,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_lessequals(X35,X34,tc_set(X37))
      | ~ c_lessequals(X36,X34,tc_set(X37))
      | c_lessequals(c_union(X36,X35,X37),X34,tc_set(X37)) ),
    inference(variable_rename,[status(thm)],[c_0_3375]) ).

fof(c_0_6313,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_lessequals(X34,X35,tc_set(X37))
      | ~ c_lessequals(X34,X36,tc_set(X37))
      | c_lessequals(X34,c_inter(X36,X35,X37),tc_set(X37)) ),
    inference(variable_rename,[status(thm)],[c_0_3376]) ).

fof(c_0_6314,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X16,X18)
      | ~ c_in(X15,c_minus(X17,X16,tc_set(X18)),X18) ),
    inference(variable_rename,[status(thm)],[c_0_3377]) ).

fof(c_0_6315,plain,
    ! [X28,X29,X30,X31] :
      ( ~ c_in(c_List_Olist_OCons(X28,X29,X31),c_List_Olists(X30,X31),tc_List_Olist(X31))
      | c_in(X28,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3378]) ).

fof(c_0_6316,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_lessequals(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15)
      | c_Numeral_Onumber__of(X14,tc_nat) != c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3379]) ).

fof(c_0_6317,plain,
    ! [X12,X13,X14] : c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X12,X14,X13),X14,X13) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_3380]) ).

fof(c_0_6318,plain,
    ! [X12,X13,X14] : c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X12,X14,X13),X14,X13) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_3381]) ).

fof(c_0_6319,plain,
    ! [X22,X23,X24] :
      ( ~ c_in(X22,c_Finite__Set_OFinites,tc_set(X24))
      | ~ c_in(X23,c_Finite__Set_OFinites,tc_set(X24))
      | c_in(c_union(X23,X22,X24),c_Finite__Set_OFinites,tc_set(X24)) ),
    inference(variable_rename,[status(thm)],[c_0_3382]) ).

fof(c_0_6320,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_lessequals(X13,c_0,X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15)
      | c_Numeral_Onumber__of(X14,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3383]) ).

fof(c_0_6321,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X85),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3384]) ).

fof(c_0_6322,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X16,X18)
      | ~ c_lessequals(X17,X16,tc_set(X18))
      | c_lessequals(c_insert(X15,X17,X18),X16,tc_set(X18)) ),
    inference(variable_rename,[status(thm)],[c_0_3385]) ).

fof(c_0_6323,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber(X14)
      | ~ class_Power_Orecpower(X14)
      | c_Nat_Opower(c_Numeral_Onumber__of(X13,X14),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X14) = c_times(c_Numeral_Onumber__of(X13,X14),c_Numeral_Onumber__of(X13,X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_3386]) ).

fof(c_0_6324,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,c_plus(X24,X23,tc_nat),tc_nat)
      | c_less(c_0,X23,tc_nat)
      | c_less(c_0,X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3387]) ).

fof(c_0_6325,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,X29,X31)
      | ~ c_less(c_0,X30,X31)
      | c_less(c_1,c_divide(X29,X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3388]) ).

fof(c_0_6326,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,X30,X31)
      | ~ c_less(X30,c_0,X31)
      | c_less(c_1,c_divide(X29,X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3389]) ).

fof(c_0_6327,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_lessequals(X30,X29,X31)
      | c_lessequals(c_1,c_divide(X29,X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3390]) ).

fof(c_0_6328,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_lessequals(X29,X30,X31)
      | c_lessequals(c_1,c_divide(X29,X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3391]) ).

fof(c_0_6329,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X29,X30,X31)
      | ~ c_less(c_0,X30,X31)
      | c_less(c_divide(X29,X30,X31),c_1,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3392]) ).

fof(c_0_6330,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,X29,X31)
      | ~ c_less(X30,c_0,X31)
      | c_less(c_divide(X29,X30,X31),c_1,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3393]) ).

fof(c_0_6331,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(c_0,X30,X31)
      | ~ c_lessequals(X29,X30,X31)
      | c_lessequals(c_divide(X29,X30,X31),c_1,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3394]) ).

fof(c_0_6332,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | ~ c_less(X30,c_0,X31)
      | ~ c_lessequals(X30,X29,X31)
      | c_lessequals(c_divide(X29,X30,X31),c_1,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3395]) ).

fof(c_0_6333,plain,
    ! [X23,X24,X25] :
      ( ~ c_less(X24,X23,tc_nat)
      | c_less(c_plus(X25,X24,tc_nat),c_plus(X25,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3396])])]) ).

fof(c_0_6334,plain,
    ! [X23,X24,X25] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_lessequals(c_plus(X25,X24,tc_nat),c_plus(X25,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3397])])]) ).

fof(c_0_6335,plain,
    ! [X23,X24,X25] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_lessequals(c_times(X24,X25,tc_nat),c_times(X23,X25,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3398])])]) ).

fof(c_0_6336,plain,
    ! [X23,X24,X25] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_lessequals(c_times(X25,X24,tc_nat),c_times(X25,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3399])])]) ).

fof(c_0_6337,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_in(c_Main_OMin__gr__iff__1(X16,X15,X17),X16,X17)
      | c_less(X15,c_Finite__Set_OMin(X16,X17),X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3400]) ).

fof(c_0_6338,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_in(c_Main_OMin__ge__iff__1(X16,X15,X17),X16,X17)
      | c_lessequals(X15,c_Finite__Set_OMin(X16,X17),X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3401]) ).

fof(c_0_6339,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_in(c_Main_OMax__less__iff__1(X16,X15,X17),X16,X17)
      | c_less(c_Finite__Set_OMax(X16,X17),X15,X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3402]) ).

fof(c_0_6340,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_in(c_Main_OMax__le__iff__1(X16,X15,X17),X16,X17)
      | c_lessequals(c_Finite__Set_OMax(X16,X17),X15,X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3403]) ).

fof(c_0_6341,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_OHPair(X91,X90),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X91,X90)),c_Message_Oanalz(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3404]) ).

fof(c_0_6342,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_less(X47,X45,X48)
      | ~ c_less(X46,X47,X48)
      | c_in(X47,c_SetInterval_OgreaterThanLessThan(X46,X45,X48),X48) ),
    inference(variable_rename,[status(thm)],[c_0_3405]) ).

fof(c_0_6343,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_less(X46,X47,X48)
      | ~ c_lessequals(X47,X45,X48)
      | c_in(X47,c_SetInterval_OgreaterThanAtMost(X46,X45,X48),X48) ),
    inference(variable_rename,[status(thm)],[c_0_3406]) ).

fof(c_0_6344,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_less(X47,X45,X48)
      | ~ c_lessequals(X46,X47,X48)
      | c_in(X47,c_SetInterval_OatLeastLessThan(X46,X45,X48),X48) ),
    inference(variable_rename,[status(thm)],[c_0_3407]) ).

fof(c_0_6345,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_lessequals(X47,X45,X48)
      | ~ c_lessequals(X46,X47,X48)
      | c_in(X47,c_SetInterval_OatLeastAtMost(X46,X45,X48),X48) ),
    inference(variable_rename,[status(thm)],[c_0_3408]) ).

fof(c_0_6346,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_lessequals(X51,X50,X53)
      | ~ c_lessequals(X52,X50,X53)
      | c_lessequals(c_Orderings_Omax(X52,X51,X53),X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3409]) ).

fof(c_0_6347,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_lessequals(X52,X50,X53)
      | ~ c_lessequals(X52,X51,X53)
      | c_lessequals(X52,c_Orderings_Omin(X51,X50,X53),X53) ),
    inference(variable_rename,[status(thm)],[c_0_3410]) ).

fof(c_0_6348,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_less(X50,X51,X53)
      | ~ c_less(X50,X52,X53)
      | c_less(X50,c_Orderings_Omin(X52,X51,X53),X53) ),
    inference(variable_rename,[status(thm)],[c_0_3411]) ).

fof(c_0_6349,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_less(X51,X50,X53)
      | ~ c_less(X52,X50,X53)
      | c_less(c_Orderings_Omax(X52,X51,X53),X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3412]) ).

fof(c_0_6350,plain,
    ! [X25,X26,X27] :
      ( ~ c_in(c_Main_Oin__listsI__1(X26,X25,X27),X26,X27)
      | c_in(X25,c_List_Olists(X26,X27),tc_List_Olist(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_3413]) ).

fof(c_0_6351,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Osynth(c_Message_Oanalz(X91)),tc_Message_Omsg)
      | c_Message_Osynth(c_Message_Oanalz(c_insert(X90,X91,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X91)) ),
    inference(variable_rename,[status(thm)],[c_0_3414]) ).

fof(c_0_6352,plain,
    ! [X20,X21,X22,X23] :
      ( ~ c_in(X20,X21,X23)
      | c_emptyset != c_inter(c_insert(X20,X22,X23),X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_3415]) ).

fof(c_0_6353,plain,
    ! [X20,X21,X22,X23] :
      ( ~ c_in(X20,X21,X23)
      | c_inter(c_insert(X20,X22,X23),X21,X23) != c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3416]) ).

fof(c_0_6354,plain,
    ! [X29,X30,X31,X32] :
      ( ~ c_in(X29,X31,X32)
      | c_emptyset != c_inter(X31,c_insert(X29,X30,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3417]) ).

fof(c_0_6355,plain,
    ! [X20,X21,X22,X23] :
      ( ~ c_in(X20,X21,X23)
      | c_inter(X21,c_insert(X20,X22,X23),X23) != c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3418]) ).

fof(c_0_6356,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_less(c_0,X13,X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15) ),
    inference(variable_rename,[status(thm)],[c_0_3419]) ).

fof(c_0_6357,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_lessequals(c_0,X13,X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15) ),
    inference(variable_rename,[status(thm)],[c_0_3420]) ).

fof(c_0_6358,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_less(X13,c_0,X15)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_less(c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),c_0,X15) ),
    inference(variable_rename,[status(thm)],[c_0_3421]) ).

fof(c_0_6359,plain,
    ! [X23,X24] :
      ( ~ class_Power_Orecpower(X24)
      | ~ class_Ring__and__Field_Oordered__idom(X24)
      | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X24),X23,X24),X24)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3422]) ).

fof(c_0_6360,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Ofield(X32)
      | X29 = c_0
      | c_divide(c_times(X31,X29,X32),c_times(X30,X29,X32),X32) = c_divide(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3423]) ).

fof(c_0_6361,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Ofield(X32)
      | X29 = c_0
      | c_divide(c_times(X29,X31,X32),c_times(X29,X30,X32),X32) = c_divide(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3424]) ).

fof(c_0_6362,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X31)
      | c_HOL_Oabs(c_plus(c_HOL_Oabs(X30,X31),c_HOL_Oabs(X29,X31),X31),X31) = c_plus(c_HOL_Oabs(X30,X31),c_HOL_Oabs(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3425]) ).

fof(c_0_6363,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Ofield(X32)
      | c_divide(X31,c_divide(X30,X29,X32),X32) = c_divide(c_times(X31,X29,X32),X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3426]) ).

fof(c_0_6364,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Ofield(X32)
      | c_divide(c_divide(X31,X30,X32),X29,X32) = c_divide(X31,c_times(X30,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3427]) ).

fof(c_0_6365,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X31)
      | ~ c_in(X29,c_IntDef_ONats,X31)
      | ~ c_in(X30,c_IntDef_ONats,X31)
      | c_in(c_times(X30,X29,X31),c_IntDef_ONats,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3428]) ).

fof(c_0_6366,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X31)
      | ~ c_in(X29,c_IntDef_ONats,X31)
      | ~ c_in(X30,c_IntDef_ONats,X31)
      | c_in(c_plus(X30,X29,X31),c_IntDef_ONats,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3429]) ).

fof(c_0_6367,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X31)
      | ~ c_in(X29,c_IntDef_OInts,X31)
      | ~ c_in(X30,c_IntDef_OInts,X31)
      | c_in(c_times(X30,X29,X31),c_IntDef_OInts,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3430]) ).

fof(c_0_6368,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X31)
      | ~ c_in(X29,c_IntDef_OInts,X31)
      | ~ c_in(X30,c_IntDef_OInts,X31)
      | c_in(c_minus(X30,X29,X31),c_IntDef_OInts,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3431]) ).

fof(c_0_6369,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X31)
      | ~ c_in(X29,c_IntDef_OInts,X31)
      | ~ c_in(X30,c_IntDef_OInts,X31)
      | c_in(c_plus(X30,X29,X31),c_IntDef_OInts,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3432]) ).

fof(c_0_6370,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X5,X6),X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X5)),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3433]) ).

fof(c_0_6371,plain,
    ! [X34,X35,X36] :
      ( ~ c_in(X35,c_Main_OInter__iff__1(X35,X34,X36),X36)
      | c_in(X35,c_Inter(X34,X36),X36) ),
    inference(variable_rename,[status(thm)],[c_0_3434]) ).

fof(c_0_6372,plain,
    ! [X34,X35,X36] :
      ( ~ c_in(X35,c_Main_OInterI__1(X35,X34,X36),X36)
      | c_in(X35,c_Inter(X34,X36),X36) ),
    inference(variable_rename,[status(thm)],[c_0_3435]) ).

fof(c_0_6373,plain,
    ! [X27,X28,X29] :
      ( ~ c_List_Odistinct(X27,X29)
      | ~ c_List_Odistinct(X28,X29)
      | c_inter(c_List_Oset(X28,X29),c_List_Oset(X27,X29),X29) != c_emptyset
      | c_List_Odistinct(c_append(X28,X27,X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_3436]) ).

fof(c_0_6374,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X16,X18)
      | ~ c_in(X15,X17,X18)
      | c_in(X15,c_inter(X17,X16,X18),X18) ),
    inference(variable_rename,[status(thm)],[c_0_3437]) ).

fof(c_0_6375,plain,
    ! [X49,X50] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X50,tc_nat),c_Numeral_Onumber__of(X49,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_nat),tc_IntDef_Oint)) ),
    inference(variable_rename,[status(thm)],[c_0_3438]) ).

fof(c_0_6376,plain,
    ! [X85,X86] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    inference(variable_rename,[status(thm)],[c_0_3439]) ).

fof(c_0_6377,plain,
    ! [X25,X26,X27] :
      ( ~ c_List_Odistinct(X25,X27)
      | c_List_Oset(c_List_Oremove1(X26,X25,X27),X27) = c_minus(c_List_Oset(X25,X27),c_insert(X26,c_emptyset,X27),tc_set(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_3440]) ).

fof(c_0_6378,plain,
    ! [X29,X30,X31,X32] :
      ( c_insert(X30,X31,X32) != c_insert(X29,c_emptyset,X32)
      | c_lessequals(X31,c_insert(X29,c_emptyset,X32),tc_set(X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3441]) ).

fof(c_0_6379,plain,
    ! [X29,X30,X31,X32] :
      ( c_insert(X29,c_emptyset,X32) != c_insert(X30,X31,X32)
      | c_lessequals(X31,c_insert(X29,c_emptyset,X32),tc_set(X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3442]) ).

fof(c_0_6380,plain,
    ! [X15,X16] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_set(X16)))
      | ~ c_in(c_Main_Ofinite__Union__1(X15,X16),c_Finite__Set_OFinites,tc_set(X16))
      | c_in(c_Union(X15,X16),c_Finite__Set_OFinites,tc_set(X16)) ),
    inference(variable_rename,[status(thm)],[c_0_3443]) ).

fof(c_0_6381,plain,
    ! [X23,X24,X25] : c_minus(c_minus(c_Suc(X24),X23,tc_nat),c_Suc(X25),tc_nat) = c_minus(c_minus(X24,X23,tc_nat),X25,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3444]) ).

fof(c_0_6382,plain,
    ! [X25,X26,X27] :
      ( ~ c_less(X26,c_Nat_Osize(X25,tc_List_Olist(X27)),tc_nat)
      | c_in(c_List_Onth(X25,X26,X27),c_List_Oset(X25,X27),X27) ),
    inference(variable_rename,[status(thm)],[c_0_3445]) ).

fof(c_0_6383,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Ofield(X32)
      | c_times(c_divide(X30,X29,X32),X31,X32) = c_divide(c_times(X30,X31,X32),X29,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3446]) ).

fof(c_0_6384,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Ofield(X32)
      | c_times(X31,c_divide(X30,X29,X32),X32) = c_divide(c_times(X31,X30,X32),X29,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3447]) ).

fof(c_0_6385,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_less(c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X50,X51)
      | c_less(c_uminus(X50,X51),c_Numeral_Onumber__of(X49,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_3448]) ).

fof(c_0_6386,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X50,X51)
      | c_lessequals(c_uminus(X50,X51),c_Numeral_Onumber__of(X49,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_3449]) ).

fof(c_0_6387,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_less(X50,c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X51)
      | c_less(c_Numeral_Onumber__of(X49,X51),c_uminus(X50,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_3450]) ).

fof(c_0_6388,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_lessequals(X50,c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X51)
      | c_lessequals(c_Numeral_Onumber__of(X49,X51),c_uminus(X50,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_3451]) ).

fof(c_0_6389,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X5)),X6),X6)
      | c_1 = c_Numeral_Onumber__of(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3452]) ).

fof(c_0_6390,plain,
    ! [X25,X26,X27] : c_List_Olast(c_append(X26,c_List_Olist_OCons(X25,c_List_Olist_ONil,X27),X27),X27) = X25,
    inference(variable_rename,[status(thm)],[c_0_3453]) ).

fof(c_0_6391,plain,
    ! [X5,X6,X7] : c_List_Obutlast(c_append(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil,X7),X7),X7) = X5,
    inference(variable_rename,[status(thm)],[c_0_3454]) ).

fof(c_0_6392,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(X15,c_Relation_Odiag(X16,X17),tc_prod(X17,X17))
      | c_in(c_Main_OdiagE__1(X16,X15,X17),X16,X17) ),
    inference(variable_rename,[status(thm)],[c_0_3455]) ).

fof(c_0_6393,plain,
    ! [X25,X26,X27,X28] : c_List_Otake(c_Suc(X27),c_List_Olist_OCons(X26,X25,X28),X28) = c_List_Olist_OCons(X26,c_List_Otake(X27,X25,X28),X28),
    inference(variable_rename,[status(thm)],[c_0_3456]) ).

fof(c_0_6394,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,c_minus(X17,X16,tc_set(X18)),X18)
      | c_in(X15,X17,X18) ),
    inference(variable_rename,[status(thm)],[c_0_3457]) ).

fof(c_0_6395,plain,
    ! [X15,X16,X17] : c_Relation_OImage(c_Relation_Odiag(X16,X17),X15,X17,X17) = c_inter(X16,X15,X17),
    inference(variable_rename,[status(thm)],[c_0_3458]) ).

fof(c_0_6396,plain,
    ! [X3,X4] :
      ( ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | ~ c_in(X4,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | c_IntDef_OAbs__Integ(X4) != c_IntDef_OAbs__Integ(X3)
      | X4 = X3 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3459])])]) ).

fof(c_0_6397,plain,
    ! [X104,X105,X106] :
      ( ~ c_in(X106,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X106,X105),X104,tc_Event_Oevent)) = c_insert(X105,c_Event_Oknows(c_Message_Oagent_OSpy,X104),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3460]) ).

fof(c_0_6398,plain,
    ! [X43,X44,X45,X46] :
      ( X45 = X43
      | c_List_Oremove1(X45,c_List_Olist_OCons(X43,X44,X46),X46) = c_List_Olist_OCons(X43,c_List_Oremove1(X45,X44,X46),X46) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3461])])]) ).

fof(c_0_6399,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_lessequals(c_insert(X15,X17,X18),X16,tc_set(X18))
      | c_lessequals(X17,X16,tc_set(X18)) ),
    inference(variable_rename,[status(thm)],[c_0_3462]) ).

fof(c_0_6400,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_lessequals(c_union(X36,X35,X37),X34,tc_set(X37))
      | c_lessequals(X35,X34,tc_set(X37)) ),
    inference(variable_rename,[status(thm)],[c_0_3463]) ).

fof(c_0_6401,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_lessequals(c_union(X36,X35,X37),X34,tc_set(X37))
      | c_lessequals(X36,X34,tc_set(X37)) ),
    inference(variable_rename,[status(thm)],[c_0_3464]) ).

fof(c_0_6402,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_lessequals(X34,c_inter(X36,X35,X37),tc_set(X37))
      | c_lessequals(X34,X35,tc_set(X37)) ),
    inference(variable_rename,[status(thm)],[c_0_3465]) ).

fof(c_0_6403,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_lessequals(X34,c_inter(X36,X35,X37),tc_set(X37))
      | c_lessequals(X34,X36,tc_set(X37)) ),
    inference(variable_rename,[status(thm)],[c_0_3466]) ).

fof(c_0_6404,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(c_1,X23,tc_nat)
      | ~ c_lessequals(c_1,X24,tc_nat)
      | c_lessequals(c_Suc(c_0),c_times(X24,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3467])])]) ).

fof(c_0_6405,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(X90,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | ~ c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3468]) ).

fof(c_0_6406,plain,
    ! [X94,X95,X96] :
      ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X95)),c_Message_Oanalz(X96),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X95,X94),c_Message_Oanalz(X96),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3469]) ).

fof(c_0_6407,plain,
    ! [X20,X21,X22,X23] : c_union(X22,c_insert(X20,X21,X23),X23) = c_insert(X20,c_union(X22,X21,X23),X23),
    inference(variable_rename,[status(thm)],[c_0_3470]) ).

fof(c_0_6408,plain,
    ! [X34,X35,X36,X37] : c_union(c_insert(X34,X36,X37),X35,X37) = c_insert(X34,c_union(X36,X35,X37),X37),
    inference(variable_rename,[status(thm)],[c_0_3471]) ).

fof(c_0_6409,plain,
    ! [X43,X44,X45,X46] : c_append(c_List_Olist_OCons(X45,X44,X46),X43,X46) = c_List_Olist_OCons(X45,c_append(X44,X43,X46),X46),
    inference(variable_rename,[status(thm)],[c_0_3472]) ).

fof(c_0_6410,plain,
    ! [X43,X44,X45,X46] : c_List_Oitrev(c_List_Olist_OCons(X45,X44,X46),X43,X46) = c_List_Oitrev(X44,c_List_Olist_OCons(X45,X43,X46),X46),
    inference(variable_rename,[status(thm)],[c_0_3473]) ).

fof(c_0_6411,plain,
    ! [X53,X54,X55,X56] : c_append(c_append(X55,X54,X56),X53,X56) = c_append(X55,c_append(X54,X53,X56),X56),
    inference(variable_rename,[status(thm)],[c_0_3474]) ).

fof(c_0_6412,plain,
    ! [X20,X21,X22] :
      ( ~ c_in(c_insert(X20,X21,X22),c_Finite__Set_OFinites,tc_set(X22))
      | c_in(X21,c_Finite__Set_OFinites,tc_set(X22)) ),
    inference(variable_rename,[status(thm)],[c_0_3475]) ).

fof(c_0_6413,plain,
    ! [X22,X23,X24] :
      ( ~ c_in(c_union(X23,X22,X24),c_Finite__Set_OFinites,tc_set(X24))
      | c_in(X22,c_Finite__Set_OFinites,tc_set(X24)) ),
    inference(variable_rename,[status(thm)],[c_0_3476]) ).

fof(c_0_6414,plain,
    ! [X22,X23,X24] :
      ( ~ c_in(c_union(X23,X22,X24),c_Finite__Set_OFinites,tc_set(X24))
      | c_in(X23,c_Finite__Set_OFinites,tc_set(X24)) ),
    inference(variable_rename,[status(thm)],[c_0_3477]) ).

fof(c_0_6415,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X24,tc_nat)
      | ~ c_less(c_0,X23,tc_nat)
      | c_less(c_minus(X24,X23,tc_nat),X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3478]) ).

fof(c_0_6416,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X24,tc_nat)
      | ~ c_less(c_1,X23,tc_nat)
      | c_less(c_div(X24,X23,tc_nat),X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3479]) ).

fof(c_0_6417,plain,
    ! [X25,X26,X27,X28] : c_List_Otake(X26,c_List_Otake(X27,X25,X28),X28) = c_List_Otake(c_Orderings_Omin(X26,X27,tc_nat),X25,X28),
    inference(variable_rename,[status(thm)],[c_0_3480]) ).

fof(c_0_6418,plain,
    ! [X45,X46,X47,X48] : c_List_Otake(X47,c_List_Oreplicate(X46,X45,X48),X48) = c_List_Oreplicate(c_Orderings_Omin(X47,X46,tc_nat),X45,X48),
    inference(variable_rename,[status(thm)],[c_0_3481]) ).

fof(c_0_6419,plain,
    ! [X45,X46,X47,X48] : c_List_Odrop(X47,c_List_Oreplicate(X46,X45,X48),X48) = c_List_Oreplicate(c_minus(X46,X47,tc_nat),X45,X48),
    inference(variable_rename,[status(thm)],[c_0_3482]) ).

fof(c_0_6420,plain,
    ! [X25,X26,X27,X28] : c_List_Odrop(X26,c_List_Odrop(X27,X25,X28),X28) = c_List_Odrop(c_plus(X26,X27,tc_nat),X25,X28),
    inference(variable_rename,[status(thm)],[c_0_3483]) ).

fof(c_0_6421,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ class_Orderings_Olinorder(X21)
      | ~ c_less(c_plus(X20,X20,X21),c_0,X21)
      | c_less(X20,c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3484]) ).

fof(c_0_6422,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_lessequals(c_insert(X15,X17,X18),X16,tc_set(X18))
      | c_in(X15,X16,X18) ),
    inference(variable_rename,[status(thm)],[c_0_3485]) ).

fof(c_0_6423,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X23,tc_nat)
      | ~ c_less(c_0,X24,tc_nat)
      | c_less(c_0,c_times(X24,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3486])])]) ).

fof(c_0_6424,plain,
    ! [X26,X27,X28,X29] :
      ( ~ c_in(X26,c_List_Olists(X28,X29),tc_List_Olist(X29))
      | ~ c_in(X27,c_List_Oset(X26,X29),X29)
      | c_in(X27,X28,X29) ),
    inference(variable_rename,[status(thm)],[c_0_3487]) ).

fof(c_0_6425,plain,
    ! [X43,X44,X45] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X44,X43,X45),X45)
      | ~ c_in(X44,c_List_Oset(X43,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_3488]) ).

fof(c_0_6426,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OgreaterThanLessThan(X46,X45,X48),X48)
      | c_less(X47,X45,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3489]) ).

fof(c_0_6427,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OgreaterThanLessThan(X46,X45,X48),X48)
      | c_less(X46,X47,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3490]) ).

fof(c_0_6428,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OgreaterThanAtMost(X46,X45,X48),X48)
      | c_lessequals(X47,X45,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3491]) ).

fof(c_0_6429,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OgreaterThanAtMost(X46,X45,X48),X48)
      | c_less(X46,X47,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3492]) ).

fof(c_0_6430,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OatLeastLessThan(X46,X45,X48),X48)
      | c_less(X47,X45,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3493]) ).

fof(c_0_6431,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OatLeastLessThan(X46,X45,X48),X48)
      | c_lessequals(X46,X47,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3494]) ).

fof(c_0_6432,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OatLeastAtMost(X46,X45,X48),X48)
      | c_lessequals(X47,X45,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3495]) ).

fof(c_0_6433,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Orderings_Oord(X48)
      | ~ c_in(X47,c_SetInterval_OatLeastAtMost(X46,X45,X48),X48)
      | c_lessequals(X46,X47,X48) ),
    inference(variable_rename,[status(thm)],[c_0_3496]) ).

fof(c_0_6434,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_lessequals(c_Orderings_Omax(X52,X51,X53),X50,X53)
      | c_lessequals(X51,X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3497]) ).

fof(c_0_6435,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_lessequals(c_Orderings_Omax(X52,X51,X53),X50,X53)
      | c_lessequals(X52,X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3498]) ).

fof(c_0_6436,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_lessequals(X52,c_Orderings_Omin(X51,X50,X53),X53)
      | c_lessequals(X52,X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3499]) ).

fof(c_0_6437,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_lessequals(X52,c_Orderings_Omin(X51,X50,X53),X53)
      | c_lessequals(X52,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3500]) ).

fof(c_0_6438,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_less(X50,c_Orderings_Omin(X52,X51,X53),X53)
      | c_less(X50,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3501]) ).

fof(c_0_6439,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_less(X50,c_Orderings_Omin(X52,X51,X53),X53)
      | c_less(X50,X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3502]) ).

fof(c_0_6440,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_less(c_Orderings_Omax(X52,X51,X53),X50,X53)
      | c_less(X51,X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3503]) ).

fof(c_0_6441,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | ~ c_less(c_Orderings_Omax(X52,X51,X53),X50,X53)
      | c_less(X52,X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_3504]) ).

fof(c_0_6442,plain,
    ! [X94,X95,X96] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X95,X94),c_Message_Oanalz(X96),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X95)),c_Message_Oanalz(X96),tc_Message_Omsg)
      | c_in(X94,c_Message_Oanalz(X96),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3505]) ).

fof(c_0_6443,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X25)
      | ~ c_lessequals(X23,X24,tc_nat)
      | c_NatArith_Oof__nat(c_minus(X24,X23,tc_nat),X25) = c_minus(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3506]) ).

fof(c_0_6444,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X17,X18)
      | c_in(X15,X16,X18)
      | c_in(X15,c_minus(X17,X16,tc_set(X18)),X18) ),
    inference(variable_rename,[status(thm)],[c_0_3507]) ).

fof(c_0_6445,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(c_Main_OsubsetI__1(X16,X15,X17),X15,X17)
      | c_lessequals(X16,X15,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3508]) ).

fof(c_0_6446,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_less(c_uminus(X50,X51),c_Numeral_Onumber__of(X49,X51),X51)
      | c_less(c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X50,X51) ),
    inference(variable_rename,[status(thm)],[c_0_3509]) ).

fof(c_0_6447,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_lessequals(c_uminus(X50,X51),c_Numeral_Onumber__of(X49,X51),X51)
      | c_lessequals(c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X50,X51) ),
    inference(variable_rename,[status(thm)],[c_0_3510]) ).

fof(c_0_6448,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_less(c_Numeral_Onumber__of(X49,X51),c_uminus(X50,X51),X51)
      | c_less(X50,c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_3511]) ).

fof(c_0_6449,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X51)
      | ~ c_lessequals(c_Numeral_Onumber__of(X49,X51),c_uminus(X50,X51),X51)
      | c_lessequals(X50,c_uminus(c_Numeral_Onumber__of(X49,X51),X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_3512]) ).

fof(c_0_6450,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_less(c_0,c_divide(c_1,X29,X30),X30)
      | c_less(c_0,X29,X30) ),
    inference(variable_rename,[status(thm)],[c_0_3513]) ).

fof(c_0_6451,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_lessequals(c_0,c_divide(c_1,X29,X30),X30)
      | c_lessequals(c_0,X29,X30) ),
    inference(variable_rename,[status(thm)],[c_0_3514]) ).

fof(c_0_6452,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_less(c_divide(c_1,X29,X30),c_0,X30)
      | c_less(X29,c_0,X30) ),
    inference(variable_rename,[status(thm)],[c_0_3515]) ).

fof(c_0_6453,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_lessequals(c_divide(c_1,X29,X30),c_0,X30)
      | c_lessequals(X29,c_0,X30) ),
    inference(variable_rename,[status(thm)],[c_0_3516]) ).

fof(c_0_6454,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X16,X18)
      | c_minus(c_insert(X15,X17,X18),X16,tc_set(X18)) = c_minus(X17,X16,tc_set(X18)) ),
    inference(variable_rename,[status(thm)],[c_0_3517]) ).

fof(c_0_6455,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3518]) ).

fof(c_0_6456,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3519]) ).

fof(c_0_6457,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_less(c_minus(X30,X29,X31),c_0,X31)
      | c_less(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3520]) ).

fof(c_0_6458,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_lessequals(c_minus(X30,X29,X31),c_0,X31)
      | c_lessequals(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3521]) ).

fof(c_0_6459,plain,
    ! [X61,X62,X63] : c_minus(c_minus(X63,X62,tc_nat),X61,tc_nat) = c_minus(X63,c_plus(X62,X61,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3522]) ).

fof(c_0_6460,plain,
    ! [X29,X30] :
      ( X30 = c_0
      | c_div(c_plus(X29,X30,tc_IntDef_Oint),X30,tc_IntDef_Oint) = c_plus(c_div(X29,X30,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3523]) ).

fof(c_0_6461,plain,
    ! [X29,X30] :
      ( X30 = c_0
      | c_div(c_plus(X30,X29,tc_IntDef_Oint),X30,tc_IntDef_Oint) = c_plus(c_div(X29,X30,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3524]) ).

fof(c_0_6462,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X5)),X6),X6)
      | ~ c_lessequals(c_Numeral_Onumber__of(X5,X6),c_0,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3525]) ).

fof(c_0_6463,plain,
    ! [X23,X24,X25] :
      ( c_less(c_0,X25,tc_nat)
      | c_lessequals(c_times(X24,X25,tc_nat),c_times(X23,X25,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3526]) ).

fof(c_0_6464,plain,
    ! [X23,X24,X25] :
      ( c_less(c_0,X25,tc_nat)
      | c_lessequals(c_times(X25,X24,tc_nat),c_times(X25,X23,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3527]) ).

fof(c_0_6465,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | ~ c_lessequals(c_0,c_plus(X20,X20,X21),X21)
      | c_lessequals(c_0,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3528]) ).

fof(c_0_6466,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | ~ c_lessequals(c_plus(X20,X20,X21),c_0,X21)
      | c_lessequals(X20,c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3529]) ).

fof(c_0_6467,plain,
    ! [X29,X30,X31,X32] :
      ( ~ c_in(X30,c_insert(X29,X31,X32),X32)
      | c_in(X30,X31,X32)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_3530]) ).

fof(c_0_6468,plain,
    ! [X43,X44,X45,X46] :
      ( ~ c_List_Oop_Amem(X45,c_List_Olist_OCons(X44,X43,X46),X46)
      | c_List_Oop_Amem(X45,X43,X46)
      | X44 = X45 ),
    inference(variable_rename,[status(thm)],[c_0_3531]) ).

fof(c_0_6469,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3532]) ).

fof(c_0_6470,plain,
    ! [X20,X21,X22,X23] :
      ( c_emptyset != c_inter(c_insert(X20,X22,X23),X21,X23)
      | c_emptyset = c_inter(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_3533]) ).

fof(c_0_6471,plain,
    ! [X20,X21,X22,X23] :
      ( c_inter(c_insert(X20,X22,X23),X21,X23) != c_emptyset
      | c_inter(X22,X21,X23) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3534]) ).

fof(c_0_6472,plain,
    ! [X29,X30,X31,X32] :
      ( c_emptyset != c_inter(X31,c_insert(X29,X30,X32),X32)
      | c_emptyset = c_inter(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_3535]) ).

fof(c_0_6473,plain,
    ! [X20,X21,X22,X23] :
      ( c_inter(X21,c_insert(X20,X22,X23),X23) != c_emptyset
      | c_inter(X21,X22,X23) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3536]) ).

fof(c_0_6474,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,c_inter(X17,X16,X18),X18)
      | c_in(X15,X16,X18) ),
    inference(variable_rename,[status(thm)],[c_0_3537]) ).

fof(c_0_6475,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,c_inter(X17,X16,X18),X18)
      | c_in(X15,X17,X18) ),
    inference(variable_rename,[status(thm)],[c_0_3538]) ).

fof(c_0_6476,plain,
    ! [X23] :
      ( ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X23,tc_IntDef_Oint),tc_IntDef_Oint)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3539]) ).

fof(c_0_6477,plain,
    ! [X2] : c_div(c_plus(X2,X2,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_3540]) ).

fof(c_0_6478,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | c_Numeral_Onumber__of(X5,X6) != c_1
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3541]) ).

fof(c_0_6479,plain,
    ! [X43,X44,X45] : c_List_Orev(c_List_Olist_OCons(X44,X43,X45),X45) = c_append(c_List_Orev(X43,X45),c_List_Olist_OCons(X44,c_List_Olist_ONil,X45),X45),
    inference(variable_rename,[status(thm)],[c_0_3542]) ).

fof(c_0_6480,plain,
    ! [X5,X6,X7] :
      ( ~ class_Numeral_Onumber__ring(X7)
      | ~ class_Ring__and__Field_Oordered__idom(X7)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X6,c_Numeral_Obin__minus(X5)),X7),X7)
      | c_less(c_Numeral_Onumber__of(X6,X7),c_Numeral_Onumber__of(X5,X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_3543]) ).

fof(c_0_6481,plain,
    ! [X85,X86] :
      ( ~ c_less(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3544]) ).

fof(c_0_6482,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(c_Suc(c_0),c_times(X24,X23,tc_nat),tc_nat)
      | c_lessequals(c_1,X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3545])])]) ).

fof(c_0_6483,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(c_Suc(c_0),c_times(X24,X23,tc_nat),tc_nat)
      | c_lessequals(c_1,X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3546]) ).

fof(c_0_6484,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | X16 = c_emptyset
      | c_Finite__Set_OMin(c_insert(X15,X16,X17),X17) = c_Orderings_Omin(X15,c_Finite__Set_OMin(X16,X17),X17) ),
    inference(variable_rename,[status(thm)],[c_0_3547]) ).

fof(c_0_6485,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | X16 = c_emptyset
      | c_Finite__Set_OMax(c_insert(X15,X16,X17),X17) = c_Orderings_Omax(X15,c_Finite__Set_OMax(X16,X17),X17) ),
    inference(variable_rename,[status(thm)],[c_0_3548]) ).

fof(c_0_6486,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OPls)),X6),X6)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3549]) ).

fof(c_0_6487,plain,
    ! [X20,X21,X22,X23] :
      ( c_emptyset != c_inter(X22,X21,X23)
      | c_in(X20,X21,X23)
      | c_emptyset = c_inter(c_insert(X20,X22,X23),X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_3550]) ).

fof(c_0_6488,plain,
    ! [X20,X21,X22,X23] :
      ( c_inter(X22,X21,X23) != c_emptyset
      | c_in(X20,X21,X23)
      | c_inter(c_insert(X20,X22,X23),X21,X23) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3551]) ).

fof(c_0_6489,plain,
    ! [X29,X30,X31,X32] :
      ( c_emptyset != c_inter(X31,X30,X32)
      | c_in(X29,X31,X32)
      | c_emptyset = c_inter(X31,c_insert(X29,X30,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3552]) ).

fof(c_0_6490,plain,
    ! [X20,X21,X22,X23] :
      ( c_inter(X21,X22,X23) != c_emptyset
      | c_in(X20,X21,X23)
      | c_inter(X21,c_insert(X20,X22,X23),X23) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3553]) ).

fof(c_0_6491,plain,
    ! [X45,X46,X47,X48] :
      ( ~ c_less(X47,X46,tc_nat)
      | c_List_Onth(c_List_Otake(X46,X45,X48),X47,X48) = c_List_Onth(X45,X47,X48) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3554])])]) ).

fof(c_0_6492,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_in(X15,X16,X17)
      | c_Finite__Set_Ocard(c_insert(X15,X16,X17),X17) = c_Suc(c_Finite__Set_Ocard(X16,X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3555]) ).

fof(c_0_6493,plain,
    ! [X5,X6,X7] :
      ( ~ class_Numeral_Onumber__ring(X7)
      | ~ class_Ring__and__Field_Oordered__idom(X7)
      | ~ c_less(c_Numeral_Onumber__of(X6,X7),c_Numeral_Onumber__of(X5,X7),X7)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X6,c_Numeral_Obin__minus(X5)),X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_3556]) ).

fof(c_0_6494,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,c_minus(X23,X24,tc_nat),tc_nat)
      | c_less(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3557]) ).

fof(c_0_6495,plain,
    ! [X27,X28,X29] :
      ( ~ c_List_Odistinct(c_append(X28,X27,X29),X29)
      | c_inter(c_List_Oset(X28,X29),c_List_Oset(X27,X29),X29) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3558]) ).

fof(c_0_6496,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_OHPair(X91,X90),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(X90,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3559]) ).

fof(c_0_6497,plain,
    ! [X67,X68,X69,X70] :
      ( c_in(X69,c_List_Oset(X67,X70),X70)
      | c_List_Olist__inter(c_List_Olist_OCons(X69,X68,X70),X67,X70) = c_List_Olist__inter(X68,X67,X70) ),
    inference(variable_rename,[status(thm)],[c_0_3560]) ).

fof(c_0_6498,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,c_times(X24,X23,tc_nat),tc_nat)
      | c_less(c_0,X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3561])])]) ).

fof(c_0_6499,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,c_times(X24,X23,tc_nat),tc_nat)
      | c_less(c_0,X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3562]) ).

fof(c_0_6500,plain,
    ! [X50,X51] :
      ( ~ c_lessequals(X51,c_minus(X50,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(X51,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3563]) ).

fof(c_0_6501,plain,
    ! [X50,X51] :
      ( ~ c_less(X51,c_plus(X50,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(X51,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3564]) ).

fof(c_0_6502,plain,
    ! [X34,X35,X36] :
      ( ~ c_in(X35,c_Union(X34,X36),X36)
      | c_in(c_Main_OUnion__iff__1(X35,X34,X36),X34,tc_set(X36)) ),
    inference(variable_rename,[status(thm)],[c_0_3565]) ).

fof(c_0_6503,plain,
    ! [X34,X35,X36] :
      ( ~ c_in(X35,c_Union(X34,X36),X36)
      | c_in(c_Main_OUnionE__1(X35,X34,X36),X34,tc_set(X36)) ),
    inference(variable_rename,[status(thm)],[c_0_3566]) ).

fof(c_0_6504,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3567])])]) ).

fof(c_0_6505,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3568]) ).

fof(c_0_6506,plain,
    ! [X27,X28,X29,X30] :
      ( c_List_Orev(X29,X30) != c_List_Olist_OCons(X28,X27,X30)
      | X29 = c_append(c_List_Orev(X27,X30),c_List_Olist_OCons(X28,c_List_Olist_ONil,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3569]) ).

fof(c_0_6507,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(c_0,X16,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X15,c_List_Olist_ONil,X17),X16,X17) = c_List_Olist_OCons(X15,c_List_Olist_ONil,X17) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3570])])]) ).

fof(c_0_6508,plain,
    ! [X103,X104] : c_Nat_Osize(c_Message_Omsg_OMPair(X104,X103),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X104,tc_Message_Omsg),c_Nat_Osize(X103,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3571]) ).

fof(c_0_6509,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X5)),X6),X6)
      | c_lessequals(c_Numeral_Onumber__of(X5,X6),c_1,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3572]) ).

fof(c_0_6510,plain,
    ! [X49,X50] : c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X50,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X49,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3573]) ).

fof(c_0_6511,plain,
    ! [X34,X35,X36] :
      ( ~ c_in(X35,c_Union(X34,X36),X36)
      | c_in(X35,c_Main_OUnion__iff__1(X35,X34,X36),X36) ),
    inference(variable_rename,[status(thm)],[c_0_3574]) ).

fof(c_0_6512,plain,
    ! [X34,X35,X36] :
      ( ~ c_in(X35,c_Union(X34,X36),X36)
      | c_in(X35,c_Main_OUnionE__1(X35,X34,X36),X36) ),
    inference(variable_rename,[status(thm)],[c_0_3575]) ).

fof(c_0_6513,plain,
    ! [X13,X14] :
      ( ~ class_Power_Orecpower(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X13,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X13,tc_nat),X14),c_0,X14)
      | c_Numeral_Onumber__of(X13,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3576]) ).

fof(c_0_6514,plain,
    ! [X15,X16] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_set(X16)))
      | c_in(c_Main_Ofinite__Union__1(X15,X16),X15,tc_set(X16))
      | c_in(c_Union(X15,X16),c_Finite__Set_OFinites,tc_set(X16)) ),
    inference(variable_rename,[status(thm)],[c_0_3577]) ).

fof(c_0_6515,plain,
    ! [X61,X62] :
      ( ~ c_lessequals(X62,X61,tc_nat)
      | c_List_Oupt(X62,c_Suc(X61)) = c_append(c_List_Oupt(X62,X61),c_List_Olist_OCons(X61,c_List_Olist_ONil,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3578]) ).

fof(c_0_6516,plain,
    ! [X94,X95] :
      ( ~ c_in(X94,c_Message_OkeysFor(c_Message_Osynth(X95)),tc_nat)
      | c_in(X94,c_Message_OkeysFor(X95),tc_nat)
      | c_in(c_Message_Omsg_OKey(v_sko__uhi(X95,X94)),X95,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3579]) ).

fof(c_0_6517,plain,
    ! [X15,X16,X17,X18] :
      ( c_in(X15,X17,X18)
      | c_minus(X17,c_insert(X15,X16,X18),tc_set(X18)) = c_minus(X17,X16,tc_set(X18)) ),
    inference(variable_rename,[status(thm)],[c_0_3580]) ).

fof(c_0_6518,plain,
    ! [X13,X14] :
      ( ~ c_less(c_0,X13,tc_nat)
      | c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3581])])]) ).

fof(c_0_6519,plain,
    ! [X43,X44,X45] :
      ( c_in(X44,c_List_Oset(X43,X45),X45)
      | c_List_Oremdups(c_List_Olist_OCons(X44,X43,X45),X45) = c_List_Olist_OCons(X44,c_List_Oremdups(X43,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_3582]) ).

fof(c_0_6520,plain,
    ! [X49] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3583]) ).

fof(c_0_6521,plain,
    ! [X104,X105,X106] :
      ( ~ c_in(X106,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X105,X106))),c_Event_Oknows(c_Message_Oagent_OSpy,X104),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3584]) ).

fof(c_0_6522,plain,
    ! [X25,X26,X27] :
      ( ~ c_less(X26,c_Nat_Osize(X25,tc_List_Olist(X27)),tc_nat)
      | c_List_Olast(c_List_Odrop(X26,X25,X27),X27) = c_List_Olast(X25,X27) ),
    inference(variable_rename,[status(thm)],[c_0_3585]) ).

fof(c_0_6523,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15)
      | X13 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3586]) ).

fof(c_0_6524,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_in(X34,X35,tc_set(X37))
      | ~ c_in(X36,c_Inter(X35,X37),X37)
      | c_in(X36,X34,X37) ),
    inference(variable_rename,[status(thm)],[c_0_3587]) ).

fof(c_0_6525,plain,
    ! [X23,X24,X25] :
      ( X24 = c_0
      | c_List_Otl(c_List_Oreplicate(X24,X23,X25),X25) = c_List_Oreplicate(c_minus(X24,c_1,tc_nat),X23,X25) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3588])])]) ).

fof(c_0_6526,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(c_uminus(X16,tc_set(X17)),c_uminus(X15,tc_set(X17)),tc_set(X17))
      | c_lessequals(X15,X16,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3589]) ).

fof(c_0_6527,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(c_times(X30,c_0,X31),c_times(X29,c_0,X31),X31) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3590]) ).

fof(c_0_6528,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(c_times(c_0,X30,X31),c_times(c_0,X29,X31),X31) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3591]) ).

fof(c_0_6529,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15) ),
    inference(variable_rename,[status(thm)],[c_0_3592]) ).

fof(c_0_6530,plain,
    ! [X20,X21,X22] :
      ( ~ class_Numeral_Onumber(X22)
      | ~ class_Ring__and__Field_Odivision__by__zero(X22)
      | ~ class_Ring__and__Field_Ofield(X22)
      | X21 = c_divide(c_times(X21,c_Numeral_Onumber__of(X20,X22),X22),c_Numeral_Onumber__of(X20,X22),X22)
      | c_Numeral_Onumber__of(X20,X22) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3593]) ).

fof(c_0_6531,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_Numeral_Onumber__of(X29,X31) = c_0
      | c_times(c_divide(X30,c_Numeral_Onumber__of(X29,X31),X31),c_Numeral_Onumber__of(X29,X31),X31) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_3594]) ).

fof(c_0_6532,plain,
    ! [X20,X21,X22] :
      ( ~ class_Numeral_Onumber(X22)
      | ~ class_Ring__and__Field_Odivision__by__zero(X22)
      | ~ class_Ring__and__Field_Ofield(X22)
      | c_Numeral_Onumber__of(X20,X22) = c_0
      | c_divide(c_times(X21,c_Numeral_Onumber__of(X20,X22),X22),c_Numeral_Onumber__of(X20,X22),X22) = X21 ),
    inference(variable_rename,[status(thm)],[c_0_3595]) ).

fof(c_0_6533,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | X30 = c_times(c_divide(X30,c_Numeral_Onumber__of(X29,X31),X31),c_Numeral_Onumber__of(X29,X31),X31)
      | c_Numeral_Onumber__of(X29,X31) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3596]) ).

fof(c_0_6534,plain,
    ! [X25,X26,X27] :
      ( c_in(X25,c_List_Olists(X26,X27),tc_List_Olist(X27))
      | c_in(c_Main_Oin__listsI__1(X26,X25,X27),c_List_Oset(X25,X27),X27) ),
    inference(variable_rename,[status(thm)],[c_0_3597]) ).

fof(c_0_6535,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Osynth(X92),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(X92),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X91,X90),X92,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3598]) ).

fof(c_0_6536,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Osynth(X92),tc_Message_Omsg)
      | c_in(X90,c_Message_Osynth(X92),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X91,X90),X92,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3599]) ).

fof(c_0_6537,plain,
    ! [X94,X95,X96] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X95,X94),c_Message_Osynth(X96),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X95),X96,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3600]) ).

fof(c_0_6538,plain,
    ! [X94,X95,X96] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X95,X94),c_Message_Osynth(X96),tc_Message_Omsg)
      | c_in(X94,c_Message_Osynth(X96),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3601]) ).

fof(c_0_6539,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3602]) ).

fof(c_0_6540,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(X90,c_Message_Osynth(X92),tc_Message_Omsg)
      | ~ c_in(X91,c_Message_Osynth(X92),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Osynth(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3603]) ).

fof(c_0_6541,plain,
    ! [X94,X95,X96] :
      ( ~ c_in(X94,c_Message_Osynth(X96),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(X95),X96,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X95,X94),c_Message_Osynth(X96),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3604]) ).

fof(c_0_6542,plain,
    ! [X23,X24,X25,X26] :
      ( ~ class_Power_Orecpower(X26)
      | ~ class_Ring__and__Field_Oordered__semidom(X26)
      | ~ c_less(c_1,X25,X26)
      | c_Nat_Opower(X25,X24,X26) != c_Nat_Opower(X25,X23,X26)
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3605]) ).

fof(c_0_6543,plain,
    ! [X48,X49,X50] :
      ( ~ c_in(X49,c_Finite__Set_OFinites,tc_set(X50))
      | c_in(c_minus(X49,X48,tc_set(X50)),c_Finite__Set_OFinites,tc_set(X50)) ),
    inference(variable_rename,[status(thm)],[c_0_3606]) ).

fof(c_0_6544,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X15,X16,X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | X16 = c_emptyset
      | c_Orderings_Omax(X15,c_Finite__Set_OMin(X16,X17),X17) = X15 ),
    inference(variable_rename,[status(thm)],[c_0_3607]) ).

fof(c_0_6545,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X15,X16,X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | X16 = c_emptyset
      | c_Orderings_Omin(X15,c_Finite__Set_OMax(X16,X17),X17) = X15 ),
    inference(variable_rename,[status(thm)],[c_0_3608]) ).

fof(c_0_6546,plain,
    ! [X94,X95,X96] :
      ( ~ c_in(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X95,X94),c_Message_Osynth(X96),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X95),X96,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3609]) ).

fof(c_0_6547,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X15,X16,X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_lessequals(c_Finite__Set_OMin(X16,X17),X15,X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3610]) ).

fof(c_0_6548,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | ~ c_in(X15,X16,X17)
      | ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_lessequals(X15,c_Finite__Set_OMax(X16,X17),X17)
      | X16 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3611]) ).

fof(c_0_6549,plain,
    ! [X23,X24,X25] : c_append(c_List_Otake(X24,X23,X25),c_List_Odrop(X24,X23,X25),X25) = X23,
    inference(variable_rename,[status(thm)],[c_0_3612]) ).

fof(c_0_6550,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X5)),X6),X6)
      | c_less(c_0,c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3613]) ).

fof(c_0_6551,plain,
    ! [X85] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    inference(variable_rename,[status(thm)],[c_0_3614]) ).

fof(c_0_6552,plain,
    ! [X34,X35,X36,X37] :
      ( ~ c_in(X36,X34,X37)
      | ~ c_in(X34,X35,tc_set(X37))
      | c_in(X36,c_Union(X35,X37),X37) ),
    inference(variable_rename,[status(thm)],[c_0_3615]) ).

fof(c_0_6553,plain,
    ! [X43,X44,X45] :
      ( ~ c_in(X44,c_List_Oset(X43,X45),X45)
      | c_List_Oremdups(c_List_Olist_OCons(X44,X43,X45),X45) = c_List_Oremdups(X43,X45) ),
    inference(variable_rename,[status(thm)],[c_0_3616]) ).

fof(c_0_6554,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X85),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3617]) ).

fof(c_0_6555,plain,
    ! [X22,X23,X24] :
      ( ~ c_in(X22,c_Finite__Set_OFinites,tc_set(X24))
      | c_in(c_inter(X23,X22,X24),c_Finite__Set_OFinites,tc_set(X24)) ),
    inference(variable_rename,[status(thm)],[c_0_3618]) ).

fof(c_0_6556,plain,
    ! [X22,X23,X24] :
      ( ~ c_in(X23,c_Finite__Set_OFinites,tc_set(X24))
      | c_in(c_inter(X23,X22,X24),c_Finite__Set_OFinites,tc_set(X24)) ),
    inference(variable_rename,[status(thm)],[c_0_3619]) ).

fof(c_0_6557,plain,
    ! [X20,X21,X22] :
      ( ~ c_in(X21,c_Finite__Set_OFinites,tc_set(X22))
      | c_in(c_insert(X20,X21,X22),c_Finite__Set_OFinites,tc_set(X22)) ),
    inference(variable_rename,[status(thm)],[c_0_3620]) ).

fof(c_0_6558,plain,
    ! [X49,X50,X51,X52] :
      ( c_Numeral_Onumber__of(X51,tc_nat) != c_0
      | c_List_Odrop(c_Numeral_Onumber__of(X51,tc_nat),c_List_Olist_OCons(X50,X49,X52),X52) = c_List_Olist_OCons(X50,X49,X52) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3621])])]) ).

fof(c_0_6559,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ class_Orderings_Olinorder(X21)
      | ~ c_less(X20,c_0,X21)
      | c_less(c_plus(X20,X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3622]) ).

fof(c_0_6560,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber(X14)
      | ~ class_Ring__and__Field_Odivision__by__zero(X14)
      | ~ class_Ring__and__Field_Ofield(X14)
      | c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(X13,X14),X14),c_Numeral_Onumber__of(X13,X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_3623]) ).

fof(c_0_6561,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber(X14)
      | ~ class_Ring__and__Field_Odivision__by__zero(X14)
      | ~ class_Ring__and__Field_Ofield(X14)
      | c_divide(c_times(c_0,c_Numeral_Onumber__of(X13,X14),X14),c_Numeral_Onumber__of(X13,X14),X14) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3624]) ).

fof(c_0_6562,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OPls)),X6),X6)
      | c_less(c_Numeral_Onumber__of(X5,X6),c_0,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3625]) ).

fof(c_0_6563,plain,
    ! [X15,X16,X17] : c_uminus(c_union(X16,X15,X17),tc_set(X17)) = c_inter(c_uminus(X16,tc_set(X17)),c_uminus(X15,tc_set(X17)),X17),
    inference(variable_rename,[status(thm)],[c_0_3626]) ).

fof(c_0_6564,plain,
    ! [X15,X16,X17] : c_uminus(c_inter(X16,X15,X17),tc_set(X17)) = c_union(c_uminus(X16,tc_set(X17)),c_uminus(X15,tc_set(X17)),X17),
    inference(variable_rename,[status(thm)],[c_0_3627]) ).

fof(c_0_6565,plain,
    ! [X94,X95] :
      ( c_in(X94,c_Message_OkeysFor(c_Message_Oanalz(X95)),tc_nat)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X94),X95,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X94),c_Message_Oanalz(X95),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3628]) ).

fof(c_0_6566,plain,
    ! [X27,X28,X29] : c_Nat_Osize(c_append(X28,X27,X29),tc_List_Olist(X29)) = c_plus(c_Nat_Osize(X28,tc_List_Olist(X29)),c_Nat_Osize(X27,tc_List_Olist(X29)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3629]) ).

fof(c_0_6567,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_less(c_0,X29,X30)
      | c_less(c_0,c_divide(c_1,X29,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3630]) ).

fof(c_0_6568,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_lessequals(c_0,X29,X30)
      | c_lessequals(c_0,c_divide(c_1,X29,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3631]) ).

fof(c_0_6569,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_less(X29,c_0,X30)
      | c_less(c_divide(c_1,X29,X30),c_0,X30) ),
    inference(variable_rename,[status(thm)],[c_0_3632]) ).

fof(c_0_6570,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | ~ c_lessequals(X29,c_0,X30)
      | c_lessequals(c_divide(c_1,X29,X30),c_0,X30) ),
    inference(variable_rename,[status(thm)],[c_0_3633]) ).

fof(c_0_6571,plain,
    ! [X3,X4] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X4,tc_nat),tc_nat) != c_0
      | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3634]) ).

fof(c_0_6572,plain,
    ! [X3,X4] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X4,tc_nat),tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3635]) ).

fof(c_0_6573,plain,
    ! [X3,X4] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X4,tc_IntDef_Oint),tc_IntDef_Oint) != c_0
      | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3636]) ).

fof(c_0_6574,plain,
    ! [X3,X4] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X4,tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3637]) ).

fof(c_0_6575,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_less(X30,X29,X31)
      | c_less(c_minus(X30,X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3638]) ).

fof(c_0_6576,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_lessequals(X30,X29,X31)
      | c_lessequals(c_minus(X30,X29,X31),c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3639]) ).

fof(c_0_6577,plain,
    ! [X29,X30,X31] :
      ( ~ c_in(X29,c_insert(X30,c_emptyset,X31),X31)
      | X29 = X30 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3640])])]) ).

fof(c_0_6578,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X14,tc_nat),tc_nat)
      | c_Nat_Opower(c_HOL_Oabs(X13,X15),c_Numeral_Onumber__of(X14,tc_nat),X15) = c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15) ),
    inference(variable_rename,[status(thm)],[c_0_3641]) ).

fof(c_0_6579,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | ~ c_lessequals(c_0,X20,X21)
      | c_lessequals(c_0,c_plus(X20,X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_3642]) ).

fof(c_0_6580,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | ~ c_lessequals(X20,c_0,X21)
      | c_lessequals(c_plus(X20,X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3643]) ).

fof(c_0_6581,plain,
    ! [X45,X46] :
      ( ~ c_less(c_0,X45,tc_nat)
      | c_less(c_minus(X45,c_Suc(X46),tc_nat),X45,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3644])])]) ).

fof(c_0_6582,plain,
    ! [X18,X19] :
      ( ~ class_Orderings_Oorder(X19)
      | c_minus(c_insert(X18,c_emptyset,X19),c_SetInterval_OlessThan(X18,X19),tc_set(X19)) = c_insert(X18,c_emptyset,X19) ),
    inference(variable_rename,[status(thm)],[c_0_3645]) ).

fof(c_0_6583,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X5,X6),X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X5)),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3646]) ).

fof(c_0_6584,plain,
    ! [X34,X35,X36] :
      ( c_in(X35,c_Inter(X34,X36),X36)
      | c_in(c_Main_OInter__iff__1(X35,X34,X36),X34,tc_set(X36)) ),
    inference(variable_rename,[status(thm)],[c_0_3647]) ).

fof(c_0_6585,plain,
    ! [X34,X35,X36] :
      ( c_in(X35,c_Inter(X34,X36),X36)
      | c_in(c_Main_OInterI__1(X35,X34,X36),X34,tc_set(X36)) ),
    inference(variable_rename,[status(thm)],[c_0_3648]) ).

fof(c_0_6586,plain,
    ! [X29,X30,X31,X32] :
      ( ~ c_in(X30,X31,X32)
      | c_in(X30,c_insert(X29,X31,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_3649]) ).

fof(c_0_6587,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X16,X18)
      | c_in(X15,c_union(X17,X16,X18),X18) ),
    inference(variable_rename,[status(thm)],[c_0_3650]) ).

fof(c_0_6588,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X17,X18)
      | c_in(X15,c_union(X17,X16,X18),X18) ),
    inference(variable_rename,[status(thm)],[c_0_3651]) ).

fof(c_0_6589,plain,
    ! [X43,X44,X45,X46] :
      ( ~ c_List_Oop_Amem(X45,X43,X46)
      | c_List_Oop_Amem(X45,c_List_Olist_OCons(X44,X43,X46),X46) ),
    inference(variable_rename,[status(thm)],[c_0_3652]) ).

fof(c_0_6590,plain,
    ! [X47,X48,X49] : c_Public_Okeymode_Okeymode__rec(X48,X47,c_Public_Okeymode_OEncryption,X49) = X47,
    inference(variable_rename,[status(thm)],[c_0_3653]) ).

fof(c_0_6591,plain,
    ! [X46,X47,X48] : c_Public_Okeymode_Okeymode__rec(X46,X47,c_Public_Okeymode_OSignature,X48) = X46,
    inference(variable_rename,[status(thm)],[c_0_3654]) ).

fof(c_0_6592,plain,
    ! [X47,X48,X49] : c_Public_Okeymode_Okeymode__case(X48,X47,c_Public_Okeymode_OEncryption,X49) = X47,
    inference(variable_rename,[status(thm)],[c_0_3655]) ).

fof(c_0_6593,plain,
    ! [X46,X47,X48] : c_Public_Okeymode_Okeymode__case(X46,X47,c_Public_Okeymode_OSignature,X48) = X46,
    inference(variable_rename,[status(thm)],[c_0_3656]) ).

fof(c_0_6594,plain,
    ! [X5,X6] : c_Relation_OImage(c_Relation_OId,X5,X6,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_3657]) ).

fof(c_0_6595,plain,
    ! [X47,X48,X49] : c_Numeral_Obit_Obit__rec(X48,X47,c_Numeral_Obit_OB1,X49) = X47,
    inference(variable_rename,[status(thm)],[c_0_3658]) ).

fof(c_0_6596,plain,
    ! [X46,X47,X48] : c_Numeral_Obit_Obit__rec(X46,X47,c_Numeral_Obit_OB0,X48) = X46,
    inference(variable_rename,[status(thm)],[c_0_3659]) ).

fof(c_0_6597,plain,
    ! [X47,X48,X49] : c_Numeral_Obit_Obit__case(X48,X47,c_Numeral_Obit_OB1,X49) = X47,
    inference(variable_rename,[status(thm)],[c_0_3660]) ).

fof(c_0_6598,plain,
    ! [X46,X47,X48] : c_Numeral_Obit_Obit__case(X46,X47,c_Numeral_Obit_OB0,X48) = X46,
    inference(variable_rename,[status(thm)],[c_0_3661]) ).

fof(c_0_6599,plain,
    ! [X47,X48,X49] : c_Extraction_Osumbool_Osumbool__rec(X48,X47,c_Extraction_Osumbool_ORight,X49) = X47,
    inference(variable_rename,[status(thm)],[c_0_3662]) ).

fof(c_0_6600,plain,
    ! [X46,X47,X48] : c_Extraction_Osumbool_Osumbool__rec(X46,X47,c_Extraction_Osumbool_OLeft,X48) = X46,
    inference(variable_rename,[status(thm)],[c_0_3663]) ).

fof(c_0_6601,plain,
    ! [X47,X48,X49] : c_Extraction_Osumbool_Osumbool__case(X48,X47,c_Extraction_Osumbool_ORight,X49) = X47,
    inference(variable_rename,[status(thm)],[c_0_3664]) ).

fof(c_0_6602,plain,
    ! [X46,X47,X48] : c_Extraction_Osumbool_Osumbool__case(X46,X47,c_Extraction_Osumbool_OLeft,X48) = X46,
    inference(variable_rename,[status(thm)],[c_0_3665]) ).

fof(c_0_6603,plain,
    ! [X61,X62] : ~ c_less(c_plus(X61,X62,tc_nat),X62,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3666]) ).

fof(c_0_6604,plain,
    ! [X61,X62] : ~ c_less(c_plus(X62,X61,tc_nat),X62,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3667]) ).

fof(c_0_6605,plain,
    ! [X87,X88,X89] : c_Relation_OImage(X87,c_emptyset,X88,X89) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_3668]) ).

fof(c_0_6606,plain,
    ! [X27,X28,X29] : c_List_Ozip(c_List_Olist_ONil,X27,X29,X28) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_3669]) ).

fof(c_0_6607,plain,
    ! [X84,X85,X86] : c_List_Ozip(X84,c_List_Olist_ONil,X86,X85) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_3670]) ).

fof(c_0_6608,plain,
    ! [X45,X46,X47,X48] :
      ( ~ c_less(X47,X46,tc_nat)
      | c_List_Onth(c_List_Oreplicate(X46,X45,X48),X47,X48) = X45 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3671])])]) ).

fof(c_0_6609,plain,
    ! [X49,X50,X51] : c_List_Olist__update(c_List_Olist_ONil,X50,X49,X51) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_3672]) ).

fof(c_0_6610,plain,
    ! [X12,X13,X14] : c_Datatype__Universe_Ontrunc(c_0,X12,X14,X13) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_3673]) ).

fof(c_0_6611,plain,
    ! [X5,X6] : c_Sum__Type_OPlus(c_UNIV,c_UNIV,X6,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_3674]) ).

fof(c_0_6612,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_less(c_Numeral_Onumber__of(X5,X6),c_0,X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OPls)),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3675]) ).

fof(c_0_6613,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_plus(X24,c_minus(X23,X24,tc_nat),tc_nat) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3676]) ).

fof(c_0_6614,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_plus(c_minus(X23,X24,tc_nat),X24,tc_nat) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3677]) ).

fof(c_0_6615,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_minus(X24,c_minus(X24,X23,tc_nat),tc_nat) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3678]) ).

fof(c_0_6616,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_HOL_Oinverse(c_times(X30,X29,X31),X31) = c_times(c_HOL_Oinverse(X30,X31),c_HOL_Oinverse(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3679]) ).

fof(c_0_6617,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | c_HOL_Oabs(c_divide(X30,X29,X31),X31) = c_divide(c_HOL_Oabs(X30,X31),c_HOL_Oabs(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3680]) ).

fof(c_0_6618,plain,
    ! [X45,X46] :
      ( ~ c_lessequals(c_1,X46,tc_nat)
      | c_lessequals(c_Suc(c_0),c_Nat_Opower(X46,X45,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3681]) ).

fof(c_0_6619,plain,
    ! [X23] :
      ( ~ c_less(c_0,c_Nat_Opower(c_0,X23,tc_nat),tc_nat)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3682]) ).

fof(c_0_6620,plain,
    ! [X13,X14,X15] :
      ( ~ class_Power_Orecpower(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | c_Numeral_Onumber__of(X14,tc_nat) != c_0
      | c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),X15),X15) ),
    inference(variable_rename,[status(thm)],[c_0_3683]) ).

fof(c_0_6621,plain,
    ! [X15,X16,X17] : c_minus(c_minus(X16,X15,tc_set(X17)),X15,tc_set(X17)) = c_minus(X16,X15,tc_set(X17)),
    inference(variable_rename,[status(thm)],[c_0_3684]) ).

fof(c_0_6622,plain,
    ! [X15,X16,X17] : c_Union(c_union(X16,X15,tc_set(X17)),X17) = c_union(c_Union(X16,X17),c_Union(X15,X17),X17),
    inference(variable_rename,[status(thm)],[c_0_3685]) ).

fof(c_0_6623,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | ~ c_lessequals(c_SetInterval_OlessThan(X6,X7),c_SetInterval_OlessThan(X5,X7),tc_set(X7))
      | c_lessequals(X6,X5,X7) ),
    inference(variable_rename,[status(thm)],[c_0_3686]) ).

fof(c_0_6624,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X6,X7),c_SetInterval_OgreaterThan(X5,X7),tc_set(X7))
      | c_lessequals(X5,X6,X7) ),
    inference(variable_rename,[status(thm)],[c_0_3687]) ).

fof(c_0_6625,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Oorder(X7)
      | ~ c_lessequals(c_SetInterval_OatMost(X6,X7),c_SetInterval_OatMost(X5,X7),tc_set(X7))
      | c_lessequals(X6,X5,X7) ),
    inference(variable_rename,[status(thm)],[c_0_3688]) ).

fof(c_0_6626,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Oorder(X7)
      | ~ c_lessequals(c_SetInterval_OatLeast(X6,X7),c_SetInterval_OatLeast(X5,X7),tc_set(X7))
      | c_lessequals(X5,X6,X7) ),
    inference(variable_rename,[status(thm)],[c_0_3689]) ).

fof(c_0_6627,plain,
    ! [X23,X24] :
      ( ~ c_less(X24,X23,tc_nat)
      | c_less(c_0,c_minus(X23,X24,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3690]) ).

fof(c_0_6628,plain,
    ! [X27,X28,X29] : c_List_Oconcat(c_append(X28,X27,tc_List_Olist(X29)),X29) = c_append(c_List_Oconcat(X28,X29),c_List_Oconcat(X27,X29),X29),
    inference(variable_rename,[status(thm)],[c_0_3691]) ).

fof(c_0_6629,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X24,tc_nat)
      | c_div(c_times(X23,X24,tc_nat),X24,tc_nat) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3692]) ).

fof(c_0_6630,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X24,tc_nat)
      | c_div(c_times(X24,X23,tc_nat),X24,tc_nat) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3693]) ).

fof(c_0_6631,plain,
    ! [X5,X6] :
      ( X5 = c_List_Olist_ONil
      | c_append(c_List_Obutlast(X5,X6),c_List_Olist_OCons(c_List_Olast(X5,X6),c_List_Olist_ONil,X6),X6) = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3694])])]) ).

fof(c_0_6632,plain,
    ! [X29,X30] :
      ( ~ c_less(c_0,X29,tc_IntDef_Oint)
      | c_less(c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),X29,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3695])])]) ).

fof(c_0_6633,plain,
    ! [X29,X30] :
      ( ~ c_less(X29,c_0,tc_IntDef_Oint)
      | c_less(X29,c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3696])])]) ).

fof(c_0_6634,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_less(c_Divides_Oop_Amod(X24,X23,tc_nat),X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3697])])]) ).

fof(c_0_6635,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_lessequals(c_Divides_Oop_Amod(X24,X23,tc_nat),X23,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3698])])]) ).

fof(c_0_6636,plain,
    ! [X50,X51] :
      ( ~ c_less(X51,X50,tc_IntDef_Oint)
      | c_lessequals(X51,c_minus(X50,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3699]) ).

fof(c_0_6637,plain,
    ! [X50,X51] :
      ( ~ c_lessequals(X51,X50,tc_IntDef_Oint)
      | c_less(X51,c_plus(X50,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3700]) ).

fof(c_0_6638,plain,
    ! [X5,X6,X7] :
      ( ~ class_Numeral_Onumber__ring(X7)
      | ~ class_Ring__and__Field_Oordered__idom(X7)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(X6)),X7),X7)
      | c_lessequals(c_Numeral_Onumber__of(X6,X7),c_Numeral_Onumber__of(X5,X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_3701]) ).

fof(c_0_6639,plain,
    ! [X55,X56,X57,X58,X59] :
      ( c_Nat_Osize(X58,tc_List_Olist(X59)) != c_Nat_Osize(X57,tc_List_Olist(X59))
      | c_append(X56,X58,X59) != c_append(X55,X57,X59)
      | X58 = X57 ),
    inference(variable_rename,[status(thm)],[c_0_3702]) ).

fof(c_0_6640,plain,
    ! [X55,X56,X57,X58,X59] :
      ( c_Nat_Osize(X58,tc_List_Olist(X59)) != c_Nat_Osize(X57,tc_List_Olist(X59))
      | c_append(X56,X58,X59) != c_append(X55,X57,X59)
      | X56 = X55 ),
    inference(variable_rename,[status(thm)],[c_0_3703]) ).

fof(c_0_6641,plain,
    ! [X55,X56,X57,X58,X59] :
      ( c_Nat_Osize(X56,tc_List_Olist(X59)) != c_Nat_Osize(X55,tc_List_Olist(X59))
      | c_append(X56,X58,X59) != c_append(X55,X57,X59)
      | X58 = X57 ),
    inference(variable_rename,[status(thm)],[c_0_3704]) ).

fof(c_0_6642,plain,
    ! [X55,X56,X57,X58,X59] :
      ( c_Nat_Osize(X56,tc_List_Olist(X59)) != c_Nat_Osize(X55,tc_List_Olist(X59))
      | c_append(X56,X58,X59) != c_append(X55,X57,X59)
      | X56 = X55 ),
    inference(variable_rename,[status(thm)],[c_0_3705]) ).

fof(c_0_6643,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_less(c_0,c_plus(X24,X23,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3706])])]) ).

fof(c_0_6644,plain,
    ! [X23,X24] :
      ( ~ c_less(c_0,X24,tc_nat)
      | c_less(c_0,c_plus(X24,X23,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3707]) ).

fof(c_0_6645,plain,
    ! [X29,X30] :
      ( ~ c_less(c_0,X29,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3708])])]) ).

fof(c_0_6646,plain,
    ! [X29,X30] :
      ( ~ c_less(X29,c_0,tc_IntDef_Oint)
      | c_lessequals(c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3709])])]) ).

fof(c_0_6647,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X15,X17,X18)
      | ~ c_lessequals(X17,X16,tc_set(X18))
      | c_in(X15,X16,X18) ),
    inference(variable_rename,[status(thm)],[c_0_3710]) ).

fof(c_0_6648,plain,
    ! [X23,X24] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X23,X24,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3711]) ).

fof(c_0_6649,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X4,X3,tc_nat),tc_nat)
      | c_less(c_0,X3,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3712])])]) ).

fof(c_0_6650,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X31)
      | c_uminus(c_LOrder_Omeet(X30,X29,X31),X31) = c_LOrder_Ojoin(c_uminus(X30,X31),c_uminus(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3713]) ).

fof(c_0_6651,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X31)
      | c_uminus(c_LOrder_Ojoin(X30,X29,X31),X31) = c_LOrder_Omeet(c_uminus(X30,X31),c_uminus(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3714]) ).

fof(c_0_6652,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Oab__group__add(X31)
      | c_uminus(c_plus(X30,X29,X31),X31) = c_plus(c_uminus(X30,X31),c_uminus(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3715]) ).

fof(c_0_6653,plain,
    ! [X30,X31,X32] :
      ( ~ c_in(X31,X30,tc_prod(X32,X32))
      | c_in(X31,c_Transitive__Closure_Ortrancl(X30,X32),tc_prod(X32,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_3716]) ).

fof(c_0_6654,plain,
    ! [X15,X16,X17] : c_Pow(c_inter(X16,X15,X17),X17) = c_inter(c_Pow(X16,X17),c_Pow(X15,X17),tc_set(X17)),
    inference(variable_rename,[status(thm)],[c_0_3717]) ).

fof(c_0_6655,plain,
    ! [X15,X16,X17] : c_List_Olists(c_inter(X16,X15,X17),X17) = c_inter(c_List_Olists(X16,X17),c_List_Olists(X15,X17),tc_List_Olist(X17)),
    inference(variable_rename,[status(thm)],[c_0_3718]) ).

fof(c_0_6656,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X15,X16,tc_set(X17))
      | c_lessequals(c_uminus(X16,tc_set(X17)),c_uminus(X15,tc_set(X17)),tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3719]) ).

fof(c_0_6657,plain,
    ! [X104,X105,X106] :
      ( c_in(X106,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X106,X105),X104,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X104) ),
    inference(variable_rename,[status(thm)],[c_0_3720]) ).

fof(c_0_6658,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(X15,X16,X17)
      | ~ c_in(X15,c_uminus(X16,tc_set(X17)),X17) ),
    inference(variable_rename,[status(thm)],[c_0_3721]) ).

fof(c_0_6659,plain,
    ! [X50,X51,X52] :
      ( ~ class_Numeral_Onumber__ring(X52)
      | c_times(c_uminus(c_Numeral_Onumber__of(X51,X52),X52),X50,X52) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X51),X52),X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_3722]) ).

fof(c_0_6660,plain,
    ! [X15,X16,X17] : c_uminus(c_minus(X16,X15,tc_set(X17)),tc_set(X17)) = c_union(c_uminus(X16,tc_set(X17)),X15,X17),
    inference(variable_rename,[status(thm)],[c_0_3723]) ).

fof(c_0_6661,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X25)
      | c_NatArith_Oof__nat(c_times(X24,X23,tc_nat),X25) = c_times(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3724]) ).

fof(c_0_6662,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X25)
      | c_NatArith_Oof__nat(c_plus(X24,X23,tc_nat),X25) = c_plus(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3725]) ).

fof(c_0_6663,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X52)
      | c_IntDef_Oof__int(c_times(X51,X50,tc_IntDef_Oint),X52) = c_times(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3726]) ).

fof(c_0_6664,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X52)
      | c_IntDef_Oof__int(c_minus(X51,X50,tc_IntDef_Oint),X52) = c_minus(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3727]) ).

fof(c_0_6665,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X52)
      | c_IntDef_Oof__int(c_plus(X51,X50,tc_IntDef_Oint),X52) = c_plus(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3728]) ).

fof(c_0_6666,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X85),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3729]) ).

fof(c_0_6667,plain,
    ! [X50,X51] :
      ( ~ c_less(X51,X50,tc_IntDef_Oint)
      | ~ c_less(c_0,X50,tc_IntDef_Oint)
      | c_less(c_IntDef_Onat(X51),c_IntDef_Onat(X50),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3730]) ).

fof(c_0_6668,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | X29 = c_0
      | c_divide(X29,c_times(X30,X29,X31),X31) = c_divide(c_1,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3731]) ).

fof(c_0_6669,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | X29 = c_0
      | c_divide(X29,c_times(X29,X30,X31),X31) = c_divide(c_1,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3732]) ).

fof(c_0_6670,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_less(c_uminus(X29,X31),c_uminus(X30,X31),X31)
      | c_less(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3733]) ).

fof(c_0_6671,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_lessequals(c_uminus(X29,X31),c_uminus(X30,X31),X31)
      | c_lessequals(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3734]) ).

fof(c_0_6672,plain,
    ! [X85] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_3735]) ).

fof(c_0_6673,plain,
    ! [X49,X50] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X50,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X50,tc_nat),c_Numeral_Onumber__of(X49,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X49,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3736]) ).

fof(c_0_6674,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X25)
      | c_Parity_Oeven(X24,tc_nat)
      | c_Nat_Opower(c_uminus(X23,X25),X24,X25) = c_uminus(c_Nat_Opower(X23,X24,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3737]) ).

fof(c_0_6675,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X25)
      | ~ c_less(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25)
      | c_less(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3738]) ).

fof(c_0_6676,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X25)
      | ~ c_lessequals(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25)
      | c_lessequals(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3739]) ).

fof(c_0_6677,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__idom(X52)
      | ~ c_less(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52)
      | c_less(X51,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3740]) ).

fof(c_0_6678,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__idom(X52)
      | ~ c_lessequals(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52)
      | c_lessequals(X51,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3741]) ).

fof(c_0_6679,plain,
    ! [X90,X91] : c_Message_Oanalz(c_union(c_Message_Oanalz(X91),X90,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X91,X90,tc_Message_Omsg)),
    inference(variable_rename,[status(thm)],[c_0_3742]) ).

fof(c_0_6680,plain,
    ! [X15,X16,X17] : c_union(X16,c_minus(X15,X16,tc_set(X17)),X17) = c_union(X16,X15,X17),
    inference(variable_rename,[status(thm)],[c_0_3743]) ).

fof(c_0_6681,plain,
    ! [X15,X16,X17] : c_union(c_minus(X15,X16,tc_set(X17)),X16,X17) = c_union(X15,X16,X17),
    inference(variable_rename,[status(thm)],[c_0_3744]) ).

fof(c_0_6682,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Oordered__idom(X25)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X24,X25),X23,X25),X25)
      | X24 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3745]) ).

fof(c_0_6683,plain,
    ! [X27,X28,X29] : c_List_Oset(c_append(X28,X27,X29),X29) = c_union(c_List_Oset(X28,X29),c_List_Oset(X27,X29),X29),
    inference(variable_rename,[status(thm)],[c_0_3746]) ).

fof(c_0_6684,plain,
    ! [X27,X28,X29] : c_List_Orev(c_append(X28,X27,X29),X29) = c_append(c_List_Orev(X27,X29),c_List_Orev(X28,X29),X29),
    inference(variable_rename,[status(thm)],[c_0_3747]) ).

fof(c_0_6685,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Oordered__idom(X25)
      | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X24,X25),X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3748]) ).

fof(c_0_6686,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | c_1 != c_Numeral_Onumber__of(X5,X6)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X5)),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3749]) ).

fof(c_0_6687,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(X90,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3750]) ).

fof(c_0_6688,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg)
      | c_in(X91,c_Message_Osynth(c_Message_Oanalz(X92)),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3751]) ).

fof(c_0_6689,plain,
    ! [X94,X95,X96] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X95,X94),X96,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X95),c_Message_OkeysFor(X96),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3752]) ).

fof(c_0_6690,plain,
    ! [X104,X105] :
      ( ~ c_in(X105,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X104)),tc_Message_Omsg)
      | c_in(X105,c_Event_Oused(X104),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3753]) ).

fof(c_0_6691,plain,
    ! [X43,X44,X45] :
      ( ~ c_List_Odistinct(X43,X45)
      | c_List_Odistinct(c_List_Olist_OCons(X44,X43,X45),X45)
      | c_in(X44,c_List_Oset(X43,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_3754]) ).

fof(c_0_6692,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X29,X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X28,X29,tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_3755]) ).

fof(c_0_6693,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X29,X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X28,X29,tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_3756]) ).

fof(c_0_6694,plain,
    ! [X20,X21] :
      ( ~ class_Power_Orecpower(X21)
      | ~ class_Ring__and__Field_Oordered__idom(X21)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X20,X21),c_0,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_3757]) ).

fof(c_0_6695,plain,
    ! [X85,X86] :
      ( c_Numeral_Onumber__of(X86,tc_nat) != c_Numeral_Onumber__of(X85,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,c_Numeral_Obin__minus(X85)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3758]) ).

fof(c_0_6696,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Olinorder(X6)
      | c_Orderings_Omax(X5,c_Orderings_Omax(X5,X4,X6),X6) = c_Orderings_Omax(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3759]) ).

fof(c_0_6697,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Olinorder(X6)
      | c_Orderings_Omin(X5,c_Orderings_Omin(X5,X4,X6),X6) = c_Orderings_Omin(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3760]) ).

fof(c_0_6698,plain,
    ! [X15,X16,X17] :
      ( c_in(c_Main_OsubsetI__1(X16,X15,X17),X16,X17)
      | c_lessequals(X16,X15,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3761]) ).

fof(c_0_6699,plain,
    ! [X90,X91] :
      ( ~ c_in(c_Message_Omsg_OHash(X90),c_Message_Osynth(X91),tc_Message_Omsg)
      | c_in(X90,c_Message_Osynth(X91),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X90),X91,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3762]) ).

fof(c_0_6700,plain,
    ! [X43,X44,X45] : c_List_Oreplicate(c_Suc(X44),X43,X45) = c_List_Olist_OCons(X43,c_List_Oreplicate(X44,X43,X45),X45),
    inference(variable_rename,[status(thm)],[c_0_3763]) ).

fof(c_0_6701,plain,
    ! [X25,X26,X27,X28] : c_List_Onth(c_List_Olist_OCons(X26,X25,X28),c_Suc(X27),X28) = c_List_Onth(X25,X27,X28),
    inference(variable_rename,[status(thm)],[c_0_3764]) ).

fof(c_0_6702,plain,
    ! [X25,X26,X27,X28] : c_List_Odrop(c_Suc(X27),c_List_Olist_OCons(X26,X25,X28),X28) = c_List_Odrop(X27,X25,X28),
    inference(variable_rename,[status(thm)],[c_0_3765]) ).

fof(c_0_6703,plain,
    ! [X13,X14] :
      ( c_Numeral_Onumber__of(X14,tc_nat) != c_0
      | c_less(c_0,c_Nat_Opower(X13,c_Numeral_Onumber__of(X14,tc_nat),tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3766]) ).

fof(c_0_6704,plain,
    ! [X66,X67,X68] : c_Nat_Osize(c_List_Olist_OCons(X67,X66,X68),tc_List_Olist(X68)) = c_plus(c_Nat_Osize(X66,tc_List_Olist(X68)),c_Suc(c_0),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3767]) ).

fof(c_0_6705,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | ~ c_less(c_Numeral_Onumber__of(X5,X6),c_0,X6)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X5,X6),X6) = c_uminus(c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3768]) ).

fof(c_0_6706,plain,
    ! [X5,X6,X7] :
      ( ~ class_Numeral_Onumber__ring(X7)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X6,c_Numeral_Obin__minus(X5)),X7),X7)
      | c_Numeral_Onumber__of(X6,X7) = c_Numeral_Onumber__of(X5,X7) ),
    inference(variable_rename,[status(thm)],[c_0_3769]) ).

fof(c_0_6707,plain,
    ! [X23,X24] :
      ( ~ c_Parity_Oeven(X23,tc_IntDef_Oint)
      | ~ c_less(c_0,X24,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X23,X24,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3770])])]) ).

fof(c_0_6708,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X4,tc_nat)
      | ~ c_less(c_0,X3,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X4,X3,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3771]) ).

fof(c_0_6709,plain,
    ! [X25,X26,X27] : c_Nat_Osize(c_List_Otake(X26,X25,X27),tc_List_Olist(X27)) = c_Orderings_Omin(c_Nat_Osize(X25,tc_List_Olist(X27)),X26,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3772]) ).

fof(c_0_6710,plain,
    ! [X25,X26,X27] : c_Nat_Osize(c_List_Odrop(X26,X25,X27),tc_List_Olist(X27)) = c_minus(c_Nat_Osize(X25,tc_List_Olist(X27)),X26,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3773]) ).

fof(c_0_6711,plain,
    ! [X49,X50] :
      ( ~ class_Numeral_Onumber__ring(X50)
      | c_minus(c_Numeral_Onumber__of(X49,X50),c_1,X50) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X49,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X50) ),
    inference(variable_rename,[status(thm)],[c_0_3774]) ).

fof(c_0_6712,plain,
    ! [X20,X21] :
      ( ~ class_HOL_Oone(X21)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_less(c_uminus(X20,X21),c_1,X21)
      | c_less(c_uminus(c_1,X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3775]) ).

fof(c_0_6713,plain,
    ! [X20,X21] :
      ( ~ class_HOL_Oone(X21)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_lessequals(c_uminus(X20,X21),c_1,X21)
      | c_lessequals(c_uminus(c_1,X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3776]) ).

fof(c_0_6714,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Odivision__by__zero(X6)
      | ~ class_Ring__and__Field_Ofield(X6)
      | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X6),X5,X6) = c_uminus(c_divide(c_1,X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3777]) ).

fof(c_0_6715,plain,
    ! [X29,X30] :
      ( ~ class_HOL_Oone(X30)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X30)
      | ~ c_less(c_1,c_uminus(X29,X30),X30)
      | c_less(X29,c_uminus(c_1,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3778]) ).

fof(c_0_6716,plain,
    ! [X29,X30] :
      ( ~ class_HOL_Oone(X30)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X30)
      | ~ c_lessequals(c_1,c_uminus(X29,X30),X30)
      | c_lessequals(X29,c_uminus(c_1,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3779]) ).

fof(c_0_6717,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3780]) ).

fof(c_0_6718,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X4,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3781])])]) ).

fof(c_0_6719,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X4,X3,tc_nat),tc_nat)
      | c_Parity_Oeven(X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3782]) ).

fof(c_0_6720,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X4,X3,tc_nat),tc_nat)
      | c_Parity_Oeven(X4,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3783])])]) ).

fof(c_0_6721,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3784]) ).

fof(c_0_6722,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X4,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3785])])]) ).

fof(c_0_6723,plain,
    ! [X20,X21] :
      ( ~ class_HOL_Oone(X21)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_less(c_uminus(c_1,X21),X20,X21)
      | c_less(c_uminus(X20,X21),c_1,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3786]) ).

fof(c_0_6724,plain,
    ! [X20,X21] :
      ( ~ class_HOL_Oone(X21)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_lessequals(c_uminus(c_1,X21),X20,X21)
      | c_lessequals(c_uminus(X20,X21),c_1,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3787]) ).

fof(c_0_6725,plain,
    ! [X29,X30] :
      ( ~ class_HOL_Oone(X30)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X30)
      | ~ c_less(X29,c_uminus(c_1,X30),X30)
      | c_less(c_1,c_uminus(X29,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3788]) ).

fof(c_0_6726,plain,
    ! [X29,X30] :
      ( ~ class_HOL_Oone(X30)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X30)
      | ~ c_lessequals(X29,c_uminus(c_1,X30),X30)
      | c_lessequals(c_1,c_uminus(X29,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_3789]) ).

fof(c_0_6727,plain,
    ! [X15,X16,X17] : c_union(X16,c_union(X15,X16,X17),X17) = c_union(X15,X16,X17),
    inference(variable_rename,[status(thm)],[c_0_3790]) ).

fof(c_0_6728,plain,
    ! [X15,X16,X17] : c_insert(X15,c_insert(X15,X16,X17),X17) = c_insert(X15,X16,X17),
    inference(variable_rename,[status(thm)],[c_0_3791]) ).

fof(c_0_6729,plain,
    ! [X30,X31] : c_Nat_Opower(X30,c_Suc(X31),tc_nat) = c_times(X30,c_Nat_Opower(X30,X31,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3792]) ).

fof(c_0_6730,plain,
    ! [X23,X24] : c_times(c_Suc(X24),X23,tc_nat) = c_plus(X23,c_times(X24,X23,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3793]) ).

fof(c_0_6731,plain,
    ! [X23,X24] : c_times(X24,c_Suc(X23),tc_nat) = c_plus(X24,c_times(X24,X23,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3794]) ).

fof(c_0_6732,plain,
    ! [X30,X31] : c_Nat_Opower(X30,c_Suc(X31),tc_IntDef_Oint) = c_times(X30,c_Nat_Opower(X30,X31,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3795]) ).

fof(c_0_6733,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(X30,c_uminus(X29,X31),X31) = c_uminus(c_divide(X30,X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3796]) ).

fof(c_0_6734,plain,
    ! [X29,X30] : c_Divides_Oop_Amod(c_uminus(X30,tc_IntDef_Oint),c_uminus(X29,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3797]) ).

fof(c_0_6735,plain,
    ! [X20,X21,X22] : c_Union(c_insert(X20,X21,tc_set(X22)),X22) = c_union(X20,c_Union(X21,X22),X22),
    inference(variable_rename,[status(thm)],[c_0_3798]) ).

fof(c_0_6736,plain,
    ! [X20,X21,X22] : c_Inter(c_insert(X20,X21,tc_set(X22)),X22) = c_inter(X20,c_Inter(X21,X22),X22),
    inference(variable_rename,[status(thm)],[c_0_3799]) ).

fof(c_0_6737,plain,
    ! [X68,X69,X70] : c_List_Olistset(c_List_Olist_OCons(X69,X68,tc_set(X70)),X70) = c_List_Oset__Cons(X69,c_List_Olistset(X68,X70),X70),
    inference(variable_rename,[status(thm)],[c_0_3800]) ).

fof(c_0_6738,plain,
    ! [X43,X44,X45] : c_List_Oconcat(c_List_Olist_OCons(X44,X43,tc_List_Olist(X45)),X45) = c_append(X44,c_List_Oconcat(X43,X45),X45),
    inference(variable_rename,[status(thm)],[c_0_3801]) ).

fof(c_0_6739,plain,
    ! [X15,X16] :
      ( ~ c_in(c_Pow(X15,X16),c_Finite__Set_OFinites,tc_set(tc_set(X16)))
      | c_in(X15,c_Finite__Set_OFinites,tc_set(X16)) ),
    inference(variable_rename,[status(thm)],[c_0_3802]) ).

fof(c_0_6740,plain,
    ! [X20,X21,X22] :
      ( ~ class_Power_Orecpower(X22)
      | ~ class_Ring__and__Field_Oordered__idom(X22)
      | c_Nat_Opower(X21,c_Numeral_Onumber__of(X20,tc_nat),X22) != c_0
      | c_less(c_0,c_Numeral_Onumber__of(X20,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3803]) ).

fof(c_0_6741,plain,
    ! [X23] : c_plus(X23,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(X23)),
    inference(variable_rename,[status(thm)],[c_0_3804]) ).

fof(c_0_6742,plain,
    ! [X23] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X23,tc_nat) = c_Suc(c_Suc(X23)),
    inference(variable_rename,[status(thm)],[c_0_3805]) ).

fof(c_0_6743,plain,
    ! [X15,X16,X17] :
      ( c_in(c_0,X16,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X15,c_List_Olist_ONil,X17),X16,X17) = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3806])])]) ).

fof(c_0_6744,plain,
    ! [X29,X30] : c_Divides_Oop_Amod(c_plus(X29,X30,tc_IntDef_Oint),X30,tc_IntDef_Oint) = c_Divides_Oop_Amod(X29,X30,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3807]) ).

fof(c_0_6745,plain,
    ! [X29,X30] : c_Divides_Oop_Amod(c_plus(X30,X29,tc_IntDef_Oint),X30,tc_IntDef_Oint) = c_Divides_Oop_Amod(X29,X30,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3808]) ).

fof(c_0_6746,plain,
    ! [X29,X30] : c_Divides_Oop_Amod(c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),X29,tc_IntDef_Oint) = c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3809]) ).

fof(c_0_6747,plain,
    ! [X23,X24] : c_Divides_Oop_Amod(c_Divides_Oop_Amod(X24,X23,tc_nat),X23,tc_nat) = c_Divides_Oop_Amod(X24,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3810]) ).

fof(c_0_6748,plain,
    ! [X23,X24] : c_Divides_Oop_Amod(c_plus(X24,X23,tc_nat),X23,tc_nat) = c_Divides_Oop_Amod(X24,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3811]) ).

fof(c_0_6749,plain,
    ! [X23,X24] : c_Divides_Oop_Amod(c_plus(X23,X24,tc_nat),X23,tc_nat) = c_Divides_Oop_Amod(X24,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3812]) ).

fof(c_0_6750,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(c_times(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X4,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3813]) ).

fof(c_0_6751,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(c_times(X4,X3,tc_nat),tc_nat)
      | c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3814]) ).

fof(c_0_6752,plain,
    ! [X85,X86] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X86,X85),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3815])])]) ).

fof(c_0_6753,plain,
    ! [X15,X16] :
      ( ~ class_Orderings_Olinorder(X16)
      | ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X16))
      | c_lessequals(c_Finite__Set_OMin(X15,X16),c_Finite__Set_OMax(X15,X16),X16)
      | X15 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3816]) ).

fof(c_0_6754,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oring(X31)
      | c_times(X30,c_uminus(X29,X31),X31) = c_uminus(c_times(X30,X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3817]) ).

fof(c_0_6755,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oring(X31)
      | c_times(c_uminus(X30,X31),X29,X31) = c_uminus(c_times(X30,X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3818]) ).

fof(c_0_6756,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(c_uminus(X30,X31),X29,X31) = c_uminus(c_divide(X30,X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3819]) ).

fof(c_0_6757,plain,
    ! [X5] :
      ( ~ class_Power_Orecpower(X5)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3820]) ).

fof(c_0_6758,plain,
    ! [X5] :
      ( ~ class_Power_Orecpower(X5)
      | c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_3821]) ).

fof(c_0_6759,plain,
    ! [X13,X14] :
      ( ~ class_Power_Orecpower(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X13,tc_nat),tc_nat)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X13,tc_nat),X14) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3822]) ).

fof(c_0_6760,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | ~ c_lessequals(X6,X5,X7)
      | c_lessequals(c_SetInterval_OlessThan(X6,X7),c_SetInterval_OlessThan(X5,X7),tc_set(X7)) ),
    inference(variable_rename,[status(thm)],[c_0_3823]) ).

fof(c_0_6761,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | ~ c_lessequals(X5,X6,X7)
      | c_lessequals(c_SetInterval_OgreaterThan(X6,X7),c_SetInterval_OgreaterThan(X5,X7),tc_set(X7)) ),
    inference(variable_rename,[status(thm)],[c_0_3824]) ).

fof(c_0_6762,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Oorder(X7)
      | ~ c_lessequals(X6,X5,X7)
      | c_lessequals(c_SetInterval_OatMost(X6,X7),c_SetInterval_OatMost(X5,X7),tc_set(X7)) ),
    inference(variable_rename,[status(thm)],[c_0_3825]) ).

fof(c_0_6763,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Oorder(X7)
      | ~ c_lessequals(X5,X6,X7)
      | c_lessequals(c_SetInterval_OatLeast(X6,X7),c_SetInterval_OatLeast(X5,X7),tc_set(X7)) ),
    inference(variable_rename,[status(thm)],[c_0_3826]) ).

fof(c_0_6764,plain,
    ! [X49,X50,X51,X52] :
      ( c_Numeral_Onumber__of(X51,tc_nat) != c_0
      | c_List_Onth(c_List_Olist_OCons(X50,X49,X52),c_Numeral_Onumber__of(X51,tc_nat),X52) = X50 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3827])])]) ).

fof(c_0_6765,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Oparts(X91),tc_Message_Omsg)
      | c_Message_Oparts(c_insert(X90,X91,tc_Message_Omsg)) = c_Message_Oparts(X91) ),
    inference(variable_rename,[status(thm)],[c_0_3828]) ).

fof(c_0_6766,plain,
    ! [X7,X8] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X7,X8,X8),X8)
      | c_Wellfounded__Recursion_Oacyclic(X7,X8) ),
    inference(variable_rename,[status(thm)],[c_0_3829]) ).

fof(c_0_6767,plain,
    ! [X25,X26,X27] :
      ( ~ c_List_Odistinct(c_List_Orotate(X26,X25,X27),X27)
      | c_List_Odistinct(X25,X27) ),
    inference(variable_rename,[status(thm)],[c_0_3830]) ).

fof(c_0_6768,plain,
    ! [X27,X28,X29] :
      ( ~ c_List_Odistinct(c_append(X28,X27,X29),X29)
      | c_List_Odistinct(X27,X29) ),
    inference(variable_rename,[status(thm)],[c_0_3831]) ).

fof(c_0_6769,plain,
    ! [X27,X28,X29] :
      ( ~ c_List_Odistinct(c_append(X28,X27,X29),X29)
      | c_List_Odistinct(X28,X29) ),
    inference(variable_rename,[status(thm)],[c_0_3832]) ).

fof(c_0_6770,plain,
    ! [X43,X44,X45] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X44,X43,X45),X45)
      | c_List_Odistinct(X43,X45) ),
    inference(variable_rename,[status(thm)],[c_0_3833]) ).

fof(c_0_6771,plain,
    ! [X49,X50,X51,X52] :
      ( c_Numeral_Onumber__of(X51,tc_nat) != c_0
      | c_List_Otake(c_Numeral_Onumber__of(X51,tc_nat),c_List_Olist_OCons(X50,X49,X52),X52) = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3834])])]) ).

fof(c_0_6772,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X5)),X6),X6)
      | c_lessequals(c_Numeral_Onumber__of(X5,X6),c_0,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3835]) ).

fof(c_0_6773,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_Numeral_Onumber__of(X86,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3836])])]) ).

fof(c_0_6774,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_Numeral_Onumber__of(X86,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3837])])]) ).

fof(c_0_6775,plain,
    ! [X94,X95] :
      ( ~ c_in(X94,c_Message_OkeysFor(c_Message_Osynth(X95)),tc_nat)
      | c_in(X94,c_Message_OkeysFor(X95),tc_nat)
      | X94 = c_Message_OinvKey(v_sko__uhi(X95,X94)) ),
    inference(variable_rename,[status(thm)],[c_0_3838]) ).

fof(c_0_6776,plain,
    ! [X27,X28,X29] :
      ( X28 = c_List_Olist_ONil
      | c_List_Otl(c_append(X28,X27,X29),X29) = c_append(c_List_Otl(X28,X29),X27,X29) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3839])])]) ).

fof(c_0_6777,plain,
    ! [X43,X44,X45] :
      ( X43 = c_List_Olist_ONil
      | c_List_Obutlast(c_List_Olist_OCons(X44,X43,X45),X45) = c_List_Olist_OCons(X44,c_List_Obutlast(X43,X45),X45) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3840])])]) ).

fof(c_0_6778,plain,
    ! [X23,X24] :
      ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X23,tc_IntDef_Oint),X24,tc_IntDef_Oint),tc_IntDef_Oint)
      | X23 = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3841])])]) ).

fof(c_0_6779,plain,
    ! [X43,X44,X45] : c_List_Oset(c_List_Olist_OCons(X44,X43,X45),X45) = c_insert(X44,c_List_Oset(X43,X45),X45),
    inference(variable_rename,[status(thm)],[c_0_3842]) ).

fof(c_0_6780,plain,
    ! [X23,X24] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X23,tc_IntDef_Oint),X24,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3843]) ).

fof(c_0_6781,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X31)
      | ~ c_lessequals(X30,X29,X31)
      | c_lessequals(c_OrderedGroup_Opprt(X30,X31),c_OrderedGroup_Opprt(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3844]) ).

fof(c_0_6782,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X31)
      | ~ c_lessequals(X30,X29,X31)
      | c_lessequals(c_OrderedGroup_Onprt(X30,X31),c_OrderedGroup_Onprt(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3845]) ).

fof(c_0_6783,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_less(X30,X29,X31)
      | c_less(c_uminus(X29,X31),c_uminus(X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3846]) ).

fof(c_0_6784,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | ~ c_lessequals(X30,X29,X31)
      | c_lessequals(c_uminus(X29,X31),c_uminus(X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_3847]) ).

fof(c_0_6785,plain,
    ! [X13,X14,X15] :
      ( ~ class_Numeral_Onumber__ring(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X14,X13),X15),X15)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X14,X15),X15) ),
    inference(variable_rename,[status(thm)],[c_0_3848]) ).

fof(c_0_6786,plain,
    ! [X23,X24,X25] :
      ( ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X25)),X24,tc_nat)
      | c_List_Otake(X24,X23,X25) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3849]) ).

fof(c_0_6787,plain,
    ! [X23,X24,X25] :
      ( c_Divides_Oop_Amod(X24,c_Nat_Osize(X23,tc_List_Olist(X25)),tc_nat) != c_0
      | c_List_Orotate(X24,X23,X25) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3850]) ).

fof(c_0_6788,plain,
    ! [X25,X26,X27] :
      ( ~ c_lessequals(c_Nat_Osize(X25,tc_List_Olist(X27)),X26,tc_nat)
      | c_List_Odrop(X26,X25,X27) = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_3851]) ).

fof(c_0_6789,plain,
    ! [X3] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3852]) ).

fof(c_0_6790,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OPls)),X6),X6)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_3853]) ).

fof(c_0_6791,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X25)
      | ~ c_less(X24,X23,tc_nat)
      | c_less(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3854]) ).

fof(c_0_6792,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X25)
      | ~ c_lessequals(X24,X23,tc_nat)
      | c_lessequals(c_NatArith_Oof__nat(X24,X25),c_NatArith_Oof__nat(X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_3855]) ).

fof(c_0_6793,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__idom(X52)
      | ~ c_less(X51,X50,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3856]) ).

fof(c_0_6794,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__idom(X52)
      | ~ c_lessequals(X51,X50,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X51,X52),c_IntDef_Oof__int(X50,X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_3857]) ).

fof(c_0_6795,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(X16,c_Pow(X15,X17),tc_set(X17))
      | c_lessequals(X16,X15,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3858]) ).

fof(c_0_6796,plain,
    ! [X24,X25,X26,X27] :
      ( ~ c_Infinite__Set_Oatmost__one(X26,X27)
      | ~ c_in(X24,X26,X27)
      | ~ c_in(X25,X26,X27)
      | X24 = X25 ),
    inference(variable_rename,[status(thm)],[c_0_3859]) ).

fof(c_0_6797,plain,
    ! [X23,X24,X25] :
      ( ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X25)),c_1,tc_nat)
      | c_List_Orotate(X24,X23,X25) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_3860]) ).

fof(c_0_6798,plain,
    ! [X61,X62,X63] : c_List_Odrop(X61,c_List_Oupt(X63,X62),tc_nat) = c_List_Oupt(c_plus(X63,X61,tc_nat),X62),
    inference(variable_rename,[status(thm)],[c_0_3861]) ).

fof(c_0_6799,plain,
    ! [X2] :
      ( ~ c_less(c_0,X2,tc_nat)
      | c_Suc(c_minus(X2,c_Suc(c_0),tc_nat)) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_3862]) ).

fof(c_0_6800,plain,
    ! [X104,X105] :
      ( ~ c_in(c_Message_Omsg_ONonce(X105),c_Event_Oused(X104),tc_Message_Omsg)
      | ~ c_lessequals(v_sko__urX(X104),X105,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3863]) ).

fof(c_0_6801,plain,
    ! [X23,X24] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X23,X24,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X23,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3864])])]) ).

fof(c_0_6802,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(c_Nat_Opower(X4,X3,tc_nat),tc_nat)
      | c_Parity_Oeven(X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3865]) ).

fof(c_0_6803,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X5)),X6),X6)
      | c_0 = c_Numeral_Onumber__of(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_3866]) ).

fof(c_0_6804,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3867]) ).

fof(c_0_6805,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3868]) ).

fof(c_0_6806,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X15,X16,tc_set(X17))
      | ~ c_lessequals(X16,X15,tc_set(X17))
      | X16 = X15 ),
    inference(variable_rename,[status(thm)],[c_0_3869]) ).

fof(c_0_6807,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Event_Oused(X92),tc_Message_Omsg)
      | c_in(X91,c_Event_Oused(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3870]) ).

fof(c_0_6808,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Event_Oused(X92),tc_Message_Omsg)
      | c_in(X90,c_Event_Oused(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3871]) ).

fof(c_0_6809,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Oanalz(X92),tc_Message_Omsg)
      | c_in(X91,c_Message_Oanalz(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3872]) ).

fof(c_0_6810,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Oanalz(X92),tc_Message_Omsg)
      | c_in(X90,c_Message_Oanalz(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3873]) ).

fof(c_0_6811,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Oparts(X92),tc_Message_Omsg)
      | c_in(X91,c_Message_Oparts(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3874]) ).

fof(c_0_6812,plain,
    ! [X90,X91,X92] :
      ( ~ c_in(c_Message_Omsg_OMPair(X91,X90),c_Message_Oparts(X92),tc_Message_Omsg)
      | c_in(X90,c_Message_Oparts(X92),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3875]) ).

fof(c_0_6813,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_less(c_0,c_HOL_Oinverse(X20,X21),X21)
      | c_less(c_0,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3876]) ).

fof(c_0_6814,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_lessequals(c_HOL_Oinverse(X20,X21),c_0,X21)
      | c_lessequals(X20,c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3877]) ).

fof(c_0_6815,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_lessequals(c_0,c_HOL_Oinverse(X20,X21),X21)
      | c_lessequals(c_0,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3878]) ).

fof(c_0_6816,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_less(c_HOL_Oinverse(X20,X21),c_0,X21)
      | c_less(X20,c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3879]) ).

fof(c_0_6817,plain,
    ! [X15,X16,X17] :
      ( ~ c_less(X16,X15,tc_set(X17))
      | ~ c_lessequals(X15,X16,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3880]) ).

fof(c_0_6818,plain,
    ! [X15,X16] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X16))
      | c_in(c_Pow(X15,X16),c_Finite__Set_OFinites,tc_set(tc_set(X16))) ),
    inference(variable_rename,[status(thm)],[c_0_3881]) ).

fof(c_0_6819,plain,
    ! [X43,X44,X45] : ~ c_List_Onull(c_List_Olist_OCons(X44,X43,X45),X45),
    inference(variable_rename,[status(thm)],[c_0_3882]) ).

fof(c_0_6820,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber__ring(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X13,c_Numeral_Obit_OB0),X14),X14)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X13,X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_3883]) ).

fof(c_0_6821,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_HOL_Oinverse(c_divide(X30,X29,X31),X31) = c_divide(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3884]) ).

fof(c_0_6822,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Ofield(X32)
      | c_divide(X31,X29,X32) != c_divide(X30,X29,X32)
      | X31 = X30
      | X29 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3885]) ).

fof(c_0_6823,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X32)
      | ~ class_Ring__and__Field_Ofield(X32)
      | c_divide(X29,X31,X32) != c_divide(X29,X30,X32)
      | X31 = X30
      | X29 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3886]) ).

fof(c_0_6824,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_in(X46,c_SetInterval_OlessThan(X45,X47),X47)
      | c_less(X46,X45,X47) ),
    inference(variable_rename,[status(thm)],[c_0_3887]) ).

fof(c_0_6825,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_in(X46,c_SetInterval_OgreaterThan(X45,X47),X47)
      | c_less(X45,X46,X47) ),
    inference(variable_rename,[status(thm)],[c_0_3888]) ).

fof(c_0_6826,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_in(X46,c_SetInterval_OatMost(X45,X47),X47)
      | c_lessequals(X46,X45,X47) ),
    inference(variable_rename,[status(thm)],[c_0_3889]) ).

fof(c_0_6827,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_in(X46,c_SetInterval_OatLeast(X45,X47),X47)
      | c_lessequals(X45,X46,X47) ),
    inference(variable_rename,[status(thm)],[c_0_3890]) ).

fof(c_0_6828,plain,
    ! [X23,X24] :
      ( ~ class_Numeral_Onumber__ring(X24)
      | ~ class_Power_Orecpower(X24)
      | ~ class_Ring__and__Field_Oordered__idom(X24)
      | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X24),X23,X24),X24) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_3891]) ).

fof(c_0_6829,plain,
    ! [X49] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X49,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X49,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3892]) ).

fof(c_0_6830,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OPls)),X6),X6)
      | c_Numeral_Onumber__of(X5,X6) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3893]) ).

fof(c_0_6831,plain,
    ! [X90,X91] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X90),X91,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X90),c_Message_Oparts(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3894]) ).

fof(c_0_6832,plain,
    ! [X90,X91] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X90),X91,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X90),c_Message_Oparts(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3895]) ).

fof(c_0_6833,plain,
    ! [X94,X95] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X94),X95,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X94),c_Message_Oparts(X95),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3896]) ).

fof(c_0_6834,plain,
    ! [X90,X91] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X90),X91,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X90),c_Message_Oparts(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3897]) ).

fof(c_0_6835,plain,
    ! [X112,X113] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X112),X113,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X112),c_Message_Oparts(X113),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3898]) ).

fof(c_0_6836,plain,
    ! [X90,X91] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X90),X91,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X90),c_Message_Oanalz(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3899]) ).

fof(c_0_6837,plain,
    ! [X90,X91] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X90),X91,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X90),c_Message_Oanalz(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3900]) ).

fof(c_0_6838,plain,
    ! [X90,X91] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X90),X91,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X90),c_Message_Oanalz(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3901]) ).

fof(c_0_6839,plain,
    ! [X112,X113] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X112),X113,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X112),c_Message_Oanalz(X113),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3902]) ).

fof(c_0_6840,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_less(c_uminus(X20,X21),c_0,X21)
      | c_less(c_0,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3903]) ).

fof(c_0_6841,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_lessequals(c_uminus(X20,X21),c_0,X21)
      | c_lessequals(c_0,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3904]) ).

fof(c_0_6842,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_less(c_0,c_uminus(X20,X21),X21)
      | c_less(X20,c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3905]) ).

fof(c_0_6843,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_lessequals(c_0,c_uminus(X20,X21),X21)
      | c_lessequals(X20,c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3906]) ).

fof(c_0_6844,plain,
    ! [X7,X8] : c_Transitive__Closure_Otrancl(c_union(X7,c_Relation_OId,tc_prod(X8,X8)),X8) = c_Transitive__Closure_Ortrancl(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_3907]) ).

fof(c_0_6845,plain,
    ! [X87,X88] : c_Transitive__Closure_Ortrancl(c_union(X87,c_Relation_OId,tc_prod(X88,X88)),X88) = c_Transitive__Closure_Ortrancl(X87,X88),
    inference(variable_rename,[status(thm)],[c_0_3908]) ).

fof(c_0_6846,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X24)
      | ~ c_less(c_0,c_NatArith_Oof__nat(X23,X24),X24)
      | c_less(c_0,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3909]) ).

fof(c_0_6847,plain,
    ! [X13,X14] :
      ( ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_less(c_IntDef_Oof__int(X13,X14),c_0,X14)
      | c_less(X13,c_0,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3910]) ).

fof(c_0_6848,plain,
    ! [X13,X14] :
      ( ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_lessequals(c_IntDef_Oof__int(X13,X14),c_0,X14)
      | c_lessequals(X13,c_0,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3911]) ).

fof(c_0_6849,plain,
    ! [X50,X51] :
      ( ~ class_Ring__and__Field_Oordered__idom(X51)
      | ~ c_less(c_0,c_IntDef_Oof__int(X50,X51),X51)
      | c_less(c_0,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3912]) ).

fof(c_0_6850,plain,
    ! [X50,X51] :
      ( ~ class_Ring__and__Field_Oordered__idom(X51)
      | ~ c_lessequals(c_0,c_IntDef_Oof__int(X50,X51),X51)
      | c_lessequals(c_0,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3913]) ).

fof(c_0_6851,plain,
    ! [X15,X16] :
      ( ~ class_Orderings_Olinorder(X16)
      | ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X16))
      | c_in(c_Finite__Set_OMin(X15,X16),X15,X16)
      | X15 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3914]) ).

fof(c_0_6852,plain,
    ! [X15,X16] :
      ( ~ class_Orderings_Olinorder(X16)
      | ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X16))
      | c_in(c_Finite__Set_OMax(X15,X16),X15,X16)
      | X15 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_3915]) ).

fof(c_0_6853,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X16,X15,tc_set(X17))
      | c_in(X16,c_Pow(X15,X17),tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_3916]) ).

fof(c_0_6854,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Oab__group__add(X31)
      | c_uminus(c_minus(X30,X29,X31),X31) = c_minus(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3917]) ).

fof(c_0_6855,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Ofield(X32)
      | c_times(X31,X29,X32) != c_times(X30,X29,X32)
      | X31 = X30
      | X29 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3918]) ).

fof(c_0_6856,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Ofield(X32)
      | c_times(X29,X31,X32) != c_times(X29,X30,X32)
      | X31 = X30
      | X29 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3919]) ).

fof(c_0_6857,plain,
    ! [X104,X105,X106] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X105,X106))),c_Event_Oused(X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3920]) ).

fof(c_0_6858,plain,
    ! [X29,X30] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X29,X30))),c_Event_OinitState(X30),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3921]) ).

fof(c_0_6859,plain,
    ! [X25,X26,X27] : c_List_Orotate(c_Suc(X26),X25,X27) = c_List_Orotate1(c_List_Orotate(X26,X25,X27),X27),
    inference(variable_rename,[status(thm)],[c_0_3922]) ).

fof(c_0_6860,plain,
    ! [X25,X26] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X25,X26),tc_List_Olist(X26)),c_Nat_Osize(X25,tc_List_Olist(X26)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3923]) ).

fof(c_0_6861,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X32)
      | c_plus(X30,X31,X32) != c_plus(X29,X31,X32)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_3924]) ).

fof(c_0_6862,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X32)
      | c_plus(X31,X30,X32) != c_plus(X31,X29,X32)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_3925]) ).

fof(c_0_6863,plain,
    ! [X104,X105,X106] : c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X106,X105),X104,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X104),
    inference(variable_rename,[status(thm)],[c_0_3926]) ).

fof(c_0_6864,plain,
    ! [X52,X53,X54] :
      ( ~ c_in(X53,c_List_Oset(X52,tc_List_Olist(X54)),tc_List_Olist(X54))
      | c_List_Oconcat(X52,X54) != c_List_Olist_ONil
      | X53 = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_3927]) ).

fof(c_0_6865,plain,
    ! [X52,X53,X54] :
      ( ~ c_in(X53,c_List_Oset(X52,tc_List_Olist(X54)),tc_List_Olist(X54))
      | c_List_Olist_ONil != c_List_Oconcat(X52,X54)
      | X53 = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_3928]) ).

fof(c_0_6866,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | X30 = c_0
      | c_times(X30,c_divide(X29,X30,X31),X31) = X29 ),
    inference(variable_rename,[status(thm)],[c_0_3929]) ).

fof(c_0_6867,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | X30 = c_0
      | c_times(c_divide(X29,X30,X31),X30,X31) = X29 ),
    inference(variable_rename,[status(thm)],[c_0_3930]) ).

fof(c_0_6868,plain,
    ! [X20,X21,X22] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X22)
      | ~ class_Ring__and__Field_Ofield(X22)
      | X20 = c_0
      | c_divide(c_times(X21,X20,X22),X20,X22) = X21 ),
    inference(variable_rename,[status(thm)],[c_0_3931]) ).

fof(c_0_6869,plain,
    ! [X20,X21,X22] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X22)
      | ~ class_Ring__and__Field_Ofield(X22)
      | X20 = c_0
      | c_divide(c_times(X20,X21,X22),X20,X22) = X21 ),
    inference(variable_rename,[status(thm)],[c_0_3932]) ).

fof(c_0_6870,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber__ring(X14)
      | c_minus(c_1,c_Numeral_Onumber__of(X13,X14),X14) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X13)),X14) ),
    inference(variable_rename,[status(thm)],[c_0_3933]) ).

fof(c_0_6871,plain,
    ! [X25,X26,X27] :
      ( c_List_Odrop(X26,X25,X27) != c_List_Olist_ONil
      | c_lessequals(c_Nat_Osize(X25,tc_List_Olist(X27)),X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3934]) ).

fof(c_0_6872,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_less(c_0,X20,X21)
      | c_less(c_0,c_HOL_Oinverse(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_3935]) ).

fof(c_0_6873,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_lessequals(X20,c_0,X21)
      | c_lessequals(c_HOL_Oinverse(X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3936]) ).

fof(c_0_6874,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_lessequals(c_0,X20,X21)
      | c_lessequals(c_0,c_HOL_Oinverse(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_3937]) ).

fof(c_0_6875,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | ~ c_less(X20,c_0,X21)
      | c_less(c_HOL_Oinverse(X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_3938]) ).

fof(c_0_6876,plain,
    ! [X104,X105] :
      ( ~ c_in(X105,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X105)),c_Event_Oknows(c_Message_Oagent_OSpy,X104),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3939]) ).

fof(c_0_6877,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X29,X28,tc_nat),tc_nat) = c_minus(X28,c_Suc(X29),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3940]) ).

fof(c_0_6878,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X29,X28,tc_nat),tc_nat) = c_minus(c_Suc(X28),X29,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3941]) ).

fof(c_0_6879,plain,
    ! [X23,X24,X25] :
      ( X24 = c_0
      | c_List_Oset(c_List_Oreplicate(X24,X23,X25),X25) = c_insert(X23,c_emptyset,X25) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3942])])]) ).

fof(c_0_6880,plain,
    ! [X23,X24,X25] : c_List_Orev(c_List_Oreplicate(X24,X23,X25),X25) = c_List_Oreplicate(X24,X23,X25),
    inference(variable_rename,[status(thm)],[c_0_3943]) ).

fof(c_0_6881,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(c_uminus(X30,X31),c_uminus(X29,X31),X31) = c_divide(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_3944]) ).

fof(c_0_6882,plain,
    ! [X23] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X23)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3945]) ).

fof(c_0_6883,plain,
    ! [X90,X91] :
      ( ~ c_lessequals(c_Message_Osynth(X91),c_Message_Osynth(X90),tc_set(tc_Message_Omsg))
      | c_lessequals(X91,c_Message_Osynth(X90),tc_set(tc_Message_Omsg)) ),
    inference(variable_rename,[status(thm)],[c_0_3946]) ).

fof(c_0_6884,plain,
    ! [X90,X91] :
      ( ~ c_lessequals(c_Message_Oparts(X91),c_Message_Oparts(X90),tc_set(tc_Message_Omsg))
      | c_lessequals(X91,c_Message_Oparts(X90),tc_set(tc_Message_Omsg)) ),
    inference(variable_rename,[status(thm)],[c_0_3947]) ).

fof(c_0_6885,plain,
    ! [X90,X91] :
      ( ~ c_lessequals(c_Message_Oanalz(X91),c_Message_Oanalz(X90),tc_set(tc_Message_Omsg))
      | c_lessequals(X91,c_Message_Oanalz(X90),tc_set(tc_Message_Omsg)) ),
    inference(variable_rename,[status(thm)],[c_0_3948]) ).

fof(c_0_6886,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_less(X46,X45,X47)
      | c_in(X46,c_SetInterval_OlessThan(X45,X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_3949]) ).

fof(c_0_6887,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_less(X45,X46,X47)
      | c_in(X46,c_SetInterval_OgreaterThan(X45,X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_3950]) ).

fof(c_0_6888,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_lessequals(X46,X45,X47)
      | c_in(X46,c_SetInterval_OatMost(X45,X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_3951]) ).

fof(c_0_6889,plain,
    ! [X45,X46,X47] :
      ( ~ class_Orderings_Oord(X47)
      | ~ c_lessequals(X45,X46,X47)
      | c_in(X46,c_SetInterval_OatLeast(X45,X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_3952]) ).

fof(c_0_6890,plain,
    ! [X15,X16,X17] : c_inter(X16,c_minus(X15,X16,tc_set(X17)),X17) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_3953]) ).

fof(c_0_6891,plain,
    ! [X61,X62] :
      ( ~ c_less(X62,X61,tc_nat)
      | c_List_Olast(c_List_Oupt(X62,X61),tc_nat) = c_minus(X61,c_1,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3954]) ).

fof(c_0_6892,plain,
    ! [X108,X109,X110,X111,X112,X113] :
      ( c_Event_Oevent_OSays(X113,X111,X109) != c_Event_Oevent_OSays(X112,X110,X108)
      | X109 = X108 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3955])])]) ).

fof(c_0_6893,plain,
    ! [X108,X109,X110,X111,X112,X113] :
      ( c_Event_Oevent_OSays(X113,X111,X109) != c_Event_Oevent_OSays(X112,X110,X108)
      | X111 = X110 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3956])])]) ).

fof(c_0_6894,plain,
    ! [X108,X109,X110,X111,X112,X113] :
      ( c_Event_Oevent_OSays(X113,X111,X109) != c_Event_Oevent_OSays(X112,X110,X108)
      | X113 = X112 ),
    inference(variable_rename,[status(thm)],[c_0_3957]) ).

fof(c_0_6895,plain,
    ! [X5,X6,X7,X8] :
      ( c_Sum__Type_OInr(X6,X7,X8) != c_Sum__Type_OInr(X5,X7,X8)
      | X6 = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3958])])]) ).

fof(c_0_6896,plain,
    ! [X5,X6,X7,X8] :
      ( c_Sum__Type_OInl(X6,X8,X7) != c_Sum__Type_OInl(X5,X8,X7)
      | X6 = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3959])])]) ).

fof(c_0_6897,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3960]) ).

fof(c_0_6898,plain,
    ! [X53,X54,X55,X56] :
      ( c_append(X55,X54,X56) != c_append(X55,X53,X56)
      | X54 = X53 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3961])])]) ).

fof(c_0_6899,plain,
    ! [X66,X67,X68,X69,X70] :
      ( c_List_Olist_OCons(X69,X67,X70) != c_List_Olist_OCons(X68,X66,X70)
      | X67 = X66 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3962])])]) ).

fof(c_0_6900,plain,
    ! [X66,X67,X68,X69,X70] :
      ( c_List_Olist_OCons(X69,X67,X70) != c_List_Olist_OCons(X68,X66,X70)
      | X69 = X68 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3963])])]) ).

fof(c_0_6901,plain,
    ! [X53,X54,X55,X56] :
      ( c_append(X54,X55,X56) != c_append(X53,X55,X56)
      | X54 = X53 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3964])])]) ).

fof(c_0_6902,plain,
    ! [X12,X13,X14,X15] :
      ( c_Datatype__Universe_OIn1(X13,X15,X14) != c_Datatype__Universe_OIn1(X12,X15,X14)
      | X13 = X12 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3965])])]) ).

fof(c_0_6903,plain,
    ! [X12,X13,X14,X15] :
      ( c_Datatype__Universe_OIn0(X13,X15,X14) != c_Datatype__Universe_OIn0(X12,X15,X14)
      | X13 = X12 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3966])])]) ).

fof(c_0_6904,plain,
    ! [X29,X30,X31,X32] :
      ( c_Datatype__Universe_OAtom(X30,X32,X31) != c_Datatype__Universe_OAtom(X29,X32,X31)
      | X30 = X29 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3967])])]) ).

fof(c_0_6905,plain,
    ! [X5,X6,X7,X8] :
      ( c_Datatype__Universe_ONumb(X6,X8,X7) != c_Datatype__Universe_ONumb(X5,X8,X7)
      | X6 = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3968])])]) ).

fof(c_0_6906,plain,
    ! [X5,X6,X7,X8] :
      ( c_Datatype__Universe_OLeaf(X6,X8,X7) != c_Datatype__Universe_OLeaf(X5,X8,X7)
      | X6 = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3969])])]) ).

fof(c_0_6907,plain,
    ! [X50,X51] :
      ( ~ c_Divides_Oop_Advd(c_uminus(X50,tc_IntDef_Oint),X51,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X50,X51,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3970]) ).

fof(c_0_6908,plain,
    ! [X50,X51] :
      ( ~ c_Divides_Oop_Advd(X50,c_uminus(X51,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X50,X51,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_3971]) ).

fof(c_0_6909,plain,
    ! [X90,X91] : c_Message_Oparts(c_union(X91,X90,tc_Message_Omsg)) = c_union(c_Message_Oparts(X91),c_Message_Oparts(X90),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_3972]) ).

fof(c_0_6910,plain,
    ! [X95,X96] : c_Message_OkeysFor(c_union(X96,X95,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X96),c_Message_OkeysFor(X95),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3973]) ).

fof(c_0_6911,plain,
    ! [X23,X24] : c_Orderings_Omin(c_Suc(X24),c_Suc(X23),tc_nat) = c_Suc(c_Orderings_Omin(X24,X23,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_3974]) ).

fof(c_0_6912,plain,
    ! [X23,X24] : c_Orderings_Omax(c_Suc(X24),c_Suc(X23),tc_nat) = c_Suc(c_Orderings_Omax(X24,X23,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_3975]) ).

fof(c_0_6913,plain,
    ! [X85,X86] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X86,X85),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3976]) ).

fof(c_0_6914,plain,
    ! [X23,X24] : c_IntDef_Oint(c_plus(X24,X23,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X23),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_3977]) ).

fof(c_0_6915,plain,
    ! [X29,X30] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X29,X30)),c_Message_OsymKeys,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_3978]) ).

fof(c_0_6916,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Osynth(c_Message_Osynth(X91)),tc_Message_Omsg)
      | c_in(X90,c_Message_Osynth(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3979]) ).

fof(c_0_6917,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Oparts(c_Message_Oparts(X91)),tc_Message_Omsg)
      | c_in(X90,c_Message_Oparts(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3980]) ).

fof(c_0_6918,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Oanalz(c_Message_Oanalz(X91)),tc_Message_Omsg)
      | c_in(X90,c_Message_Oanalz(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_3981]) ).

fof(c_0_6919,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Ofield(X30)
      | c_times(c_0,c_divide(X29,c_0,X30),X30) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3982]) ).

fof(c_0_6920,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Ofield(X30)
      | c_times(c_divide(X29,c_0,X30),c_0,X30) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3983]) ).

fof(c_0_6921,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Ofield(X21)
      | c_divide(c_times(X20,c_0,X21),c_0,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3984]) ).

fof(c_0_6922,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Ofield(X30)
      | c_divide(c_0,c_times(X29,c_0,X30),X30) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3985]) ).

fof(c_0_6923,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Ofield(X21)
      | c_divide(c_times(c_0,X20,X21),c_0,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3986]) ).

fof(c_0_6924,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Ofield(X30)
      | c_divide(c_0,c_times(c_0,X29,X30),X30) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_3987]) ).

fof(c_0_6925,plain,
    ! [X29,X30,X31,X32] : c_Sum__Type_OInr(X29,X31,X32) != c_Sum__Type_OInl(X30,X32,X31),
    inference(variable_rename,[status(thm)],[c_0_3988]) ).

fof(c_0_6926,plain,
    ! [X29,X30,X31,X32] : c_Sum__Type_OInl(X30,X32,X31) != c_Sum__Type_OInr(X29,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_3989]) ).

fof(c_0_6927,plain,
    ! [X20,X21,X22,X23] : c_Datatype__Universe_ONumb(X20,X23,X22) != c_Datatype__Universe_OLeaf(X21,X23,X22),
    inference(variable_rename,[status(thm)],[c_0_3990]) ).

fof(c_0_6928,plain,
    ! [X20,X21,X22,X23] : c_Datatype__Universe_OLeaf(X21,X23,X22) != c_Datatype__Universe_ONumb(X20,X23,X22),
    inference(variable_rename,[status(thm)],[c_0_3991]) ).

fof(c_0_6929,plain,
    ! [X12,X13,X14,X15] : c_Datatype__Universe_OIn1(X12,X15,X14) != c_Datatype__Universe_OIn0(X13,X15,X14),
    inference(variable_rename,[status(thm)],[c_0_3992]) ).

fof(c_0_6930,plain,
    ! [X12,X13,X14,X15] : c_Datatype__Universe_OIn0(X13,X15,X14) != c_Datatype__Universe_OIn1(X12,X15,X14),
    inference(variable_rename,[status(thm)],[c_0_3993]) ).

fof(c_0_6931,plain,
    ! [X90,X91] :
      ( ~ c_in(c_Message_Omsg_OKey(X90),X91,tc_Message_Omsg)
      | c_in(c_Message_OinvKey(X90),c_Message_OkeysFor(c_Message_Osynth(X91)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_3994]) ).

fof(c_0_6932,plain,
    ! [X29,X30,X31,X32] :
      ( c_insert(X30,X31,X32) != c_insert(X29,c_emptyset,X32)
      | X30 = X29 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3995])])]) ).

fof(c_0_6933,plain,
    ! [X29,X30,X31,X32] :
      ( c_insert(X29,c_emptyset,X32) != c_insert(X30,X31,X32)
      | X30 = X29 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_3996])])]) ).

fof(c_0_6934,plain,
    ! [X90,X91] :
      ( ~ c_lessequals(X91,c_Message_Osynth(X90),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Osynth(X91),c_Message_Osynth(X90),tc_set(tc_Message_Omsg)) ),
    inference(variable_rename,[status(thm)],[c_0_3997]) ).

fof(c_0_6935,plain,
    ! [X90,X91] :
      ( ~ c_lessequals(X91,c_Message_Oparts(X90),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oparts(X91),c_Message_Oparts(X90),tc_set(tc_Message_Omsg)) ),
    inference(variable_rename,[status(thm)],[c_0_3998]) ).

fof(c_0_6936,plain,
    ! [X90,X91] :
      ( ~ c_lessequals(X91,c_Message_Oanalz(X90),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oanalz(X91),c_Message_Oanalz(X90),tc_set(tc_Message_Omsg)) ),
    inference(variable_rename,[status(thm)],[c_0_3999]) ).

fof(c_0_6937,plain,
    ! [X5,X6] : c_List_Olist_OCons(X5,c_List_Olist_ONil,X6) = c_List_Orev(c_List_Olist_OCons(X5,c_List_Olist_ONil,X6),X6),
    inference(variable_rename,[status(thm)],[c_0_4000]) ).

fof(c_0_6938,plain,
    ! [X5,X6] : c_List_Orev(c_List_Olist_OCons(X5,c_List_Olist_ONil,X6),X6) = c_List_Olist_OCons(X5,c_List_Olist_ONil,X6),
    inference(variable_rename,[status(thm)],[c_0_4001]) ).

fof(c_0_6939,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_less(c_0,X20,X21)
      | c_less(c_uminus(X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4002]) ).

fof(c_0_6940,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_lessequals(c_0,X20,X21)
      | c_lessequals(c_uminus(X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4003]) ).

fof(c_0_6941,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_less(X20,c_0,X21)
      | c_less(c_0,c_uminus(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_4004]) ).

fof(c_0_6942,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | ~ c_lessequals(X20,c_0,X21)
      | c_lessequals(c_0,c_uminus(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_4005]) ).

fof(c_0_6943,plain,
    ! [X23,X24,X25] :
      ( c_times(X24,X25,tc_nat) != c_times(X23,X25,tc_nat)
      | X24 = X23
      | X25 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4006]) ).

fof(c_0_6944,plain,
    ! [X23,X24,X25] :
      ( c_times(X25,X24,tc_nat) != c_times(X25,X23,tc_nat)
      | X24 = X23
      | X25 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4007]) ).

fof(c_0_6945,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X21)
      | ~ c_in(X20,c_IntDef_OInts,X21)
      | c_in(c_uminus(X20,X21),c_IntDef_OInts,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4008]) ).

fof(c_0_6946,plain,
    ! [X13,X14,X15] :
      ( ~ class_Numeral_Onumber__ring(X15)
      | ~ class_Ring__and__Field_Oordered__idom(X15)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X14,X15),X15)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X14,X13),X15),X15) ),
    inference(variable_rename,[status(thm)],[c_0_4009]) ).

fof(c_0_6947,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X25)
      | ~ c_Parity_Oeven(X24,tc_nat)
      | c_Nat_Opower(c_uminus(X23,X25),X24,X25) = c_Nat_Opower(X23,X24,X25) ),
    inference(variable_rename,[status(thm)],[c_0_4010]) ).

fof(c_0_6948,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X29,X28,tc_nat),tc_nat) = c_minus(X28,X29,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4011]) ).

fof(c_0_6949,plain,
    ! [X28,X29] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X29,X28,tc_nat),tc_nat) = c_minus(X28,X29,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4012]) ).

fof(c_0_6950,plain,
    ! [X23,X24,X25] :
      ( c_plus(X24,X25,tc_nat) != c_plus(X23,X25,tc_nat)
      | X24 = X23 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4013])])]) ).

fof(c_0_6951,plain,
    ! [X23,X24,X25] :
      ( c_plus(X25,X24,tc_nat) != c_plus(X25,X23,tc_nat)
      | X24 = X23 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4014])])]) ).

fof(c_0_6952,plain,
    ! [X29,X30,X31] :
      ( c_insert(X30,c_emptyset,X31) != c_insert(X29,c_emptyset,X31)
      | X30 = X29 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4015])])]) ).

fof(c_0_6953,plain,
    ! [X5,X6,X7] :
      ( ~ class_Numeral_Onumber__ring(X7)
      | c_Numeral_Onumber__of(X6,X7) != c_Numeral_Onumber__of(X5,X7)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X6,c_Numeral_Obin__minus(X5)),X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_4016]) ).

fof(c_0_6954,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oring(X31)
      | c_times(c_uminus(X30,X31),c_uminus(X29,X31),X31) = c_times(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_4017]) ).

fof(c_0_6955,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X24)
      | ~ c_less(c_0,X23,tc_nat)
      | c_less(c_0,c_NatArith_Oof__nat(X23,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_4018]) ).

fof(c_0_6956,plain,
    ! [X13,X14] :
      ( ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_less(X13,c_0,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X13,X14),c_0,X14) ),
    inference(variable_rename,[status(thm)],[c_0_4019]) ).

fof(c_0_6957,plain,
    ! [X13,X14] :
      ( ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_lessequals(X13,c_0,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X13,X14),c_0,X14) ),
    inference(variable_rename,[status(thm)],[c_0_4020]) ).

fof(c_0_6958,plain,
    ! [X50,X51] :
      ( ~ class_Ring__and__Field_Oordered__idom(X51)
      | ~ c_less(c_0,X50,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Oof__int(X50,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4021]) ).

fof(c_0_6959,plain,
    ! [X50,X51] :
      ( ~ class_Ring__and__Field_Oordered__idom(X51)
      | ~ c_lessequals(c_0,X50,tc_IntDef_Oint)
      | c_lessequals(c_0,c_IntDef_Oof__int(X50,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4022]) ).

fof(c_0_6960,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4023]) ).

fof(c_0_6961,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) != c_Numeral_Onumber__of(X85,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4024])])]) ).

fof(c_0_6962,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) != c_Numeral_Onumber__of(X85,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4025]) ).

fof(c_0_6963,plain,
    ! [X2] :
      ( ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X2)) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_4026]) ).

fof(c_0_6964,plain,
    ! [X23,X24] : c_plus(c_Suc(X24),X23,tc_nat) = c_Suc(c_plus(X24,X23,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4027]) ).

fof(c_0_6965,plain,
    ! [X23,X24] : c_plus(X24,c_Suc(X23),tc_nat) = c_Suc(c_plus(X24,X23,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4028]) ).

fof(c_0_6966,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber__ring(X51)
      | c_minus(c_Numeral_Onumber__of(X50,X51),c_Numeral_Onumber__of(X49,X51),X51) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X50,c_Numeral_Obin__minus(X49)),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4029]) ).

fof(c_0_6967,plain,
    ! [X49,X50] :
      ( ~ class_Numeral_Onumber__ring(X50)
      | c_plus(c_Numeral_Onumber__of(X49,X50),c_1,X50) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X49,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X50) ),
    inference(variable_rename,[status(thm)],[c_0_4030]) ).

fof(c_0_6968,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber__ring(X14)
      | c_plus(c_1,c_Numeral_Onumber__of(X13,X14),X14) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X13),X14) ),
    inference(variable_rename,[status(thm)],[c_0_4031]) ).

fof(c_0_6969,plain,
    ! [X49] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X49,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X49),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4032]) ).

fof(c_0_6970,plain,
    ! [X94,X95] :
      ( ~ c_in(X94,c_Message_OkeysFor(X95),tc_nat)
      | c_in(X94,c_Message_OkeysFor(c_Message_Osynth(X95)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4033]) ).

fof(c_0_6971,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber__ring(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X13,X14),X14)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X13,c_Numeral_Obit_OB0),X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_4034]) ).

fof(c_0_6972,plain,
    ! [X90,X91,X92] : c_Message_OkeysFor(c_insert(c_Message_OHPair(X91,X90),X92,tc_Message_Omsg)) = c_Message_OkeysFor(X92),
    inference(variable_rename,[status(thm)],[c_0_4035]) ).

fof(c_0_6973,plain,
    ! [X104,X105,X106] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X106,X105),X104,tc_Event_Oevent)) = c_Event_Oused(X104),
    inference(variable_rename,[status(thm)],[c_0_4036]) ).

fof(c_0_6974,plain,
    ! [X90,X91,X92] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X91,X90),X92,tc_Message_Omsg)) = c_Message_OkeysFor(X92),
    inference(variable_rename,[status(thm)],[c_0_4037]) ).

fof(c_0_6975,plain,
    ! [X19,X20] :
      ( c_Divides_Oop_Amod(X19,X20,tc_IntDef_Oint) != c_0
      | X19 = c_times(X20,c_Main_Ozmod__eq__0D__dest__1(X20,X19),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4038]) ).

fof(c_0_6976,plain,
    ! [X19,X20] :
      ( c_Divides_Oop_Amod(X19,X20,tc_nat) != c_0
      | X19 = c_times(X20,c_Main_Omod__eq__0D__dest__1(X20,X19),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4039]) ).

fof(c_0_6977,plain,
    ! [X104,X105,X106] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X105,X106)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X104)),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4040]) ).

fof(c_0_6978,plain,
    ! [X90,X91] :
      ( ~ c_in(c_Message_Omsg_ONonce(X90),c_Message_Osynth(X91),tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X90),X91,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4041]) ).

fof(c_0_6979,plain,
    ! [X94,X95] :
      ( ~ c_in(c_Message_Omsg_OKey(X94),c_Message_Osynth(X95),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X94),X95,tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4042]) ).

fof(c_0_6980,plain,
    ! [X5,X6,X7] : c_Relation_Oconverse(c_Relation_Oconverse(X5,X7,X6),X6,X7) = X5,
    inference(variable_rename,[status(thm)],[c_0_4043]) ).

fof(c_0_6981,plain,
    ! [X25,X26,X27] : c_List_Oremove1(X26,c_List_Olist_OCons(X26,X25,X27),X27) = X25,
    inference(variable_rename,[status(thm)],[c_0_4044]) ).

fof(c_0_6982,plain,
    ! [X15,X16,X17] : c_in(X15,c_insert(X15,X16,X17),X17),
    inference(variable_rename,[status(thm)],[c_0_4045]) ).

fof(c_0_6983,plain,
    ! [X27,X28,X29] : c_List_Oop_Amem(X28,c_List_Olist_OCons(X28,X27,X29),X29),
    inference(variable_rename,[status(thm)],[c_0_4046]) ).

fof(c_0_6984,plain,
    ! [X25,X26,X27] : c_List_Onth(c_List_Olist_OCons(X25,X26,X27),c_0,X27) = X25,
    inference(variable_rename,[status(thm)],[c_0_4047]) ).

fof(c_0_6985,plain,
    ! [X50,X51] :
      ( ~ c_Divides_Oop_Advd(X50,X51,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X50,tc_IntDef_Oint),X51,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4048]) ).

fof(c_0_6986,plain,
    ! [X50,X51] :
      ( ~ c_Divides_Oop_Advd(X50,X51,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X50,c_uminus(X51,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4049]) ).

fof(c_0_6987,plain,
    ! [X28,X29] : c_in(c_SetInterval_OgreaterThanLessThan(X29,X28,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_4050]) ).

fof(c_0_6988,plain,
    ! [X28,X29] : c_in(c_SetInterval_OgreaterThanLessThan(X29,X28,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4051]) ).

fof(c_0_6989,plain,
    ! [X28,X29] : c_in(c_SetInterval_OgreaterThanAtMost(X29,X28,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_4052]) ).

fof(c_0_6990,plain,
    ! [X28,X29] : c_in(c_SetInterval_OgreaterThanAtMost(X29,X28,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4053]) ).

fof(c_0_6991,plain,
    ! [X28,X29] : c_in(c_SetInterval_OatLeastLessThan(X29,X28,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_4054]) ).

fof(c_0_6992,plain,
    ! [X28,X29] : c_in(c_SetInterval_OatLeastLessThan(X29,X28,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4055]) ).

fof(c_0_6993,plain,
    ! [X28,X29] : c_in(c_SetInterval_OatLeastAtMost(X29,X28,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_4056]) ).

fof(c_0_6994,plain,
    ! [X28,X29] : c_in(c_SetInterval_OatLeastAtMost(X29,X28,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4057]) ).

fof(c_0_6995,plain,
    ! [X25,X26,X27] :
      ( c_List_Olist_OCons(X26,c_List_Olist_ONil,X27) != c_List_Orev(X25,X27)
      | X25 = c_List_Olist_OCons(X26,c_List_Olist_ONil,X27) ),
    inference(variable_rename,[status(thm)],[c_0_4058]) ).

fof(c_0_6996,plain,
    ! [X25,X26,X27] :
      ( c_List_Orev(X25,X27) != c_List_Olist_OCons(X26,c_List_Olist_ONil,X27)
      | X25 = c_List_Olist_OCons(X26,c_List_Olist_ONil,X27) ),
    inference(variable_rename,[status(thm)],[c_0_4059]) ).

fof(c_0_6997,plain,
    ! [X29,X30] :
      ( X30 = c_0
      | c_div(c_times(X30,X29,tc_IntDef_Oint),X30,tc_IntDef_Oint) = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4060]) ).

fof(c_0_6998,plain,
    ! [X29,X30] :
      ( X30 = c_0
      | c_div(c_times(X29,X30,tc_IntDef_Oint),X30,tc_IntDef_Oint) = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4061]) ).

fof(c_0_6999,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X16,X15,tc_set(X17))
      | c_less(X16,X15,tc_set(X17))
      | X16 = X15 ),
    inference(variable_rename,[status(thm)],[c_0_4062]) ).

fof(c_0_7000,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Osynth(X91),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X90),c_Message_Osynth(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4063]) ).

fof(c_0_7001,plain,
    ! [X90,X91] :
      ( ~ c_in(c_Message_Omsg_ONonce(X90),X91,tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X90),c_Message_Osynth(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4064]) ).

fof(c_0_7002,plain,
    ! [X94,X95] :
      ( ~ c_in(c_Message_Omsg_OKey(X94),X95,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OKey(X94),c_Message_Osynth(X95),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4065]) ).

fof(c_0_7003,plain,
    ! [X20,X21] : c_in(X20,c_insert(X20,c_emptyset,X21),X21),
    inference(variable_rename,[status(thm)],[c_0_4066]) ).

fof(c_0_7004,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4067])])]) ).

fof(c_0_7005,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | ~ c_Parity_Oeven(X4,tc_nat)
      | c_Parity_Oeven(c_plus(X4,X3,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4068])])]) ).

fof(c_0_7006,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4069])])]) ).

fof(c_0_7007,plain,
    ! [X23,X24] : c_lessequals(X23,c_plus(X24,X23,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4070]) ).

fof(c_0_7008,plain,
    ! [X23,X24] : c_lessequals(X23,c_plus(X23,X24,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4071]) ).

fof(c_0_7009,plain,
    ! [X23,X24] :
      ( c_less(c_0,c_Nat_Opower(X23,X24,tc_nat),tc_nat)
      | X23 = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4072])])]) ).

fof(c_0_7010,plain,
    ! [X23,X24] : c_lessequals(c_minus(X24,X23,tc_nat),X24,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4073]) ).

fof(c_0_7011,plain,
    ! [X29,X30] : c_Divides_Oop_Amod(c_times(X29,X30,tc_IntDef_Oint),X29,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4074]) ).

fof(c_0_7012,plain,
    ! [X29,X30] : c_Divides_Oop_Amod(c_times(X30,X29,tc_IntDef_Oint),X29,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4075]) ).

fof(c_0_7013,plain,
    ! [X29,X30] : c_div(c_Divides_Oop_Amod(X30,X29,tc_IntDef_Oint),X29,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4076]) ).

fof(c_0_7014,plain,
    ! [X23,X24] : c_div(c_Divides_Oop_Amod(X24,X23,tc_nat),X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4077]) ).

fof(c_0_7015,plain,
    ! [X23,X24] : c_Divides_Oop_Amod(c_times(X24,X23,tc_nat),X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4078]) ).

fof(c_0_7016,plain,
    ! [X23,X24] : c_Divides_Oop_Amod(c_times(X23,X24,tc_nat),X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4079]) ).

fof(c_0_7017,plain,
    ! [X23,X24] : c_lessequals(c_div(X24,X23,tc_nat),X24,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4080]) ).

fof(c_0_7018,plain,
    ! [X18,X19] : c_Divides_Oop_Advd(X19,c_times(X18,X19,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4081]) ).

fof(c_0_7019,plain,
    ! [X18,X19] : c_Divides_Oop_Advd(X19,c_times(X19,X18,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4082]) ).

fof(c_0_7020,plain,
    ! [X18,X19] : c_Divides_Oop_Advd(X19,c_times(X18,X19,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4083]) ).

fof(c_0_7021,plain,
    ! [X18,X19] : c_Divides_Oop_Advd(X19,c_times(X19,X18,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4084]) ).

fof(c_0_7022,plain,
    ! [X15,X16,X17] :
      ( ~ c_lessequals(X16,X15,tc_set(X17))
      | c_minus(X16,X15,tc_set(X17)) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4085]) ).

fof(c_0_7023,plain,
    ! [X15,X16,X17] :
      ( c_minus(X16,X15,tc_set(X17)) != c_emptyset
      | c_lessequals(X16,X15,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_4086]) ).

fof(c_0_7024,plain,
    ! [X15,X16,X17] :
      ( ~ c_less(X16,X15,tc_set(X17))
      | c_lessequals(X16,X15,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_4087]) ).

fof(c_0_7025,plain,
    ! [X5,X6] :
      ( ~ c_lessequals(c_Nat_Osize(X5,tc_List_Olist(X6)),c_1,tc_nat)
      | c_List_Orotate1(X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4088]) ).

fof(c_0_7026,plain,
    ! [X23,X24] :
      ( ~ c_less(c_Suc(X24),c_Suc(X23),tc_nat)
      | c_less(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4089]) ).

fof(c_0_7027,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(c_Suc(X23),c_Suc(X24),tc_nat)
      | c_lessequals(X23,X24,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4090]) ).

fof(c_0_7028,plain,
    ! [X50,X51] :
      ( ~ c_less(c_IntDef_Onat(X51),c_IntDef_Onat(X50),tc_nat)
      | c_less(X51,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4091]) ).

fof(c_0_7029,plain,
    ! [X23,X24] :
      ( ~ c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X23),tc_IntDef_Oint)
      | c_less(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4092]) ).

fof(c_0_7030,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X23),tc_IntDef_Oint)
      | c_lessequals(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4093]) ).

fof(c_0_7031,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4094]) ).

fof(c_0_7032,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4095]) ).

fof(c_0_7033,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X86,tc_nat),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4096]) ).

fof(c_0_7034,plain,
    ! [X50,X51] :
      ( ~ c_less(c_IntDef_Onat(X51),c_IntDef_Onat(X50),tc_nat)
      | c_less(c_0,X50,tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4097])])]) ).

fof(c_0_7035,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber__ring(X51)
      | c_times(c_Numeral_Onumber__of(X50,X51),c_Numeral_Onumber__of(X49,X51),X51) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X50,X49),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4098]) ).

fof(c_0_7036,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber__ring(X51)
      | c_plus(c_Numeral_Onumber__of(X50,X51),c_Numeral_Onumber__of(X49,X51),X51) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X50,X49),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4099]) ).

fof(c_0_7037,plain,
    ! [X15,X16,X17] : c_minus(X16,c_uminus(X15,tc_set(X17)),tc_set(X17)) = c_inter(X16,X15,X17),
    inference(variable_rename,[status(thm)],[c_0_4100]) ).

fof(c_0_7038,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,c_Message_Oanalz(X91),tc_Message_Omsg)
      | c_in(X90,c_Message_Oparts(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4101]) ).

fof(c_0_7039,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Oordered__idom(X25)
      | c_Nat_Opower(X24,X23,X25) != c_0
      | c_less(c_0,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4102]) ).

fof(c_0_7040,plain,
    ! [X3] : c_less(c_0,c_Nat_Opower(X3,c_0,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4103]) ).

fof(c_0_7041,plain,
    ! [X29,X30] : c_div(c_uminus(X30,tc_IntDef_Oint),c_uminus(X29,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X30,X29,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4104]) ).

fof(c_0_7042,plain,
    ! [X49] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X49),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,c_Numeral_Onumber__of(X49,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4105]) ).

fof(c_0_7043,plain,
    ! [X50] :
      ( ~ c_less(c_Suc(c_0),c_IntDef_Onat(X50),tc_nat)
      | c_less(c_1,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4106]) ).

fof(c_0_7044,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber__ring(X14)
      | ~ class_Ring__and__Field_Oordered__idom(X14)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X13,c_Numeral_Obit_OB1),X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_4107]) ).

fof(c_0_7045,plain,
    ! [X23,X24] :
      ( ~ c_less(X24,X23,tc_nat)
      | c_less(c_Suc(X24),c_Suc(X23),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4108]) ).

fof(c_0_7046,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_lessequals(c_Suc(X23),c_Suc(X24),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4109]) ).

fof(c_0_7047,plain,
    ! [X23,X24] :
      ( ~ c_less(X24,X23,tc_nat)
      | c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X23),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4110]) ).

fof(c_0_7048,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X23),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4111]) ).

fof(c_0_7049,plain,
    ! [X23,X24] :
      ( ~ class_Power_Orecpower(X24)
      | ~ class_Ring__and__Field_Oordered__idom(X24)
      | ~ c_less(c_0,X23,tc_nat)
      | c_Nat_Opower(c_0,X23,X24) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4112]) ).

fof(c_0_7050,plain,
    ! [X23,X24] : ~ c_less(c_IntDef_Oint(X23),c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4113]) ).

fof(c_0_7051,plain,
    ! [X28,X29,X30] :
      ( ~ class_Orderings_Oorder(X30)
      | ~ c_lessequals(X28,X29,X30)
      | c_SetInterval_OgreaterThanAtMost(X29,X28,X30) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4114]) ).

fof(c_0_7052,plain,
    ! [X23,X24,X25] :
      ( ~ class_Orderings_Oorder(X25)
      | ~ c_lessequals(X23,X24,X25)
      | c_SetInterval_OatLeastLessThan(X24,X23,X25) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4115]) ).

fof(c_0_7053,plain,
    ! [X23,X24,X25] :
      ( ~ class_Orderings_Oorder(X25)
      | ~ c_less(X23,X24,X25)
      | c_SetInterval_OatLeastAtMost(X24,X23,X25) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4116]) ).

fof(c_0_7054,plain,
    ! [X15,X16,X17] :
      ( c_in(X15,X16,X17)
      | c_in(X15,c_uminus(X16,tc_set(X17)),X17) ),
    inference(variable_rename,[status(thm)],[c_0_4117]) ).

fof(c_0_7055,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_less(c_Numeral_Onumber__of(X5,X6),c_0,X6)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X5,X6),X6) = c_Numeral_Onumber__of(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4118]) ).

fof(c_0_7056,plain,
    ! [X25,X26,X27] : c_Nat_Osize(c_List_Orotate(X26,X25,X27),tc_List_Olist(X27)) = c_Nat_Osize(X25,tc_List_Olist(X27)),
    inference(variable_rename,[status(thm)],[c_0_4119]) ).

fof(c_0_7057,plain,
    ! [X29,X30,X31] : c_Nat_Osize(c_Sum__Type_OInr(X29,X30,X31),tc_sum(X31,X30)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4120]) ).

fof(c_0_7058,plain,
    ! [X20,X21,X22] : c_Nat_Osize(c_Sum__Type_OInl(X20,X22,X21),tc_sum(X22,X21)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4121]) ).

fof(c_0_7059,plain,
    ! [X23,X24] :
      ( ~ c_less(X24,c_Suc(X23),tc_nat)
      | c_lessequals(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4122]) ).

fof(c_0_7060,plain,
    ! [X7,X8] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X7,X8)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X7,X8,X8),X8) ),
    inference(variable_rename,[status(thm)],[c_0_4123]) ).

fof(c_0_7061,plain,
    ! [X45,X46,X47] :
      ( ~ c_List_Odistinct(X45,X47)
      | c_List_Odistinct(c_List_Otake(X46,X45,X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_4124]) ).

fof(c_0_7062,plain,
    ! [X60,X61,X62] :
      ( ~ c_List_Odistinct(X60,X62)
      | c_List_Odistinct(c_List_Osublist(X60,X61,X62),X62) ),
    inference(variable_rename,[status(thm)],[c_0_4125]) ).

fof(c_0_7063,plain,
    ! [X25,X26,X27] :
      ( ~ c_List_Odistinct(X25,X27)
      | c_List_Odistinct(c_List_Orotate(X26,X25,X27),X27) ),
    inference(variable_rename,[status(thm)],[c_0_4126]) ).

fof(c_0_7064,plain,
    ! [X25,X26,X27] :
      ( ~ c_List_Odistinct(X25,X27)
      | c_List_Odistinct(c_List_Oremove1(X26,X25,X27),X27) ),
    inference(variable_rename,[status(thm)],[c_0_4127]) ).

fof(c_0_7065,plain,
    ! [X45,X46,X47] :
      ( ~ c_List_Odistinct(X45,X47)
      | c_List_Odistinct(c_List_Odrop(X46,X45,X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_4128]) ).

fof(c_0_7066,plain,
    ! [X50] :
      ( ~ c_less(c_1,X50,tc_IntDef_Oint)
      | c_less(c_Suc(c_0),c_IntDef_Onat(X50),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4129]) ).

fof(c_0_7067,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_less(X24,c_Suc(X23),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4130]) ).

fof(c_0_7068,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,X91,tc_Message_Omsg)
      | c_in(X90,c_Message_Osynth(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4131]) ).

fof(c_0_7069,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,X91,tc_Message_Omsg)
      | c_in(X90,c_Message_Oanalz(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4132]) ).

fof(c_0_7070,plain,
    ! [X90,X91] :
      ( ~ c_in(X90,X91,tc_Message_Omsg)
      | c_in(X90,c_Message_Oparts(X91),tc_Message_Omsg) ),
    inference(variable_rename,[status(thm)],[c_0_4133]) ).

fof(c_0_7071,plain,
    ! [X23,X24] : c_Binomial_Obinomial(c_Suc(X23),c_Suc(X24)) = c_plus(c_Binomial_Obinomial(X23,X24),c_Binomial_Obinomial(X23,c_Suc(X24)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4134]) ).

fof(c_0_7072,plain,
    ! [X94] :
      ( ~ c_in(c_Message_OinvKey(X94),c_Message_OsymKeys,tc_nat)
      | c_in(X94,c_Message_OsymKeys,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4135]) ).

fof(c_0_7073,plain,
    ! [X50] :
      ( ~ c_less(c_0,c_IntDef_Onat(X50),tc_nat)
      | c_less(c_0,X50,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4136]) ).

fof(c_0_7074,plain,
    ! [X23] :
      ( ~ c_less(c_0,c_IntDef_Oint(X23),tc_IntDef_Oint)
      | c_less(c_0,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4137]) ).

fof(c_0_7075,plain,
    ! [X3,X4] :
      ( c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X4,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4138])])]) ).

fof(c_0_7076,plain,
    ! [X3,X4] :
      ( c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(X4,tc_nat)
      | c_Parity_Oeven(c_plus(X4,X3,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4139])])]) ).

fof(c_0_7077,plain,
    ! [X3,X4] :
      ( c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X4,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4140])])]) ).

fof(c_0_7078,plain,
    ! [X42,X43,X44] :
      ( ~ c_in(X43,c_Datatype_Oo2s(X42,X44),X44)
      | X42 = c_Datatype_Ooption_OSome(X43,X44) ),
    inference(variable_rename,[status(thm)],[c_0_4141]) ).

fof(c_0_7079,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Oab__group__add(X31)
      | c_minus(X30,c_uminus(X29,X31),X31) = c_plus(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_4142]) ).

fof(c_0_7080,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | c_0 != c_Numeral_Onumber__of(X5,X6)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X5)),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_4143]) ).

fof(c_0_7081,plain,
    ! [X52,X53] :
      ( c_in(c_Main_Oconcat__eq__Nil__conv__1(X52,X53),c_List_Oset(X52,tc_List_Olist(X53)),tc_List_Olist(X53))
      | c_List_Oconcat(X52,X53) = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_4144]) ).

fof(c_0_7082,plain,
    ! [X52,X53] :
      ( c_in(c_Main_ONil__eq__concat__conv__1(X52,X53),c_List_Oset(X52,tc_List_Olist(X53)),tc_List_Olist(X53))
      | c_List_Olist_ONil = c_List_Oconcat(X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_4145]) ).

fof(c_0_7083,plain,
    ! [X94] :
      ( ~ c_in(X94,c_Message_OsymKeys,tc_nat)
      | c_in(c_Message_OinvKey(X94),c_Message_OsymKeys,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4146]) ).

fof(c_0_7084,plain,
    ! [X50] :
      ( ~ c_less(c_0,X50,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Onat(X50),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4147]) ).

fof(c_0_7085,plain,
    ! [X23] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_less(c_0,c_IntDef_Oint(X23),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4148]) ).

fof(c_0_7086,plain,
    ! [X20,X21,X22] :
      ( ~ class_Power_Orecpower(X22)
      | ~ class_Ring__and__Field_Oordered__idom(X22)
      | c_Nat_Opower(X21,c_Numeral_Onumber__of(X20,tc_nat),X22) != c_0
      | X21 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4149]) ).

fof(c_0_7087,plain,
    ! [X23,X24] :
      ( ~ c_less(X23,X24,tc_nat)
      | c_Divides_Oop_Amod(X23,X24,tc_nat) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_4150]) ).

fof(c_0_7088,plain,
    ! [X85] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X85,tc_nat),tc_nat) = c_Suc(c_0) ),
    inference(variable_rename,[status(thm)],[c_0_4151]) ).

fof(c_0_7089,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4152])])]) ).

fof(c_0_7090,plain,
    ! [X85,X86] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X86,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X85,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X86,tc_nat) = c_Numeral_Onumber__of(X85,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4153]) ).

fof(c_0_7091,plain,
    ! [X49] :
      ( ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X49,tc_nat)),tc_IntDef_Oint)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X49,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4154]) ).

fof(c_0_7092,plain,
    ! [X23,X24] :
      ( ~ c_lessequals(X24,X23,tc_nat)
      | c_minus(X24,X23,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4155]) ).

fof(c_0_7093,plain,
    ! [X23,X24] :
      ( c_minus(X24,X23,tc_nat) != c_0
      | c_lessequals(X24,X23,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4156]) ).

fof(c_0_7094,plain,
    ! [X23,X24] :
      ( ~ c_less(X24,X23,tc_nat)
      | c_div(X24,X23,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4157]) ).

fof(c_0_7095,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4158])])]) ).

fof(c_0_7096,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X4,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4159]) ).

fof(c_0_7097,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(c_times(X4,X3,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4160])])]) ).

fof(c_0_7098,plain,
    ! [X3,X4] :
      ( ~ c_Parity_Oeven(X4,tc_nat)
      | c_Parity_Oeven(c_times(X4,X3,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4161]) ).

fof(c_0_7099,plain,
    ! [X5] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4162]) ).

fof(c_0_7100,plain,
    ! [X27,X28,X29] :
      ( X27 = c_List_Olist_ONil
      | c_List_Olast(c_append(X28,X27,X29),X29) = c_List_Olast(X27,X29) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4163])])]) ).

fof(c_0_7101,plain,
    ! [X25,X26,X27] :
      ( X25 = c_List_Olist_ONil
      | c_List_Olast(c_List_Olist_OCons(X26,X25,X27),X27) = c_List_Olast(X25,X27) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4164])])]) ).

fof(c_0_7102,plain,
    ! [X27,X28,X29] :
      ( X28 = c_List_Olist_ONil
      | c_List_Ohd(c_append(X28,X27,X29),X29) = c_List_Ohd(X28,X29) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4165])])]) ).

fof(c_0_7103,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | c_LOrder_Omeet(X20,c_uminus(X20,X21),X21) != c_0
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4166]) ).

fof(c_0_7104,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | c_LOrder_Ojoin(X20,c_uminus(X20,X21),X21) != c_0
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4167]) ).

fof(c_0_7105,plain,
    ! [X25,X26] : c_Nat_Osize(c_List_Otl(X25,X26),tc_List_Olist(X26)) = c_minus(c_Nat_Osize(X25,tc_List_Olist(X26)),c_1,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4168]) ).

fof(c_0_7106,plain,
    ! [X25,X26] : c_Nat_Osize(c_List_Obutlast(X25,X26),tc_List_Olist(X26)) = c_minus(c_Nat_Osize(X25,tc_List_Olist(X26)),c_1,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4169]) ).

fof(c_0_7107,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X5) ),
    inference(variable_rename,[status(thm)],[c_0_4170]) ).

fof(c_0_7108,plain,
    ! [X7,X8] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X7,X8),X8,X8) = c_Relation_ORange(X7,X8,X8),
    inference(variable_rename,[status(thm)],[c_0_4171]) ).

fof(c_0_7109,plain,
    ! [X7,X8] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X7,X8),X8,X8) = c_Relation_ODomain(X7,X8,X8),
    inference(variable_rename,[status(thm)],[c_0_4172]) ).

fof(c_0_7110,plain,
    ! [X25,X26,X27] : c_List_Oset(c_List_Orotate(X26,X25,X27),X27) = c_List_Oset(X25,X27),
    inference(variable_rename,[status(thm)],[c_0_4173]) ).

fof(c_0_7111,plain,
    ! [X25,X26,X27] : c_List_Oitrev(X25,X26,X27) = c_append(c_List_Orev(X25,X27),X26,X27),
    inference(variable_rename,[status(thm)],[c_0_4174]) ).

fof(c_0_7112,plain,
    ! [X23] :
      ( ~ c_less(c_0,X23,tc_nat)
      | c_div(X23,X23,tc_nat) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4175]) ).

fof(c_0_7113,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | c_Numeral_Onumber__of(X5,X6) != c_0
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X5,c_Numeral_Obin__minus(c_Numeral_OPls)),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_4176]) ).

fof(c_0_7114,plain,
    ! [X104,X105,X106] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X105,X106)),c_Event_Oknows(c_Message_Oagent_OSpy,X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4177]) ).

fof(c_0_7115,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | ~ c_lessequals(c_HOL_Oabs(X20,X21),c_0,X21)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4178]) ).

fof(c_0_7116,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber(X14)
      | ~ class_Ring__and__Field_Ofield(X14)
      | c_HOL_Oinverse(c_Numeral_Onumber__of(X13,X14),X14) = c_divide(c_1,c_Numeral_Onumber__of(X13,X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_4179]) ).

fof(c_0_7117,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | ~ c_lessequals(c_NatArith_Oof__nat(X17,X18),c_0,X18)
      | X17 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4180]) ).

fof(c_0_7118,plain,
    ! [X5,X6] : c_in(X5,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X5,X6),X6),X6),
    inference(variable_rename,[status(thm)],[c_0_4181]) ).

fof(c_0_7119,plain,
    ! [X28,X29,X30] : c_List_Osublist(X29,c_SetInterval_OlessThan(X28,tc_nat),X30) = c_List_Otake(X28,X29,X30),
    inference(variable_rename,[status(thm)],[c_0_4182]) ).

fof(c_0_7120,plain,
    ! [X25,X26] : c_List_Olast(c_append(X25,c_List_Olist_ONil,X26),X26) = c_List_Olast(X25,X26),
    inference(variable_rename,[status(thm)],[c_0_4183]) ).

fof(c_0_7121,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | ~ c_less(c_HOL_Oabs(X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4184]) ).

fof(c_0_7122,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | ~ c_less(c_NatArith_Oof__nat(X17,X18),c_0,X18) ),
    inference(variable_rename,[status(thm)],[c_0_4185]) ).

fof(c_0_7123,plain,
    ! [X94,X95] : ~ c_in(c_Message_Omsg_OCrypt(X95,X94),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4186]) ).

fof(c_0_7124,plain,
    ! [X50,X51] : c_plus(X50,c_uminus(X51,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X50,X51,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4187]) ).

fof(c_0_7125,plain,
    ! [X5,X6,X7] : c_Nat_Osize(c_List_Oreplicate(X5,X6,X7),tc_List_Olist(X7)) = X5,
    inference(variable_rename,[status(thm)],[c_0_4188]) ).

fof(c_0_7126,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
      | ~ c_less(c_0,c_HOL_Oabs(c_0,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_4189]) ).

fof(c_0_7127,plain,
    ! [X5,X6] :
      ( ~ class_Orderings_Olinorder(X6)
      | c_Finite__Set_OMin(c_insert(X5,c_emptyset,X6),X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4190]) ).

fof(c_0_7128,plain,
    ! [X5,X6] :
      ( ~ class_Orderings_Olinorder(X6)
      | c_Finite__Set_OMax(c_insert(X5,c_emptyset,X6),X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4191]) ).

fof(c_0_7129,plain,
    ! [X49,X50] : c_Numeral_Obin__mult(c_Numeral_OBit(X50,c_Numeral_Obit_OB1),X49) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X50,X49),c_Numeral_Obit_OB0),X49),
    inference(variable_rename,[status(thm)],[c_0_4192]) ).

fof(c_0_7130,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_Numeral_Onumber__of(X29,X31) != c_0
      | c_0 = c_divide(X30,c_Numeral_Onumber__of(X29,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_4193]) ).

fof(c_0_7131,plain,
    ! [X29,X30,X31] :
      ( ~ class_Numeral_Onumber(X31)
      | ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_Numeral_Onumber__of(X29,X31) != c_0
      | c_divide(X30,c_Numeral_Onumber__of(X29,X31),X31) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4194]) ).

fof(c_0_7132,plain,
    ! [X90,X91] : c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X90),X91,tc_Message_Omsg)) = c_Message_OkeysFor(X91),
    inference(variable_rename,[status(thm)],[c_0_4195]) ).

fof(c_0_7133,plain,
    ! [X90,X91] : c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X90),X91,tc_Message_Omsg)) = c_Message_OkeysFor(X91),
    inference(variable_rename,[status(thm)],[c_0_4196]) ).

fof(c_0_7134,plain,
    ! [X94,X95] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X94),X95,tc_Message_Omsg)) = c_Message_OkeysFor(X95),
    inference(variable_rename,[status(thm)],[c_0_4197]) ).

fof(c_0_7135,plain,
    ! [X90,X91] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X90),X91,tc_Message_Omsg)) = c_Message_OkeysFor(X91),
    inference(variable_rename,[status(thm)],[c_0_4198]) ).

fof(c_0_7136,plain,
    ! [X90,X91] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X91),X90,tc_Message_Omsg)) = c_Message_OkeysFor(X90),
    inference(variable_rename,[status(thm)],[c_0_4199]) ).

fof(c_0_7137,plain,
    ! [X23,X24,X25] :
      ( X24 = c_0
      | c_List_Olast(c_List_Oreplicate(X24,X23,X25),X25) = X23 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4200])])]) ).

fof(c_0_7138,plain,
    ! [X61,X62] :
      ( ~ c_less(X61,X62,tc_nat)
      | c_List_Ohd(c_List_Oupt(X61,X62),tc_nat) = X61 ),
    inference(variable_rename,[status(thm)],[c_0_4201]) ).

fof(c_0_7139,plain,
    ! [X23,X24,X25] :
      ( X24 = c_0
      | c_List_Ohd(c_List_Oreplicate(X24,X23,X25),X25) = X23 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4202])])]) ).

fof(c_0_7140,plain,
    ! [X29,X30] : ~ c_in(c_Public_OpublicKey(X29,X30),c_Message_OsymKeys,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4203]) ).

fof(c_0_7141,plain,
    ! [X14,X15] : ~ c_in(c_Message_Omsg_ONonce(X14),c_Message_Oparts(c_Event_OinitState(X15)),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4204]) ).

fof(c_0_7142,plain,
    ! [X43,X44,X45] : c_List_Otl(c_List_Olist_OCons(X44,X43,X45),X45) = X43,
    inference(variable_rename,[status(thm)],[c_0_4205]) ).

fof(c_0_7143,plain,
    ! [X25,X26,X27] : c_List_Ohd(c_List_Olist_OCons(X25,X26,X27),X27) = X25,
    inference(variable_rename,[status(thm)],[c_0_4206]) ).

fof(c_0_7144,plain,
    ! [X49] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X49,tc_nat),tc_nat)
      | c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X49,tc_nat)),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4207]) ).

fof(c_0_7145,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(X30,c_0,X31) = c_divide(X29,c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_4208]) ).

fof(c_0_7146,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(c_0,X30,X31) = c_divide(c_0,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_4209]) ).

fof(c_0_7147,plain,
    ! [X49,X50] :
      ( ~ class_Numeral_Onumber(X50)
      | ~ class_OrderedGroup_Oab__group__add(X50)
      | c_uminus(c_uminus(c_Numeral_Onumber__of(X49,X50),X50),X50) = c_Numeral_Onumber__of(X49,X50) ),
    inference(variable_rename,[status(thm)],[c_0_4210]) ).

fof(c_0_7148,plain,
    ! [X49,X50] :
      ( ~ class_Numeral_Onumber(X50)
      | ~ class_OrderedGroup_Oab__group__add(X50)
      | c_Numeral_Onumber__of(X49,X50) = c_uminus(c_uminus(c_Numeral_Onumber__of(X49,X50),X50),X50) ),
    inference(variable_rename,[status(thm)],[c_0_4211]) ).

fof(c_0_7149,plain,
    ! [X26,X27,X28] :
      ( ~ c_in(X26,X27,tc_set(X28))
      | c_emptyset != c_Union(X27,X28)
      | X26 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4212]) ).

fof(c_0_7150,plain,
    ! [X26,X27,X28] :
      ( ~ c_in(X26,X27,tc_set(X28))
      | c_Union(X27,X28) != c_emptyset
      | X26 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4213]) ).

fof(c_0_7151,plain,
    ! [X26,X27,X28] :
      ( ~ c_in(X26,X27,tc_set(X28))
      | c_UNIV != c_Inter(X27,X28)
      | X26 = c_UNIV ),
    inference(variable_rename,[status(thm)],[c_0_4214]) ).

fof(c_0_7152,plain,
    ! [X26,X27,X28] :
      ( ~ c_in(X26,X27,tc_set(X28))
      | c_Inter(X27,X28) != c_UNIV
      | X26 = c_UNIV ),
    inference(variable_rename,[status(thm)],[c_0_4215]) ).

fof(c_0_7153,plain,
    ! [X106,X107,X108] : c_Nat_Osize(c_Event_Oevent_OSays(X108,X107,X106),tc_Event_Oevent) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4216]) ).

fof(c_0_7154,plain,
    ! [X25,X26] :
      ( c_Nat_Osize(c_List_Oremdups(X25,X26),tc_List_Olist(X26)) != c_Nat_Osize(X25,tc_List_Olist(X26))
      | c_List_Oremdups(X25,X26) = X25 ),
    inference(variable_rename,[status(thm)],[c_0_4217]) ).

fof(c_0_7155,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | ~ c_lessequals(X20,c_0,X21)
      | c_HOL_Oabs(X20,X21) = c_uminus(X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4218]) ).

fof(c_0_7156,plain,
    ! [X7,X8] : c_union(c_Transitive__Closure_Otrancl(X7,X8),c_Relation_OId,tc_prod(X8,X8)) = c_Transitive__Closure_Ortrancl(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_4219]) ).

fof(c_0_7157,plain,
    ! [X5,X6] : c_Set_Ocontents(c_insert(X5,c_emptyset,X6),X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4220]) ).

fof(c_0_7158,plain,
    ! [X5,X6] : c_List_Olast(c_List_Olist_OCons(X5,c_List_Olist_ONil,X6),X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4221]) ).

fof(c_0_7159,plain,
    ! [X50] :
      ( ~ c_less(c_HOL_Oabs(X50,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
      | X50 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4222]) ).

fof(c_0_7160,plain,
    ! [X23,X24] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X23)),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4223]) ).

fof(c_0_7161,plain,
    ! [X23,X24] : c_minus(c_Suc(X24),c_Suc(X23),tc_nat) = c_minus(X24,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4224]) ).

fof(c_0_7162,plain,
    ! [X43,X44] : c_List_Obutlast(c_List_Olist_OCons(X43,c_List_Olist_ONil,X44),X44) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4225]) ).

fof(c_0_7163,plain,
    ! [X15,X16] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X16))
      | c_Finite__Set_Ocard(X15,X16) != c_0
      | X15 = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4226]) ).

fof(c_0_7164,plain,
    ! [X104,X105,X106] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X105,X106)),c_Event_Oused(X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4227]) ).

fof(c_0_7165,plain,
    ! [X29,X30,X31] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X29,X31)),c_Event_OinitState(X30),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4228]) ).

fof(c_0_7166,plain,
    ! [X99,X100] : c_Nat_Osize(c_Message_Omsg_OCrypt(X99,X100),tc_Message_Omsg) = c_plus(c_Nat_Osize(X100,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4229]) ).

fof(c_0_7167,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Power_Orecpower(X6)
      | c_Parity_Oeven(X5,tc_nat)
      | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X6),X5,X6) = c_Numeral_Onumber__of(c_Numeral_OMin,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4230]) ).

fof(c_0_7168,plain,
    ! [X5,X6] :
      ( ~ class_Power_Orecpower(X6)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X6)
      | c_Parity_Oeven(X5,tc_nat)
      | c_Nat_Opower(c_uminus(c_1,X6),X5,X6) = c_uminus(c_1,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4231]) ).

fof(c_0_7169,plain,
    ! [X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_SetInterval_OatLeastAtMost(X20,X20,X21) = c_insert(X20,c_emptyset,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4232]) ).

fof(c_0_7170,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ofield(X31)
      | c_times(X30,c_0,X31) = c_times(X29,c_0,X31) ),
    inference(variable_rename,[status(thm)],[c_0_4233]) ).

fof(c_0_7171,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ofield(X31)
      | c_times(c_0,X30,X31) = c_times(c_0,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_4234]) ).

fof(c_0_7172,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Ring__and__Field_Odivision__by__zero(X6)
      | ~ class_Ring__and__Field_Ofield(X6)
      | c_divide(X5,c_Numeral_Onumber__of(c_Numeral_OMin,X6),X6) = c_uminus(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4235]) ).

fof(c_0_7173,plain,
    ! [X5,X6] :
      ( ~ class_Numeral_Onumber__ring(X6)
      | ~ class_Power_Orecpower(X6)
      | ~ c_Parity_Oeven(X5,tc_nat)
      | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X6),X5,X6) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4236]) ).

fof(c_0_7174,plain,
    ! [X5,X6] :
      ( ~ class_Power_Orecpower(X6)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X6)
      | ~ c_Parity_Oeven(X5,tc_nat)
      | c_Nat_Opower(c_uminus(c_1,X6),X5,X6) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4237]) ).

fof(c_0_7175,plain,
    ! [X5,X6] : c_Nat_Opower(X5,c_1,tc_set(tc_prod(X6,X6))) = X5,
    inference(variable_rename,[status(thm)],[c_0_4238]) ).

fof(c_0_7176,plain,
    ! [X87,X88] : c_Nat_Opower(X87,c_0,tc_set(tc_prod(X88,X88))) = c_Relation_OId,
    inference(variable_rename,[status(thm)],[c_0_4239]) ).

fof(c_0_7177,plain,
    ! [X17] : c_SetInterval_OatLeastLessThan(X17,c_Suc(X17),tc_nat) = c_insert(X17,c_emptyset,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4240]) ).

fof(c_0_7178,plain,
    ! [X49,X50] : c_Numeral_Obin__add(c_Numeral_OBit(X50,c_Numeral_Obit_OB1),c_Numeral_OBit(X49,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X50,c_Numeral_Obin__succ(X49)),c_Numeral_Obit_OB0),
    inference(variable_rename,[status(thm)],[c_0_4241]) ).

fof(c_0_7179,plain,
    ! [X5,X6] :
      ( X5 = c_List_Olist_ONil
      | c_List_Olist_OCons(c_List_Ohd(X5,X6),c_List_Otl(X5,X6),X6) = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4242])])]) ).

fof(c_0_7180,plain,
    ! [X62,X63] :
      ( c_in(c_List_Olast(X62,X63),c_List_Oset(X62,X63),X63)
      | X62 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4243])])]) ).

fof(c_0_7181,plain,
    ! [X25,X26] :
      ( c_in(c_List_Ohd(X25,X26),c_List_Oset(X25,X26),X26)
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4244])])]) ).

fof(c_0_7182,plain,
    ! [X106,X107,X108,X109,X110] : c_Event_Oevent_ONotes(X108,X106) != c_Event_Oevent_OSays(X110,X109,X107),
    inference(variable_rename,[status(thm)],[c_0_4245]) ).

fof(c_0_7183,plain,
    ! [X106,X107,X108,X109,X110] : c_Event_Oevent_OSays(X110,X109,X107) != c_Event_Oevent_ONotes(X108,X106),
    inference(variable_rename,[status(thm)],[c_0_4246]) ).

fof(c_0_7184,plain,
    ! [X106,X107,X108,X109,X110] : c_Event_Oevent_OGets(X108,X106) != c_Event_Oevent_OSays(X110,X109,X107),
    inference(variable_rename,[status(thm)],[c_0_4247]) ).

fof(c_0_7185,plain,
    ! [X106,X107,X108,X109,X110] : c_Event_Oevent_OSays(X110,X109,X107) != c_Event_Oevent_OGets(X108,X106),
    inference(variable_rename,[status(thm)],[c_0_4248]) ).

fof(c_0_7186,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X6)
      | ~ c_lessequals(c_0,X5,X6)
      | c_OrderedGroup_Opprt(X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4249]) ).

fof(c_0_7187,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X6)
      | ~ c_lessequals(X5,c_0,X6)
      | c_OrderedGroup_Onprt(X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4250]) ).

fof(c_0_7188,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X6)
      | ~ c_lessequals(c_0,X5,X6)
      | c_HOL_Oabs(X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4251]) ).

fof(c_0_7189,plain,
    ! [X43,X44] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X44)
      | c_NatArith_Oof__nat(c_Suc(X43),X44) = c_plus(c_NatArith_Oof__nat(X43,X44),c_1,X44) ),
    inference(variable_rename,[status(thm)],[c_0_4252]) ).

fof(c_0_7190,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X6)
      | ~ c_lessequals(X5,c_0,X6)
      | c_OrderedGroup_Opprt(X5,X6) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4253]) ).

fof(c_0_7191,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X6)
      | ~ c_lessequals(c_0,X5,X6)
      | c_OrderedGroup_Onprt(X5,X6) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4254]) ).

fof(c_0_7192,plain,
    ! [X5] :
      ( ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5))
      | c_Finite__Set_Ocard(c_emptyset,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4255]) ).

fof(c_0_7193,plain,
    ! [X13,X14] :
      ( ~ class_Power_Orecpower(X14)
      | c_Numeral_Onumber__of(X13,tc_nat) != c_0
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X13,tc_nat),X14) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4256]) ).

fof(c_0_7194,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(X30,X29,X31) != c_0
      | X29 = c_0
      | X30 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4257]) ).

fof(c_0_7195,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_1 != c_divide(X30,X29,X31)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4258]) ).

fof(c_0_7196,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | c_1 != c_divide(X29,X30,X31)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4259]) ).

fof(c_0_7197,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Oordered__field(X31)
      | c_divide(X29,X30,X31) != c_1
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4260]) ).

fof(c_0_7198,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_divide(X30,X29,X31) != c_1
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4261]) ).

fof(c_0_7199,plain,
    ! [X49,X50,X51] : c_Numeral_Obin__add(c_Numeral_OBit(X51,c_Numeral_Obit_OB0),c_Numeral_OBit(X50,X49)) = c_Numeral_OBit(c_Numeral_Obin__add(X51,X50),X49),
    inference(variable_rename,[status(thm)],[c_0_4262]) ).

fof(c_0_7200,plain,
    ! [X23,X24] : c_times(X24,c_0,tc_nat) = c_times(X23,c_0,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4263]) ).

fof(c_0_7201,plain,
    ! [X23,X24] : c_times(c_0,X24,tc_nat) = c_times(c_0,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4264]) ).

fof(c_0_7202,plain,
    ! [X23,X24,X25] :
      ( ~ class_Power_Orecpower(X25)
      | ~ class_Ring__and__Field_Oordered__idom(X25)
      | c_Nat_Opower(X24,X23,X25) != c_0
      | X24 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4265]) ).

fof(c_0_7203,plain,
    ! [X15,X16] :
      ( c_in(c_Main_Oempty__Union__conv__1(X15,X16),X15,tc_set(X16))
      | c_emptyset = c_Union(X15,X16) ),
    inference(variable_rename,[status(thm)],[c_0_4266]) ).

fof(c_0_7204,plain,
    ! [X15,X16] :
      ( c_in(c_Main_OUnion__empty__conv__1(X15,X16),X15,tc_set(X16))
      | c_Union(X15,X16) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4267]) ).

fof(c_0_7205,plain,
    ! [X15,X16] :
      ( c_in(c_Main_OInter__UNIV__conv__2__1(X15,X16),X15,tc_set(X16))
      | c_UNIV = c_Inter(X15,X16) ),
    inference(variable_rename,[status(thm)],[c_0_4268]) ).

fof(c_0_7206,plain,
    ! [X15,X16] :
      ( c_in(c_Main_OInter__UNIV__conv__1__1(X15,X16),X15,tc_set(X16))
      | c_Inter(X15,X16) = c_UNIV ),
    inference(variable_rename,[status(thm)],[c_0_4269]) ).

fof(c_0_7207,plain,
    ! [X49,X50] :
      ( c_IntDef_Oint(X50) != c_Numeral_Onumber__of(X49,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4270])])]) ).

fof(c_0_7208,plain,
    ! [X49,X50] :
      ( ~ class_Numeral_Onumber__ring(X50)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X49,tc_nat),X50) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4271]) ).

fof(c_0_7209,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Oab__group__add(X51)
      | c_uminus(X50,X51) != c_Numeral_Onumber__of(X49,X51)
      | c_uminus(c_Numeral_Onumber__of(X49,X51),X51) = X50 ),
    inference(variable_rename,[status(thm)],[c_0_4272]) ).

fof(c_0_7210,plain,
    ! [X49,X50,X51] :
      ( ~ class_Numeral_Onumber(X51)
      | ~ class_OrderedGroup_Oab__group__add(X51)
      | c_Numeral_Onumber__of(X49,X51) != c_uminus(X50,X51)
      | X50 = c_uminus(c_Numeral_Onumber__of(X49,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4273]) ).

fof(c_0_7211,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | c_0 != c_divide(c_1,X20,X21)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4274]) ).

fof(c_0_7212,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | c_divide(c_1,X20,X21) != c_0
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4275]) ).

fof(c_0_7213,plain,
    ! [X50,X51] :
      ( ~ class_Numeral_Onumber__ring(X51)
      | c_times(X50,c_Numeral_Onumber__of(c_Numeral_OMin,X51),X51) = c_uminus(X50,X51) ),
    inference(variable_rename,[status(thm)],[c_0_4276]) ).

fof(c_0_7214,plain,
    ! [X50,X51] :
      ( ~ class_Numeral_Onumber__ring(X51)
      | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X51),X50,X51) = c_uminus(X50,X51) ),
    inference(variable_rename,[status(thm)],[c_0_4277]) ).

fof(c_0_7215,plain,
    ! [X49,X50] : c_Numeral_Obin__add(c_Numeral_OBit(X50,c_Numeral_Obit_OB1),c_Numeral_OBit(X49,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X50,X49),c_Numeral_Obit_OB1),
    inference(variable_rename,[status(thm)],[c_0_4278]) ).

fof(c_0_7216,plain,
    ! [X61,X62] :
      ( ~ c_lessequals(X61,X62,tc_nat)
      | c_List_Oupt(X62,X61) = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_4279]) ).

fof(c_0_7217,plain,
    ! [X10] : ~ c_in(c_Message_Omsg_ONonce(X10),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4280]) ).

fof(c_0_7218,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | c_1 != c_divide(X29,c_0,X30) ),
    inference(variable_rename,[status(thm)],[c_0_4281]) ).

fof(c_0_7219,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Oordered__field(X30)
      | c_divide(X29,c_0,X30) != c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4282]) ).

fof(c_0_7220,plain,
    ! [X20,X21,X22] :
      ( ~ class_Ring__and__Field_Oordered__idom(X22)
      | c_times(X21,X20,X22) != X20
      | X20 = c_0
      | X21 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4283]) ).

fof(c_0_7221,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__idom(X31)
      | X29 != c_times(X30,X29,X31)
      | X29 = c_0
      | X30 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4284]) ).

fof(c_0_7222,plain,
    ! [X20,X21,X22] :
      ( ~ class_Ring__and__Field_Oordered__idom(X22)
      | c_times(X20,X21,X22) != X20
      | X20 = c_0
      | X21 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4285]) ).

fof(c_0_7223,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__idom(X31)
      | X29 != c_times(X29,X30,X31)
      | X29 = c_0
      | X30 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4286]) ).

fof(c_0_7224,plain,
    ! [X104,X105] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X105)),c_Event_Oknows(X105,X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4287]) ).

fof(c_0_7225,plain,
    ! [X99] : c_Nat_Osize(c_Message_Omsg_OHash(X99),tc_Message_Omsg) = c_plus(c_Nat_Osize(X99,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4288]) ).

fof(c_0_7226,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X31)
      | c_times(X30,X29,X31) != c_0
      | X29 = c_0
      | X30 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4289]) ).

fof(c_0_7227,plain,
    ! [X13,X14] :
      ( ~ class_Power_Orecpower(X14)
      | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X13,tc_nat),X14) = c_0
      | c_Numeral_Onumber__of(X13,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4290]) ).

fof(c_0_7228,plain,
    ! [X61,X62] : c_Nat_Osize(c_List_Oupt(X62,X61),tc_List_Olist(tc_nat)) = c_minus(X61,X62,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4291]) ).

fof(c_0_7229,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Oab__group__add(X31)
      | c_minus(X30,X29,X31) != c_0
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4292]) ).

fof(c_0_7230,plain,
    ! [X15,X16] :
      ( ~ c_lessequals(X15,c_emptyset,tc_set(X16))
      | X15 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4293])])]) ).

fof(c_0_7231,plain,
    ! [X15,X16] : c_Relation_Oconverse(c_Relation_Odiag(X15,X16),X16,X16) = c_Relation_Odiag(X15,X16),
    inference(variable_rename,[status(thm)],[c_0_4294]) ).

fof(c_0_7232,plain,
    ! [X23,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X23),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4295]) ).

fof(c_0_7233,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Ofield(X21)
      | c_HOL_Oinverse(c_uminus(X20,X21),X21) = c_uminus(c_HOL_Oinverse(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_4296]) ).

fof(c_0_7234,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Oordered__field(X21)
      | c_HOL_Oabs(c_HOL_Oinverse(X20,X21),X21) = c_HOL_Oinverse(c_HOL_Oabs(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_4297]) ).

fof(c_0_7235,plain,
    ! [X49,X50] :
      ( ~ class_Numeral_Onumber__ring(X50)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X49,tc_nat),X50) = c_Numeral_Onumber__of(X49,X50) ),
    inference(variable_rename,[status(thm)],[c_0_4298]) ).

fof(c_0_7236,plain,
    ! [X15,X16] : ~ c_less(X15,c_emptyset,tc_set(X16)),
    inference(variable_rename,[status(thm)],[c_0_4299]) ).

fof(c_0_7237,plain,
    ! [X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | ~ c_less(X5,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4300]) ).

fof(c_0_7238,plain,
    ! [X15,X16] : c_inter(X15,c_uminus(X15,tc_set(X16)),X16) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4301]) ).

fof(c_0_7239,plain,
    ! [X15,X16] : c_inter(c_uminus(X15,tc_set(X16)),X15,X16) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4302]) ).

fof(c_0_7240,plain,
    ! [X43,X44] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X43,X44),X44) = c_insert(X43,c_emptyset,X44),
    inference(variable_rename,[status(thm)],[c_0_4303]) ).

fof(c_0_7241,plain,
    ! [X50] :
      ( ~ c_lessequals(c_0,X50,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X50)) = X50 ),
    inference(variable_rename,[status(thm)],[c_0_4304]) ).

fof(c_0_7242,plain,
    ! [X23] :
      ( ~ c_lessequals(c_IntDef_Oint(X23),c_0,tc_IntDef_Oint)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4305]) ).

fof(c_0_7243,plain,
    ! [X17] :
      ( ~ c_Divides_Oop_Advd(X17,c_Suc(c_0),tc_nat)
      | X17 = c_Suc(c_0) ),
    inference(variable_rename,[status(thm)],[c_0_4306]) ).

fof(c_0_7244,plain,
    ! [X49] :
      ( c_Numeral_Onumber__of(X49,tc_nat) != c_0
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4307]) ).

fof(c_0_7245,plain,
    ! [X49] :
      ( c_0 != c_Numeral_Onumber__of(X49,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4308]) ).

fof(c_0_7246,plain,
    ! [X25,X26] :
      ( c_less(c_0,c_Nat_Osize(X25,tc_List_Olist(X26)),tc_nat)
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4309])])]) ).

fof(c_0_7247,plain,
    ! [X18] : ~ c_less(c_IntDef_Oint(X18),c_0,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4310]) ).

fof(c_0_7248,plain,
    ! [X25,X26] :
      ( c_List_Oremdups(X25,X26) != X25
      | c_Nat_Osize(c_List_Oremdups(X25,X26),tc_List_Olist(X26)) = c_Nat_Osize(X25,tc_List_Olist(X26)) ),
    inference(variable_rename,[status(thm)],[c_0_4311]) ).

fof(c_0_7249,plain,
    ! [X23] :
      ( ~ c_less(X23,c_Suc(c_0),tc_nat)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4312]) ).

fof(c_0_7250,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Ofield(X21)
      | X20 = c_0
      | c_times(X20,c_HOL_Oinverse(X20,X21),X21) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4313]) ).

fof(c_0_7251,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Ofield(X21)
      | X20 = c_0
      | c_times(c_HOL_Oinverse(X20,X21),X20,X21) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4314]) ).

fof(c_0_7252,plain,
    ! [X25,X26,X27] :
      ( c_List_Otake(X26,X25,X27) != c_List_Olist_ONil
      | X26 = c_0
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4315])])]) ).

fof(c_0_7253,plain,
    ! [X23,X24] :
      ( c_Suc(c_0) != c_times(X24,X23,tc_nat)
      | X23 = c_1 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4316])])]) ).

fof(c_0_7254,plain,
    ! [X23,X24] :
      ( c_Suc(c_0) != c_times(X24,X23,tc_nat)
      | X24 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4317]) ).

fof(c_0_7255,plain,
    ! [X23,X24] :
      ( c_times(X24,X23,tc_nat) != c_Suc(c_0)
      | X23 = c_1 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4318])])]) ).

fof(c_0_7256,plain,
    ! [X23,X24] :
      ( c_times(X24,X23,tc_nat) != c_Suc(c_0)
      | X24 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4319]) ).

fof(c_0_7257,plain,
    ! [X27,X28,X29] :
      ( X28 != c_append(X28,X27,X29)
      | X27 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4320])])]) ).

fof(c_0_7258,plain,
    ! [X27,X28,X29] :
      ( X27 != c_append(X28,X27,X29)
      | X28 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4321])])]) ).

fof(c_0_7259,plain,
    ! [X27,X28,X29] :
      ( c_append(X28,X27,X29) != X28
      | X27 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4322])])]) ).

fof(c_0_7260,plain,
    ! [X27,X28,X29] :
      ( c_append(X28,X27,X29) != X27
      | X28 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4323])])]) ).

fof(c_0_7261,plain,
    ! [X89] : ~ c_in(X89,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4324]) ).

fof(c_0_7262,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | ~ c_less(c_1,c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4325]) ).

fof(c_0_7263,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | ~ c_lessequals(c_1,c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4326]) ).

fof(c_0_7264,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | c_less(c_0,c_HOL_Oabs(X20,X21),X21)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4327]) ).

fof(c_0_7265,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_plus(X20,c_uminus(X20,X21),X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4328]) ).

fof(c_0_7266,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_plus(c_uminus(X20,X21),X20,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4329]) ).

fof(c_0_7267,plain,
    ! [X15,X16,X17] :
      ( c_union(X16,X15,X17) != c_emptyset
      | X15 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4330])])]) ).

fof(c_0_7268,plain,
    ! [X15,X16,X17] :
      ( c_union(X16,X15,X17) != c_emptyset
      | X16 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4331])])]) ).

fof(c_0_7269,plain,
    ! [X15,X16,X17] :
      ( c_inter(X16,X15,X17) != c_UNIV
      | X15 = c_UNIV ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4332])])]) ).

fof(c_0_7270,plain,
    ! [X15,X16,X17] :
      ( c_inter(X16,X15,X17) != c_UNIV
      | X16 = c_UNIV ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4333])])]) ).

fof(c_0_7271,plain,
    ! [X25,X26,X27] :
      ( c_List_Orotate(X26,X25,X27) != c_List_Olist_ONil
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4334])])]) ).

fof(c_0_7272,plain,
    ! [X27,X28,X29] :
      ( c_append(X28,X27,X29) != c_List_Olist_ONil
      | X27 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4335])])]) ).

fof(c_0_7273,plain,
    ! [X27,X28,X29] :
      ( c_append(X28,X27,X29) != c_List_Olist_ONil
      | X28 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4336])])]) ).

fof(c_0_7274,plain,
    ! [X27,X28,X29] :
      ( c_List_Olist_ONil != c_append(X28,X27,X29)
      | X27 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4337])])]) ).

fof(c_0_7275,plain,
    ! [X27,X28,X29] :
      ( c_List_Olist_ONil != c_append(X28,X27,X29)
      | X28 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4338])])]) ).

fof(c_0_7276,plain,
    ! [X15,X16,X17] :
      ( c_Equiv__Relations_Oquotient(X16,X15,X17) != c_emptyset
      | X16 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4339])])]) ).

fof(c_0_7277,plain,
    ! [X15,X16,X17] :
      ( c_emptyset != c_Equiv__Relations_Oquotient(X16,X15,X17)
      | X16 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4340])])]) ).

fof(c_0_7278,plain,
    ! [X83,X84,X85] : c_List_Olist_OCons(X83,X84,X85) != X84,
    inference(variable_rename,[status(thm)],[c_0_4341]) ).

fof(c_0_7279,plain,
    ! [X25,X26,X27] : X25 != c_List_Olist_OCons(X26,X25,X27),
    inference(variable_rename,[status(thm)],[c_0_4342]) ).

fof(c_0_7280,plain,
    ! [X23,X24] :
      ( c_times(X24,X23,tc_nat) != c_0
      | X23 = c_0
      | X24 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4343]) ).

fof(c_0_7281,plain,
    ! [X2] :
      ( ~ c_in(X2,c_Message_OsymKeys,tc_nat)
      | c_Message_OinvKey(X2) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_4344]) ).

fof(c_0_7282,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | c_lessequals(c_0,c_OrderedGroup_Opprt(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_4345]) ).

fof(c_0_7283,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X21)
      | c_lessequals(c_OrderedGroup_Onprt(X20,X21),c_0,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4346]) ).

fof(c_0_7284,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | c_lessequals(c_0,c_HOL_Oabs(X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_4347]) ).

fof(c_0_7285,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X24)
      | c_lessequals(c_0,c_NatArith_Oof__nat(X23,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_4348]) ).

fof(c_0_7286,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X24)
      | c_in(c_NatArith_Oof__nat(X23,X24),c_IntDef_ONats,X24) ),
    inference(variable_rename,[status(thm)],[c_0_4349]) ).

fof(c_0_7287,plain,
    ! [X20,X21,X22] : c_insert(X20,X21,X22) != c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4350]) ).

fof(c_0_7288,plain,
    ! [X20,X21,X22] : c_emptyset != c_insert(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_4351]) ).

fof(c_0_7289,plain,
    ! [X65,X66,X67] : c_List_Olist_OCons(X66,X65,X67) != c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4352]) ).

fof(c_0_7290,plain,
    ! [X65,X66,X67] : c_List_Olist_ONil != c_List_Olist_OCons(X66,X65,X67),
    inference(variable_rename,[status(thm)],[c_0_4353]) ).

fof(c_0_7291,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4354 ).

fof(c_0_7292,plain,
    ! [X89,X90] : c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X90,X89)),X89) = c_Message_OHPair(X90,X89),
    inference(variable_rename,[status(thm)],[c_0_4355]) ).

fof(c_0_7293,plain,
    ! [X89,X90] : c_Message_OHPair(X90,X89) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X90,X89)),X89),
    inference(variable_rename,[status(thm)],[c_0_4356]) ).

fof(c_0_7294,plain,
    ! [X50] :
      ( ~ c_lessequals(X50,c_0,tc_IntDef_Oint)
      | c_IntDef_Onat(X50) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4357]) ).

fof(c_0_7295,plain,
    ! [X23,X24] :
      ( c_plus(X24,X23,tc_nat) != c_0
      | X23 = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4358])])]) ).

fof(c_0_7296,plain,
    ! [X23,X24] :
      ( c_plus(X24,X23,tc_nat) != c_0
      | X24 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4359]) ).

fof(c_0_7297,plain,
    ! [X20] : c_div(X20,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X20,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4360]) ).

fof(c_0_7298,plain,
    ! [X15,X16] : c_in(c_List_Olist_ONil,c_List_Olists(X15,X16),tc_List_Olist(X16)),
    inference(variable_rename,[status(thm)],[c_0_4361]) ).

fof(c_0_7299,plain,
    ! [X25,X26] : c_in(c_List_Oset(X25,X26),c_Finite__Set_OFinites,tc_set(X26)),
    inference(variable_rename,[status(thm)],[c_0_4362]) ).

fof(c_0_7300,plain,
    ! [X50,X51] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X51)
      | c_IntDef_Oof__int(c_uminus(X50,tc_IntDef_Oint),X51) = c_uminus(c_IntDef_Oof__int(X50,X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_4363]) ).

fof(c_0_7301,plain,
    ! [X8,X9] : ~ c_in(X8,c_emptyset,X9),
    inference(variable_rename,[status(thm)],[c_0_4364]) ).

fof(c_0_7302,plain,
    ! [X43,X44] : ~ c_List_Oop_Amem(X43,c_List_Olist_ONil,X44),
    inference(variable_rename,[status(thm)],[c_0_4365]) ).

fof(c_0_7303,plain,
    ! [X23] : ~ c_less(X23,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4366]) ).

fof(c_0_7304,plain,
    ! [X49] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_Numeral_Onumber__of(X49,tc_nat)) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4367]) ).

fof(c_0_7305,plain,
    ! [X49] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X49,tc_nat)) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4368]) ).

fof(c_0_7306,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X5)
      | c_LOrder_Omeet(c_0,c_uminus(c_0,X5),X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4369]) ).

fof(c_0_7307,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X5)
      | c_LOrder_Ojoin(c_0,c_uminus(c_0,X5),X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4370]) ).

fof(c_0_7308,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
      | c_lessequals(c_HOL_Oabs(c_0,X5),c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4371]) ).

fof(c_0_7309,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | c_lessequals(c_NatArith_Oof__nat(c_0,X5),c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4372]) ).

fof(c_0_7310,plain,
    ! [X23] :
      ( ~ c_less(X23,c_1,tc_nat)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4373]) ).

fof(c_0_7311,plain,
    ! [X45] :
      ( ~ c_lessequals(X45,c_0,tc_nat)
      | X45 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4374]) ).

fof(c_0_7312,plain,
    ! [X17] :
      ( ~ c_Divides_Oop_Advd(c_0,X17,tc_IntDef_Oint)
      | X17 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4375]) ).

fof(c_0_7313,plain,
    ! [X17] :
      ( ~ c_Divides_Oop_Advd(c_0,X17,tc_nat)
      | X17 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4376]) ).

fof(c_0_7314,plain,
    ! [X15,X16] :
      ( c_in(c_Main_Oall__not__in__conv__1(X15,X16),X15,X16)
      | X15 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4377])])]) ).

fof(c_0_7315,plain,
    ! [X5,X6] : c_Relation_ORange(c_Relation_Odiag(X5,X6),X6,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4378]) ).

fof(c_0_7316,plain,
    ! [X5,X6] : c_Relation_ODomain(c_Relation_Odiag(X5,X6),X6,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4379]) ).

fof(c_0_7317,plain,
    ! [X49] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X49,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X49),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4380]) ).

fof(c_0_7318,plain,
    ! [X23] : ~ c_less(X23,c_0,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4381]) ).

fof(c_0_7319,plain,
    ! [X87,X88] : c_Relation_ORange(c_Transitive__Closure_Ortrancl(X87,X88),X88,X88) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4382]) ).

fof(c_0_7320,plain,
    ! [X87,X88] : c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X87,X88),X88,X88) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4383]) ).

fof(c_0_7321,plain,
    ! [X18] : c_in(c_SetInterval_OlessThan(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4384]) ).

fof(c_0_7322,plain,
    ! [X18] : c_in(c_SetInterval_OatMost(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_4385]) ).

fof(c_0_7323,plain,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    c_0_4386 ).

fof(c_0_7324,plain,
    ~ c_less(c_0,c_0,tc_nat),
    c_0_4387 ).

fof(c_0_7325,plain,
    ! [X25,X26] :
      ( ~ c_List_Odistinct(c_List_Orev(X25,X26),X26)
      | c_List_Odistinct(X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_4388]) ).

fof(c_0_7326,plain,
    ! [X25,X26] :
      ( ~ c_List_Odistinct(c_List_Orotate1(X25,X26),X26)
      | c_List_Odistinct(X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_4389]) ).

fof(c_0_7327,plain,
    ! [X104,X105] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X105)),c_Event_Oused(X104),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4390]) ).

fof(c_0_7328,plain,
    ! [X15] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X15)),c_Event_OinitState(X15),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4391]) ).

fof(c_0_7329,plain,
    ! [X61,X62] :
      ( c_List_Oupt(X62,X61) != c_List_Olist_ONil
      | c_lessequals(X61,X62,tc_nat)
      | X61 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4392]) ).

fof(c_0_7330,plain,
    ! [X110,X111,X112,X113] :
      ( c_Message_Omsg_OMPair(X112,X110) != c_Message_OHPair(X113,X111)
      | X112 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X113,X111)) ),
    inference(variable_rename,[status(thm)],[c_0_4393]) ).

fof(c_0_7331,plain,
    ! [X110,X111,X112,X113] :
      ( c_Message_OHPair(X113,X111) != c_Message_Omsg_OMPair(X112,X110)
      | X112 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X113,X111)) ),
    inference(variable_rename,[status(thm)],[c_0_4394]) ).

fof(c_0_7332,plain,
    ! [X90] : c_Message_Oparts(c_Message_Osynth(X90)) = c_union(c_Message_Oparts(X90),c_Message_Osynth(X90),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4395]) ).

fof(c_0_7333,plain,
    ! [X90] : c_Message_Oanalz(c_Message_Osynth(X90)) = c_union(c_Message_Oanalz(X90),c_Message_Osynth(X90),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4396]) ).

fof(c_0_7334,plain,
    ! [X49,X50] : c_Numeral_Obin__mult(c_Numeral_OBit(X50,c_Numeral_Obit_OB0),X49) = c_Numeral_OBit(c_Numeral_Obin__mult(X50,X49),c_Numeral_Obit_OB0),
    inference(variable_rename,[status(thm)],[c_0_4397]) ).

fof(c_0_7335,plain,
    ! [X49] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oint(c_Numeral_Onumber__of(X49,tc_nat)) = c_Numeral_Onumber__of(X49,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4398]) ).

fof(c_0_7336,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_minus(c_0,X20,X21) = c_uminus(X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4399]) ).

fof(c_0_7337,plain,
    ! [X61,X62] :
      ( c_lessequals(X62,X61,tc_nat)
      | c_List_Oupt(X62,c_Suc(X61)) = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_4400]) ).

fof(c_0_7338,plain,
    ! [X15,X16] :
      ( c_in(X15,c_Finite__Set_OFinites,tc_set(X16))
      | c_Finite__Set_Ocard(X15,X16) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4401]) ).

fof(c_0_7339,plain,
    ! [X20] : c_Divides_Oop_Amod(X20,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4402]) ).

fof(c_0_7340,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | ~ class_Ring__and__Field_Oordered__idom(X5)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_4403]) ).

fof(c_0_7341,plain,
    ! [X23] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X23)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4404]) ).

fof(c_0_7342,axiom,
    c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
    c_0_4405 ).

fof(c_0_7343,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X6)
      | ~ class_Ring__and__Field_Oordered__field(X6)
      | X5 = c_0
      | c_1 = c_divide(X5,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4406]) ).

fof(c_0_7344,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X6)
      | ~ class_Ring__and__Field_Oordered__field(X6)
      | X5 = c_0
      | c_divide(X5,X5,X6) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4407]) ).

fof(c_0_7345,plain,
    ! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5)),
    inference(variable_rename,[status(thm)],[c_0_4408]) ).

fof(c_0_7346,plain,
    ! [X43] : c_List_Olistset(c_List_Olist_ONil,X43) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X43)),
    inference(variable_rename,[status(thm)],[c_0_4409]) ).

fof(c_0_7347,plain,
    ! [X113,X114,X115,X116] : c_Public_OpublicKey(X113,X115) != c_Message_OinvKey(c_Public_OpublicKey(X114,X116)),
    inference(variable_rename,[status(thm)],[c_0_4410]) ).

fof(c_0_7348,plain,
    ! [X113,X114,X115,X116] : c_Message_OinvKey(c_Public_OpublicKey(X114,X116)) != c_Public_OpublicKey(X113,X115),
    inference(variable_rename,[status(thm)],[c_0_4411]) ).

fof(c_0_7349,plain,
    ! [X3] :
      ( ~ c_Parity_Oeven(c_uminus(X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4412]) ).

fof(c_0_7350,plain,
    ! [X49] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X49,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4413]) ).

fof(c_0_7351,plain,
    ! [X49] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X49,tc_nat) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4414]) ).

fof(c_0_7352,plain,
    ! [X49] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X49,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4415]) ).

fof(c_0_7353,plain,
    ! [X49] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X49,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X49,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4416]) ).

fof(c_0_7354,plain,
    ! [X7,X8] :
      ( ~ c_Wellfounded__Recursion_Owf(X7,X8)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X7,X8),tc_List_Olist(X8)) ),
    inference(variable_rename,[status(thm)],[c_0_4417]) ).

fof(c_0_7355,plain,
    ! [X7,X8] :
      ( ~ c_Wellfounded__Recursion_Owf(X7,X8)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X7,X8),tc_List_Olist(X8)) ),
    inference(variable_rename,[status(thm)],[c_0_4418]) ).

fof(c_0_7356,plain,
    ! [X17] : c_IntDef_Oint(c_Suc(X17)) = c_plus(c_1,c_IntDef_Oint(X17),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4419]) ).

fof(c_0_7357,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Ofield(X21)
      | c_divide(X20,c_0,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4420]) ).

fof(c_0_7358,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X30)
      | ~ class_Ring__and__Field_Ofield(X30)
      | c_divide(c_0,X29,X30) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4421]) ).

fof(c_0_7359,plain,
    ! [X18,X19] :
      ( ~ class_Orderings_Olinorder(X19)
      | c_uminus(c_SetInterval_OlessThan(X18,X19),tc_set(X19)) = c_SetInterval_OatLeast(X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_4422]) ).

fof(c_0_7360,plain,
    ! [X18,X19] :
      ( ~ class_Orderings_Olinorder(X19)
      | c_uminus(c_SetInterval_OgreaterThan(X18,X19),tc_set(X19)) = c_SetInterval_OatMost(X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_4423]) ).

fof(c_0_7361,plain,
    ! [X18,X19] :
      ( ~ class_Orderings_Olinorder(X19)
      | c_uminus(c_SetInterval_OatMost(X18,X19),tc_set(X19)) = c_SetInterval_OgreaterThan(X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_4424]) ).

fof(c_0_7362,plain,
    ! [X18,X19] :
      ( ~ class_Orderings_Olinorder(X19)
      | c_uminus(c_SetInterval_OatLeast(X18,X19),tc_set(X19)) = c_SetInterval_OlessThan(X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_4425]) ).

fof(c_0_7363,plain,
    ! [X13,X14] :
      ( ~ class_Numeral_Onumber__ring(X14)
      | c_uminus(c_Numeral_Onumber__of(X13,X14),X14) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X13),X14) ),
    inference(variable_rename,[status(thm)],[c_0_4426]) ).

fof(c_0_7364,plain,
    ! [X23,X24] :
      ( ~ class_Power_Orecpower(X24)
      | c_Nat_Opower(c_0,c_Suc(X23),X24) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4427]) ).

fof(c_0_7365,plain,
    ! [X25,X26] : c_Nat_Osize(c_List_Orotate1(X25,X26),tc_List_Olist(X26)) = c_Nat_Osize(X25,tc_List_Olist(X26)),
    inference(variable_rename,[status(thm)],[c_0_4428]) ).

fof(c_0_7366,plain,
    ! [X25,X26] : c_Nat_Osize(c_List_Orev(X25,X26),tc_List_Olist(X26)) = c_Nat_Osize(X25,tc_List_Olist(X26)),
    inference(variable_rename,[status(thm)],[c_0_4429]) ).

fof(c_0_7367,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X5)
      | ~ class_Ring__and__Field_Oordered__field(X5)
      | c_0 = c_divide(c_1,c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4430]) ).

fof(c_0_7368,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X5)
      | ~ class_Ring__and__Field_Oordered__field(X5)
      | c_divide(c_1,c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4431]) ).

fof(c_0_7369,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X5)
      | ~ class_Ring__and__Field_Ofield(X5)
      | c_divide(c_0,c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4432]) ).

fof(c_0_7370,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_4433]) ).

fof(c_0_7371,plain,
    ! [X15,X16,X17] :
      ( c_uminus(X16,tc_set(X17)) != c_uminus(X15,tc_set(X17))
      | X16 = X15 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4434])])]) ).

fof(c_0_7372,plain,
    ! [X90,X91] : c_in(c_Message_Omsg_ONumber(X90),c_Message_Osynth(X91),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4435]) ).

fof(c_0_7373,plain,
    ! [X90,X91] : c_in(c_Message_Omsg_OAgent(X91),c_Message_Osynth(X90),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_4436]) ).

fof(c_0_7374,plain,
    ! [X25,X26] :
      ( ~ c_List_Odistinct(X25,X26)
      | c_List_Odistinct(c_List_Orev(X25,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_4437]) ).

fof(c_0_7375,plain,
    ! [X25,X26] :
      ( ~ c_List_Odistinct(X25,X26)
      | c_List_Odistinct(c_List_Orotate1(X25,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_4438]) ).

fof(c_0_7376,plain,
    ! [X4,X5] :
      ( ~ class_Orderings_Olinorder(X5)
      | c_Orderings_Omax(X4,X4,X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_4439]) ).

fof(c_0_7377,plain,
    ! [X4,X5] :
      ( ~ class_Orderings_Olinorder(X5)
      | c_Orderings_Omin(X4,X4,X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_4440]) ).

fof(c_0_7378,plain,
    ! [X5,X6] :
      ( ~ class_LOrder_Omeet__semilorder(X6)
      | c_LOrder_Omeet(X5,X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4441]) ).

fof(c_0_7379,plain,
    ! [X5,X6] :
      ( ~ class_LOrder_Ojoin__semilorder(X6)
      | c_LOrder_Ojoin(X5,X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4442]) ).

fof(c_0_7380,plain,
    ! [X50] :
      ( c_lessequals(c_0,X50,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X50)) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4443]) ).

fof(c_0_7381,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_minus(X20,X20,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4444]) ).

fof(c_0_7382,plain,
    ! [X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | c_lessequals(X5,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_4445]) ).

fof(c_0_7383,plain,
    ! [X8,X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | X8 = c_times(c_1,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_4446]) ).

fof(c_0_7384,plain,
    ! [X8,X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | X8 = c_times(X8,c_1,X9) ),
    inference(variable_rename,[status(thm)],[c_0_4447]) ).

fof(c_0_7385,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Ofield(X6)
      | c_divide(X5,c_1,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4448]) ).

fof(c_0_7386,plain,
    ! [X5,X6] :
      ( ~ class_Power_Orecpower(X6)
      | c_Nat_Opower(X5,c_1,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4449]) ).

fof(c_0_7387,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Omonoid__mult(X6)
      | c_times(X5,c_1,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4450]) ).

fof(c_0_7388,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Omonoid__mult(X6)
      | c_times(c_1,X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4451]) ).

fof(c_0_7389,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Oab__group__add(X6)
      | c_minus(X5,c_0,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4452]) ).

fof(c_0_7390,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | c_plus(c_0,X5,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4453]) ).

fof(c_0_7391,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | c_plus(X5,c_0,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4454]) ).

fof(c_0_7392,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | c_HOL_Oabs(c_uminus(X20,X21),X21) = c_HOL_Oabs(X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4455]) ).

fof(c_0_7393,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | c_HOL_Oabs(c_HOL_Oabs(X20,X21),X21) = c_HOL_Oabs(X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_4456]) ).

fof(c_0_7394,plain,
    ! [X15,X16] : c_minus(X15,X15,tc_set(X16)) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4457]) ).

fof(c_0_7395,axiom,
    c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
    c_0_4458 ).

fof(c_0_7396,plain,
    ! [X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X31)
      | ~ class_Ring__and__Field_Ofield(X31)
      | c_HOL_Oinverse(X30,X31) != c_HOL_Oinverse(X29,X31)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4459]) ).

fof(c_0_7397,plain,
    ! [X15,X16] : c_lessequals(X15,X15,tc_set(X16)),
    inference(variable_rename,[status(thm)],[c_0_4460]) ).

fof(c_0_7398,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X21)
      | c_times(X20,c_0,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4461]) ).

fof(c_0_7399,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X21)
      | c_times(c_0,X20,X21) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4462]) ).

fof(c_0_7400,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Oordered__idom(X30)
      | c_0 = c_times(X29,c_0,X30) ),
    inference(variable_rename,[status(thm)],[c_0_4463]) ).

fof(c_0_7401,plain,
    ! [X29,X30] :
      ( ~ class_Ring__and__Field_Oordered__idom(X30)
      | c_0 = c_times(c_0,X29,X30) ),
    inference(variable_rename,[status(thm)],[c_0_4464]) ).

fof(c_0_7402,plain,
    ! [X20,X21] :
      ( ~ class_Power_Orecpower(X21)
      | c_Nat_Opower(X20,c_0,X21) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4465]) ).

fof(c_0_7403,plain,
    ! [X23,X24] :
      ( ~ class_Power_Orecpower(X24)
      | c_Nat_Opower(c_1,X23,X24) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4466]) ).

fof(c_0_7404,plain,
    ! [X5,X6] : c_minus(X5,c_emptyset,tc_set(X6)) = X5,
    inference(variable_rename,[status(thm)],[c_0_4467]) ).

fof(c_0_7405,plain,
    ! [X15,X16] : c_lessequals(X15,c_UNIV,tc_set(X16)),
    inference(variable_rename,[status(thm)],[c_0_4468]) ).

fof(c_0_7406,plain,
    ! [X15,X16] : c_minus(c_emptyset,X15,tc_set(X16)) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4469]) ).

fof(c_0_7407,plain,
    ! [X5,X6] : c_uminus(c_uminus(X5,tc_set(X6)),tc_set(X6)) = X5,
    inference(variable_rename,[status(thm)],[c_0_4470]) ).

fof(c_0_7408,plain,
    ! [X15,X16] : c_minus(X15,c_UNIV,tc_set(X16)) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4471]) ).

fof(c_0_7409,axiom,
    c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
    c_0_4472 ).

fof(c_0_7410,plain,
    ! [X15,X16] : c_lessequals(c_emptyset,X15,tc_set(X16)),
    inference(variable_rename,[status(thm)],[c_0_4473]) ).

fof(c_0_7411,plain,
    ! [X23] : c_less(X23,c_Suc(X23),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4474]) ).

fof(c_0_7412,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | c_lessequals(c_0,c_1,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4475]) ).

fof(c_0_7413,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | c_less(c_0,c_1,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4476]) ).

fof(c_0_7414,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
      | c_in(c_1,c_IntDef_ONats,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4477]) ).

fof(c_0_7415,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
      | c_in(c_0,c_IntDef_ONats,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4478]) ).

fof(c_0_7416,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
      | c_in(c_1,c_IntDef_OInts,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4479]) ).

fof(c_0_7417,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
      | c_in(c_0,c_IntDef_OInts,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4480]) ).

fof(c_0_7418,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X24)
      | c_IntDef_Oof__int(c_NatArith_Oof__nat(X23,tc_IntDef_Oint),X24) = c_NatArith_Oof__nat(X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_4481]) ).

fof(c_0_7419,plain,
    ! [X89] : c_in(c_Public_OshrK(X89),c_Message_OsymKeys,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4482]) ).

fof(c_0_7420,plain,
    ! [X5] : c_lessequals(c_emptyset,c_emptyset,tc_set(X5)),
    inference(variable_rename,[status(thm)],[c_0_4483]) ).

fof(c_0_7421,plain,
    ! [X13] : c_Numeral_Obin__minus(c_Numeral_OBit(X13,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X13)),c_Numeral_Obit_OB1),
    inference(variable_rename,[status(thm)],[c_0_4484]) ).

fof(c_0_7422,plain,
    ! [X23] : c_lessequals(c_0,c_IntDef_Oint(X23),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4485]) ).

fof(c_0_7423,plain,
    ! [X23] : c_less(c_0,c_Suc(X23),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4486]) ).

fof(c_0_7424,plain,
    ! [X5] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5)),
    inference(variable_rename,[status(thm)],[c_0_4487]) ).

fof(c_0_7425,plain,
    ! [X2] : c_div(X2,c_Suc(c_0),tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4488]) ).

fof(c_0_7426,plain,
    ! [X17] : c_Divides_Oop_Amod(X17,c_Suc(c_0),tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4489]) ).

fof(c_0_7427,plain,
    ! [X18] : c_Divides_Oop_Advd(c_Suc(c_0),X18,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4490]) ).

fof(c_0_7428,plain,
    ! [X3] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(c_uminus(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_4491]) ).

fof(c_0_7429,plain,
    ! [X5,X6] : c_union(X5,X5,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4492]) ).

fof(c_0_7430,plain,
    ! [X5,X6] : c_inter(X5,X5,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4493]) ).

fof(c_0_7431,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X6)
      | ~ class_Ring__and__Field_Ofield(X6)
      | c_HOL_Oinverse(c_HOL_Oinverse(X5,X6),X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4494]) ).

fof(c_0_7432,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    c_0_4495 ).

fof(c_0_7433,plain,
    ! [X20] :
      ( X20 = c_0
      | c_div(X20,X20,tc_IntDef_Oint) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4496]) ).

fof(c_0_7434,axiom,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    c_0_4497 ).

fof(c_0_7435,plain,
    ! [X49,X50] :
      ( c_IntDef_Oint(X50) != c_Numeral_Onumber__of(X49,tc_IntDef_Oint)
      | X50 = c_IntDef_Onat(c_Numeral_Onumber__of(X49,tc_IntDef_Oint)) ),
    inference(variable_rename,[status(thm)],[c_0_4498]) ).

fof(c_0_7436,plain,
    ! [X7,X8] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X7,X8),X8) = c_Transitive__Closure_Ortrancl(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_4499]) ).

fof(c_0_7437,plain,
    ! [X5,X6] : c_union(X5,c_emptyset,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4500]) ).

fof(c_0_7438,plain,
    ! [X5,X6] : c_union(c_emptyset,X5,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4501]) ).

fof(c_0_7439,plain,
    ! [X5,X6] : c_inter(X5,c_UNIV,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4502]) ).

fof(c_0_7440,plain,
    ! [X5,X6] : c_inter(c_UNIV,X5,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4503]) ).

fof(c_0_7441,plain,
    ! [X25,X26] : c_List_Oset(c_List_Orotate1(X25,X26),X26) = c_List_Oset(X25,X26),
    inference(variable_rename,[status(thm)],[c_0_4504]) ).

fof(c_0_7442,plain,
    ! [X25,X26] : c_List_Oset(c_List_Orev(X25,X26),X26) = c_List_Oset(X25,X26),
    inference(variable_rename,[status(thm)],[c_0_4505]) ).

fof(c_0_7443,plain,
    ! [X25,X26] : c_List_Oset(c_List_Oremdups(X25,X26),X26) = c_List_Oset(X25,X26),
    inference(variable_rename,[status(thm)],[c_0_4506]) ).

fof(c_0_7444,plain,
    ! [X25,X26] : X25 = c_append(X25,c_List_Olist_ONil,X26),
    inference(variable_rename,[status(thm)],[c_0_4507]) ).

fof(c_0_7445,plain,
    ! [X27,X28] : X27 = c_append(c_List_Olist_ONil,X27,X28),
    inference(variable_rename,[status(thm)],[c_0_4508]) ).

fof(c_0_7446,plain,
    ! [X43,X44] : c_List_Oitrev(c_List_Olist_ONil,X43,X44) = X43,
    inference(variable_rename,[status(thm)],[c_0_4509]) ).

fof(c_0_7447,plain,
    ! [X5,X6] : c_List_Odrop(c_0,X5,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4510]) ).

fof(c_0_7448,plain,
    ! [X25,X26] : c_append(X25,c_List_Olist_ONil,X26) = X25,
    inference(variable_rename,[status(thm)],[c_0_4511]) ).

fof(c_0_7449,plain,
    ! [X27,X28] : c_append(c_List_Olist_ONil,X27,X28) = X27,
    inference(variable_rename,[status(thm)],[c_0_4512]) ).

fof(c_0_7450,plain,
    ! [X5,X6] : c_Datatype_Ounit_Ounit__rec(X5,c_Product__Type_OUnity,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4513]) ).

fof(c_0_7451,plain,
    ! [X5,X6] : c_Datatype_Ounit_Ounit__case(X5,c_Product__Type_OUnity,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4514]) ).

fof(c_0_7452,plain,
    ! [X34,X35,X36] : c_Message_OinvKey(c_Public_OpublicKey(X34,X35)) != c_Public_OshrK(X36),
    inference(variable_rename,[status(thm)],[c_0_4515]) ).

fof(c_0_7453,plain,
    ! [X34,X35,X36] : c_Public_OshrK(X36) != c_Message_OinvKey(c_Public_OpublicKey(X34,X35)),
    inference(variable_rename,[status(thm)],[c_0_4516]) ).

fof(c_0_7454,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | c_SetInterval_OlessThan(X6,X7) != c_SetInterval_OlessThan(X5,X7)
      | X6 = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4517]) ).

fof(c_0_7455,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | c_SetInterval_OgreaterThan(X6,X7) != c_SetInterval_OgreaterThan(X5,X7)
      | X6 = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4518]) ).

fof(c_0_7456,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | c_SetInterval_OatMost(X6,X7) != c_SetInterval_OatMost(X5,X7)
      | X6 = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4519]) ).

fof(c_0_7457,plain,
    ! [X5,X6,X7] :
      ( ~ class_Orderings_Olinorder(X7)
      | c_SetInterval_OatLeast(X6,X7) != c_SetInterval_OatLeast(X5,X7)
      | X6 = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4520]) ).

fof(c_0_7458,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Oab__group__add(X31)
      | c_uminus(X30,X31) != c_uminus(X29,X31)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_4521]) ).

fof(c_0_7459,plain,
    ! [X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X25)
      | c_NatArith_Oof__nat(X24,X25) != c_NatArith_Oof__nat(X23,X25)
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_4522]) ).

fof(c_0_7460,plain,
    ! [X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__idom(X52)
      | c_IntDef_Oof__int(X51,X52) != c_IntDef_Oof__int(X50,X52)
      | X51 = X50 ),
    inference(variable_rename,[status(thm)],[c_0_4523]) ).

fof(c_0_7461,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) = c_Numeral_Onumber__of(c_Numeral_OMin,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4524]) ).

fof(c_0_7462,plain,
    ! [X15,X16] : c_union(X15,c_UNIV,X16) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4525]) ).

fof(c_0_7463,plain,
    ! [X14,X15] : c_union(c_UNIV,X14,X15) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4526]) ).

fof(c_0_7464,plain,
    ! [X15,X16] : c_inter(X15,c_emptyset,X16) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4527]) ).

fof(c_0_7465,plain,
    ! [X14,X15] : c_inter(c_emptyset,X14,X15) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4528]) ).

fof(c_0_7466,plain,
    ! [X5] : c_Relation_Oconverse(c_Relation_OId,X5,X5) = c_Relation_OId,
    inference(variable_rename,[status(thm)],[c_0_4529]) ).

fof(c_0_7467,plain,
    ! [X5,X6] : c_Relation_ORange(c_emptyset,X5,X6) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4530]) ).

fof(c_0_7468,plain,
    ! [X5] : c_Relation_ORange(c_Relation_OId,X5,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4531]) ).

fof(c_0_7469,plain,
    ! [X5,X6] : c_Relation_ODomain(c_emptyset,X6,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4532]) ).

fof(c_0_7470,plain,
    ! [X5] : c_Relation_ODomain(c_Relation_OId,X5,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4533]) ).

fof(c_0_7471,plain,
    ! [X23] :
      ( c_less(c_0,X23,tc_nat)
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4534]) ).

fof(c_0_7472,plain,
    ! [X17] : c_minus(X17,X17,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4535]) ).

fof(c_0_7473,plain,
    ! [X23,X24] : c_List_Otake(X23,c_List_Olist_ONil,X24) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4536]) ).

fof(c_0_7474,plain,
    ! [X25,X26] : c_List_Otake(c_0,X25,X26) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4537]) ).

fof(c_0_7475,plain,
    ! [X15,X16] : c_List_Osublist(c_List_Olist_ONil,X15,X16) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4538]) ).

fof(c_0_7476,plain,
    ! [X25,X26] : c_List_Osublist(X25,c_emptyset,X26) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4539]) ).

fof(c_0_7477,plain,
    ! [X23,X24] : c_List_Orotate(X23,c_List_Olist_ONil,X24) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4540]) ).

fof(c_0_7478,plain,
    ! [X43,X44] : c_List_Oreplicate(c_0,X43,X44) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4541]) ).

fof(c_0_7479,plain,
    ! [X43,X44] : c_List_Oremove1(X43,c_List_Olist_ONil,X44) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4542]) ).

fof(c_0_7480,plain,
    ! [X67,X68] : c_List_Olist__inter(c_List_Olist_ONil,X67,X68) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4543]) ).

fof(c_0_7481,plain,
    ! [X43,X44] : c_List_Olexn(X43,c_0,X44) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4544]) ).

fof(c_0_7482,plain,
    ! [X43,X44] : c_List_Odrop(X43,c_List_Olist_ONil,X44) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4545]) ).

fof(c_0_7483,plain,
    ! [X20] : c_Divides_Oop_Amod(X20,X20,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4546]) ).

fof(c_0_7484,plain,
    ! [X17] : c_Divides_Oop_Advd(X17,X17,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4547]) ).

fof(c_0_7485,plain,
    ! [X7,X8] : c_Equiv__Relations_Oquotient(c_emptyset,X7,X8) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4548]) ).

fof(c_0_7486,plain,
    ! [X7,X8] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_4549]) ).

fof(c_0_7487,plain,
    ! [X23] : c_Divides_Oop_Amod(X23,X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4550]) ).

fof(c_0_7488,plain,
    ! [X17] : c_Divides_Oop_Advd(X17,X17,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4551]) ).

fof(c_0_7489,plain,
    ! [X5,X6] : c_in(X5,c_UNIV,X6),
    inference(variable_rename,[status(thm)],[c_0_4552]) ).

fof(c_0_7490,plain,
    ! [X2] : c_minus(X2,c_0,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4553]) ).

fof(c_0_7491,plain,
    ! [X2] : c_plus(c_0,X2,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4554]) ).

fof(c_0_7492,axiom,
    c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
    c_0_4555 ).

fof(c_0_7493,axiom,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    c_0_4556 ).

fof(c_0_7494,plain,
    ! [X2] : c_Orderings_Omax(X2,c_0,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4557]) ).

fof(c_0_7495,plain,
    ! [X2] : c_Orderings_Omax(c_0,X2,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4558]) ).

fof(c_0_7496,plain,
    ! [X2] : c_plus(X2,c_0,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4559]) ).

fof(c_0_7497,plain,
    ! [X2] : c_div(X2,c_1,tc_IntDef_Oint) = X2,
    inference(variable_rename,[status(thm)],[c_0_4560]) ).

fof(c_0_7498,plain,
    ! [X2] : c_Divides_Oop_Amod(X2,c_0,tc_IntDef_Oint) = X2,
    inference(variable_rename,[status(thm)],[c_0_4561]) ).

fof(c_0_7499,plain,
    ! [X2] : c_Divides_Oop_Amod(X2,c_0,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4562]) ).

fof(c_0_7500,plain,
    ! [X5] : c_union(c_emptyset,c_emptyset,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4563]) ).

fof(c_0_7501,plain,
    ! [X5] : c_inter(c_UNIV,c_UNIV,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4564]) ).

fof(c_0_7502,plain,
    ! [X30] : c_Nat_Opower(X30,c_0,tc_nat) = c_1,
    inference(variable_rename,[status(thm)],[c_0_4565]) ).

fof(c_0_7503,plain,
    ! [X23] : c_times(c_0,X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4566]) ).

fof(c_0_7504,plain,
    ! [X17] : c_times(X17,c_0,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4567]) ).

fof(c_0_7505,plain,
    ! [X23] : c_Orderings_Omin(X23,c_0,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4568]) ).

fof(c_0_7506,plain,
    ! [X23] : c_Orderings_Omin(c_0,X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4569]) ).

fof(c_0_7507,plain,
    ! [X23] : c_minus(c_0,X23,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4570]) ).

fof(c_0_7508,plain,
    ! [X5] : c_append(c_List_Olist_ONil,c_List_Olist_ONil,X5) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4571]) ).

fof(c_0_7509,plain,
    ! [X5] : c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X5),
    inference(variable_rename,[status(thm)],[c_0_4572]) ).

fof(c_0_7510,plain,
    ! [X29] : c_Divides_Oop_Amod(c_0,X29,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4573]) ).

fof(c_0_7511,plain,
    ! [X20] : c_Divides_Oop_Amod(X20,c_1,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4574]) ).

fof(c_0_7512,plain,
    ! [X29] : c_div(c_0,X29,tc_IntDef_Oint) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4575]) ).

fof(c_0_7513,plain,
    ! [X30] : c_Nat_Opower(X30,c_0,tc_IntDef_Oint) = c_1,
    inference(variable_rename,[status(thm)],[c_0_4576]) ).

fof(c_0_7514,plain,
    ! [X17] : c_Divides_Oop_Amod(c_0,X17,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4577]) ).

fof(c_0_7515,plain,
    ! [X17] : c_div(c_0,X17,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4578]) ).

fof(c_0_7516,plain,
    ! [X20] : c_div(X20,c_0,tc_nat) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4579]) ).

fof(c_0_7517,plain,
    ! [X23] : c_lessequals(c_0,X23,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4580]) ).

fof(c_0_7518,plain,
    ! [X17] : c_Divides_Oop_Advd(c_1,X17,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4581]) ).

fof(c_0_7519,plain,
    ! [X17] : c_Divides_Oop_Advd(X17,c_0,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4582]) ).

fof(c_0_7520,plain,
    ! [X17] : c_Divides_Oop_Advd(X17,c_0,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4583]) ).

fof(c_0_7521,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_4584]) ).

fof(c_0_7522,plain,
    ! [X4] :
      ( ~ class_HOL_Oone(X4)
      | ~ class_OrderedGroup_Oab__group__add(X4)
      | c_uminus(c_uminus(c_1,X4),X4) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4585]) ).

fof(c_0_7523,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4586]) ).

fof(c_0_7524,plain,
    ! [X29,X30] :
      ( ~ class_HOL_Oone(X30)
      | ~ class_OrderedGroup_Oab__group__add(X30)
      | c_uminus(X29,X30) != c_1
      | X29 = c_uminus(c_1,X30) ),
    inference(variable_rename,[status(thm)],[c_0_4587]) ).

fof(c_0_7525,axiom,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    c_0_4588 ).

fof(c_0_7526,plain,
    ! [X3] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | ~ c_Parity_Oeven(c_Suc(X3),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4589]) ).

fof(c_0_7527,axiom,
    c_less(c_0,c_1,tc_nat),
    c_0_4590 ).

fof(c_0_7528,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    c_0_4591 ).

fof(c_0_7529,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    c_0_4592 ).

fof(c_0_7530,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    c_0_4593 ).

fof(c_0_7531,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    c_0_4594 ).

fof(c_0_7532,plain,
    ! [X15,X16] : c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,X16)) != c_Public_OshrK(X15),
    inference(variable_rename,[status(thm)],[c_0_4595]) ).

fof(c_0_7533,plain,
    ! [X5,X6] :
      ( ~ class_OrderedGroup_Oab__group__add(X6)
      | c_uminus(c_uminus(X5,X6),X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_4596]) ).

fof(c_0_7534,plain,
    ! [X113,X114,X115,X116] :
      ( c_Public_OpublicKey(X114,X116) != c_Public_OpublicKey(X113,X115)
      | X116 = X115 ),
    inference(variable_rename,[status(thm)],[c_0_4597]) ).

fof(c_0_7535,plain,
    ! [X113,X114,X115,X116] :
      ( c_Public_OpublicKey(X114,X116) != c_Public_OpublicKey(X113,X115)
      | X114 = X113 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4598])])]) ).

fof(c_0_7536,plain,
    ! [X110,X111,X112,X113] :
      ( c_Message_Omsg_OMPair(X112,X110) != c_Message_OHPair(X113,X111)
      | X110 = X111 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4599])])]) ).

fof(c_0_7537,plain,
    ! [X110,X111,X112,X113] :
      ( c_Message_OHPair(X113,X111) != c_Message_Omsg_OMPair(X112,X110)
      | X110 = X111 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4600])])]) ).

fof(c_0_7538,plain,
    ! [X110,X111,X112,X113] :
      ( c_Message_OHPair(X112,X110) != c_Message_OHPair(X113,X111)
      | X110 = X111 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4601])])]) ).

fof(c_0_7539,plain,
    ! [X110,X111,X112,X113] :
      ( c_Message_OHPair(X112,X110) != c_Message_OHPair(X113,X111)
      | X112 = X113 ),
    inference(variable_rename,[status(thm)],[c_0_4602]) ).

fof(c_0_7540,plain,
    ! [X99,X100,X101,X102] :
      ( c_Event_Oevent_ONotes(X102,X100) != c_Event_Oevent_ONotes(X101,X99)
      | X100 = X99 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4603])])]) ).

fof(c_0_7541,plain,
    ! [X99,X100,X101,X102] :
      ( c_Event_Oevent_ONotes(X102,X100) != c_Event_Oevent_ONotes(X101,X99)
      | X102 = X101 ),
    inference(variable_rename,[status(thm)],[c_0_4604]) ).

fof(c_0_7542,plain,
    ! [X99,X100,X101,X102] :
      ( c_Event_Oevent_OGets(X102,X100) != c_Event_Oevent_OGets(X101,X99)
      | X100 = X99 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4605])])]) ).

fof(c_0_7543,plain,
    ! [X99,X100,X101,X102] :
      ( c_Event_Oevent_OGets(X102,X100) != c_Event_Oevent_OGets(X101,X99)
      | X102 = X101 ),
    inference(variable_rename,[status(thm)],[c_0_4606]) ).

fof(c_0_7544,plain,
    ! [X99,X100,X101,X102] :
      ( c_Message_Omsg_OCrypt(X100,X102) != c_Message_Omsg_OCrypt(X99,X101)
      | X102 = X101 ),
    inference(variable_rename,[status(thm)],[c_0_4607]) ).

fof(c_0_7545,plain,
    ! [X99,X100,X101,X102] :
      ( c_Message_Omsg_OCrypt(X100,X102) != c_Message_Omsg_OCrypt(X99,X101)
      | X100 = X99 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4608])])]) ).

fof(c_0_7546,plain,
    ! [X103,X104,X105,X106] :
      ( c_Message_Omsg_OMPair(X106,X104) != c_Message_Omsg_OMPair(X105,X103)
      | X104 = X103 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4609])])]) ).

fof(c_0_7547,plain,
    ! [X103,X104,X105,X106] :
      ( c_Message_Omsg_OMPair(X106,X104) != c_Message_Omsg_OMPair(X105,X103)
      | X106 = X105 ),
    inference(variable_rename,[status(thm)],[c_0_4610]) ).

fof(c_0_7548,plain,
    ! [X27,X28,X29] :
      ( c_List_Orev(X28,X29) != c_List_Orev(X27,X29)
      | X28 = X27 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4611])])]) ).

fof(c_0_7549,plain,
    ! [X59,X60,X61,X62] :
      ( c_List_Ochar_OChar(X62,X60) != c_List_Ochar_OChar(X61,X59)
      | X60 = X59 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4612])])]) ).

fof(c_0_7550,plain,
    ! [X59,X60,X61,X62] :
      ( c_List_Ochar_OChar(X62,X60) != c_List_Ochar_OChar(X61,X59)
      | X62 = X61 ),
    inference(variable_rename,[status(thm)],[c_0_4613]) ).

fof(c_0_7551,plain,
    ! [X44,X45,X46] :
      ( c_Datatype_Ooption_OSome(X45,X46) != c_Datatype_Ooption_OSome(X44,X46)
      | X45 = X44 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4614])])]) ).

fof(c_0_7552,plain,
    ! [X20,X21] : c_Nat_Osize(c_Datatype_Ooption_OSome(X20,X21),tc_Datatype_Ooption(X21)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4615]) ).

fof(c_0_7553,plain,
    ! [X13] : c_Numeral_Obin__succ(c_Numeral_OBit(X13,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X13),c_Numeral_Obit_OB0),
    inference(variable_rename,[status(thm)],[c_0_4616]) ).

fof(c_0_7554,plain,
    ! [X13] : c_Numeral_Obin__pred(c_Numeral_OBit(X13,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X13),c_Numeral_Obit_OB1),
    inference(variable_rename,[status(thm)],[c_0_4617]) ).

fof(c_0_7555,plain,
    ! [X13] : c_Numeral_Obin__minus(c_Numeral_OBit(X13,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X13),c_Numeral_Obit_OB0),
    inference(variable_rename,[status(thm)],[c_0_4618]) ).

fof(c_0_7556,plain,
    ! [X40,X41] :
      ( class_Finite__Set_Ofinite(tc_sum(X40,X41))
      | ~ class_Finite__Set_Ofinite(X41)
      | ~ class_Finite__Set_Ofinite(X40) ),
    inference(variable_rename,[status(thm)],[c_0_4619]) ).

fof(c_0_7557,plain,
    ! [X40,X41] :
      ( class_Finite__Set_Ofinite(tc_prod(X40,X41))
      | ~ class_Finite__Set_Ofinite(X41)
      | ~ class_Finite__Set_Ofinite(X40) ),
    inference(variable_rename,[status(thm)],[c_0_4620]) ).

fof(c_0_7558,plain,
    ! [X40,X41] :
      ( class_Finite__Set_Ofinite(tc_fun(X40,X41))
      | ~ class_Finite__Set_Ofinite(X41)
      | ~ class_Finite__Set_Ofinite(X40) ),
    inference(variable_rename,[status(thm)],[c_0_4621]) ).

fof(c_0_7559,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_4622]) ).

fof(c_0_7560,plain,
    ! [X110,X111,X112,X113] : c_Message_OHPair(X112,X110) != c_Message_Omsg_OCrypt(X113,X111),
    inference(variable_rename,[status(thm)],[c_0_4623]) ).

fof(c_0_7561,plain,
    ! [X110,X111,X112,X113] : c_Message_Omsg_OCrypt(X113,X111) != c_Message_OHPair(X112,X110),
    inference(variable_rename,[status(thm)],[c_0_4624]) ).

fof(c_0_7562,plain,
    ! [X99,X100,X101,X102] : c_Event_Oevent_ONotes(X101,X99) != c_Event_Oevent_OGets(X102,X100),
    inference(variable_rename,[status(thm)],[c_0_4625]) ).

fof(c_0_7563,plain,
    ! [X99,X100,X101,X102] : c_Event_Oevent_OGets(X102,X100) != c_Event_Oevent_ONotes(X101,X99),
    inference(variable_rename,[status(thm)],[c_0_4626]) ).

fof(c_0_7564,plain,
    ! [X5,X6] :
      ( X5 = c_Datatype_Ooption_ONone
      | X5 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X5,X6),X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4627])])]) ).

fof(c_0_7565,plain,
    ! [X5,X6] :
      ( X5 = c_Datatype_Ooption_ONone
      | X5 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X5,X6),X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4628])])]) ).

fof(c_0_7566,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4629]) ).

fof(c_0_7567,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X24)
      | c_IntDef_Oof__int(c_IntDef_Oint(X23),X24) = c_NatArith_Oof__nat(X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_4630]) ).

fof(c_0_7568,plain,
    ! [X5,X6] : c_Union(c_Pow(X5,X6),X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4631]) ).

fof(c_0_7569,plain,
    ! [X5,X6] : c_List_Orev(c_List_Orev(X5,X6),X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4632]) ).

fof(c_0_7570,plain,
    ! [X5,X6] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X5,X6),X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4633]) ).

fof(c_0_7571,plain,
    ! [X25,X26] : c_List_Odistinct(c_List_Oremdups(X25,X26),X26),
    inference(variable_rename,[status(thm)],[c_0_4634]) ).

fof(c_0_7572,plain,
    ! [X16] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat) = c_Suc(X16),
    inference(variable_rename,[status(thm)],[c_0_4635]) ).

fof(c_0_7573,plain,
    ! [X13] : c_Numeral_Obin__succ(c_Numeral_OBit(X13,c_Numeral_Obit_OB0)) = c_Numeral_OBit(X13,c_Numeral_Obit_OB1),
    inference(variable_rename,[status(thm)],[c_0_4636]) ).

fof(c_0_7574,plain,
    ! [X13] : c_Numeral_Obin__pred(c_Numeral_OBit(X13,c_Numeral_Obit_OB1)) = c_Numeral_OBit(X13,c_Numeral_Obit_OB0),
    inference(variable_rename,[status(thm)],[c_0_4637]) ).

fof(c_0_7575,plain,
    ! [X13] : c_IntDef_Onat(c_Numeral_Onumber__of(X13,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X13,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4638]) ).

fof(c_0_7576,plain,
    ! [X23] : c_IntDef_Onat(c_uminus(c_IntDef_Oint(X23),tc_IntDef_Oint)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4639]) ).

fof(c_0_7577,plain,
    ! [X99,X100] : c_Nat_Osize(c_Event_Oevent_ONotes(X100,X99),tc_Event_Oevent) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4640]) ).

fof(c_0_7578,plain,
    ! [X99,X100] : c_Nat_Osize(c_Event_Oevent_OGets(X100,X99),tc_Event_Oevent) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4641]) ).

fof(c_0_7579,plain,
    ! [X61,X62] : c_List_Odistinct(c_List_Oupt(X62,X61),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_4642]) ).

fof(c_0_7580,plain,
    ! [X59,X60] : c_Nat_Osize(c_List_Ochar_OChar(X60,X59),tc_List_Ochar) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4643]) ).

fof(c_0_7581,plain,
    ! [X20,X21] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X21)
      | ~ class_Ring__and__Field_Ofield(X21)
      | c_HOL_Oinverse(X20,X21) != c_0
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4644]) ).

fof(c_0_7582,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X6)
      | ~ class_Ring__and__Field_Ofield(X6)
      | c_HOL_Oinverse(X5,X6) != c_1
      | X5 = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4645]) ).

fof(c_0_7583,plain,
    ! [X23,X24] :
      ( c_uminus(c_IntDef_Oint(X23),tc_IntDef_Oint) != c_IntDef_Oint(X24)
      | X24 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4646]) ).

fof(c_0_7584,plain,
    ! [X23,X24] :
      ( c_uminus(c_IntDef_Oint(X23),tc_IntDef_Oint) != c_IntDef_Oint(X24)
      | X23 = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4647])])]) ).

fof(c_0_7585,plain,
    ! [X15,X16] :
      ( c_Main_Oempty__Union__conv__1(X15,X16) != c_emptyset
      | c_emptyset = c_Union(X15,X16) ),
    inference(variable_rename,[status(thm)],[c_0_4648]) ).

fof(c_0_7586,plain,
    ! [X15,X16] :
      ( c_Main_OUnion__empty__conv__1(X15,X16) != c_emptyset
      | c_Union(X15,X16) = c_emptyset ),
    inference(variable_rename,[status(thm)],[c_0_4649]) ).

fof(c_0_7587,plain,
    ! [X15,X16] :
      ( c_Main_OInter__UNIV__conv__2__1(X15,X16) != c_UNIV
      | c_UNIV = c_Inter(X15,X16) ),
    inference(variable_rename,[status(thm)],[c_0_4650]) ).

fof(c_0_7588,plain,
    ! [X15,X16] :
      ( c_Main_OInter__UNIV__conv__1__1(X15,X16) != c_UNIV
      | c_Inter(X15,X16) = c_UNIV ),
    inference(variable_rename,[status(thm)],[c_0_4651]) ).

fof(c_0_7589,plain,
    ! [X52,X53] :
      ( c_Main_Oconcat__eq__Nil__conv__1(X52,X53) != c_List_Olist_ONil
      | c_List_Oconcat(X52,X53) = c_List_Olist_ONil ),
    inference(variable_rename,[status(thm)],[c_0_4652]) ).

fof(c_0_7590,plain,
    ! [X52,X53] :
      ( c_Main_ONil__eq__concat__conv__1(X52,X53) != c_List_Olist_ONil
      | c_List_Olist_ONil = c_List_Oconcat(X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_4653]) ).

fof(c_0_7591,plain,
    ! [X2] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X2,tc_nat),tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4654]) ).

fof(c_0_7592,plain,
    ! [X25,X26] :
      ( c_Nat_Osize(X25,tc_List_Olist(X26)) != c_0
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4655])])]) ).

fof(c_0_7593,axiom,
    c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1,
    c_0_4656 ).

fof(c_0_7594,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | c_uminus(c_1,X5) = c_Numeral_Onumber__of(c_Numeral_OMin,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4657]) ).

fof(c_0_7595,plain,
    ! [X3] :
      ( c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(c_Suc(X3),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_4658]) ).

fof(c_0_7596,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_uminus(X20,X21) != c_0
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4659]) ).

fof(c_0_7597,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_0 != c_uminus(X20,X21)
      | c_0 = X20 ),
    inference(variable_rename,[status(thm)],[c_0_4660]) ).

fof(c_0_7598,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | c_HOL_Oabs(X20,X21) != c_0
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4661]) ).

fof(c_0_7599,plain,
    ! [X20,X21] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X21)
      | c_0 != c_HOL_Oabs(X20,X21)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4662]) ).

fof(c_0_7600,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_NatArith_Oof__nat(X17,X18) != c_0
      | X17 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4663]) ).

fof(c_0_7601,plain,
    ! [X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X24)
      | c_0 != c_NatArith_Oof__nat(X23,X24)
      | c_0 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_4664]) ).

fof(c_0_7602,plain,
    ! [X13,X14] :
      ( ~ class_Ring__and__Field_Oordered__idom(X14)
      | c_IntDef_Oof__int(X13,X14) != c_0
      | X13 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4665]) ).

fof(c_0_7603,plain,
    ! [X50,X51] :
      ( ~ class_Ring__and__Field_Oordered__idom(X51)
      | c_0 != c_IntDef_Oof__int(X50,X51)
      | c_0 = X50 ),
    inference(variable_rename,[status(thm)],[c_0_4666]) ).

fof(c_0_7604,plain,
    ! [X40,X41] : class_Nat_Opower(tc_fun(X40,X41)),
    inference(variable_rename,[status(thm)],[c_0_4667]) ).

fof(c_0_7605,plain,
    ! [X23] : ~ c_IntDef_Oneg(c_IntDef_Oint(X23),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_4668]) ).

fof(c_0_7606,plain,
    ! [X34,X35,X36] : c_Public_OpublicKey(X34,X35) != c_Public_OshrK(X36),
    inference(variable_rename,[status(thm)],[c_0_4669]) ).

fof(c_0_7607,plain,
    ! [X34,X35,X36] : c_Public_OshrK(X36) != c_Public_OpublicKey(X34,X35),
    inference(variable_rename,[status(thm)],[c_0_4670]) ).

fof(c_0_7608,plain,
    ! [X89,X90,X91] : c_Message_OHPair(X90,X89) != c_Message_Omsg_ONumber(X91),
    inference(variable_rename,[status(thm)],[c_0_4671]) ).

fof(c_0_7609,plain,
    ! [X89,X90,X91] : c_Message_OHPair(X90,X89) != c_Message_Omsg_ONonce(X91),
    inference(variable_rename,[status(thm)],[c_0_4672]) ).

fof(c_0_7610,plain,
    ! [X94,X95,X96] : c_Message_OHPair(X95,X94) != c_Message_Omsg_OKey(X96),
    inference(variable_rename,[status(thm)],[c_0_4673]) ).

fof(c_0_7611,plain,
    ! [X111,X112,X113] : c_Message_OHPair(X113,X112) != c_Message_Omsg_OHash(X111),
    inference(variable_rename,[status(thm)],[c_0_4674]) ).

fof(c_0_7612,plain,
    ! [X89,X90,X91] : c_Message_OHPair(X90,X89) != c_Message_Omsg_OAgent(X91),
    inference(variable_rename,[status(thm)],[c_0_4675]) ).

fof(c_0_7613,plain,
    ! [X111,X112,X113] : c_Message_Omsg_OHash(X111) != c_Message_OHPair(X113,X112),
    inference(variable_rename,[status(thm)],[c_0_4676]) ).

fof(c_0_7614,plain,
    ! [X94,X95,X96] : c_Message_Omsg_OKey(X96) != c_Message_OHPair(X95,X94),
    inference(variable_rename,[status(thm)],[c_0_4677]) ).

fof(c_0_7615,plain,
    ! [X89,X90,X91] : c_Message_Omsg_ONumber(X91) != c_Message_OHPair(X90,X89),
    inference(variable_rename,[status(thm)],[c_0_4678]) ).

fof(c_0_7616,plain,
    ! [X89,X90,X91] : c_Message_Omsg_ONonce(X91) != c_Message_OHPair(X90,X89),
    inference(variable_rename,[status(thm)],[c_0_4679]) ).

fof(c_0_7617,plain,
    ! [X89,X90,X91] : c_Message_Omsg_OAgent(X91) != c_Message_OHPair(X90,X89),
    inference(variable_rename,[status(thm)],[c_0_4680]) ).

fof(c_0_7618,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | ~ c_IntDef_Oneg(c_1,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4681]) ).

fof(c_0_7619,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | ~ c_IntDef_Oneg(c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4682]) ).

fof(c_0_7620,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
      | ~ c_IntDef_Oiszero(c_1,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4683]) ).

fof(c_0_7621,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X5)
      | ~ class_Ring__and__Field_Ofield(X5)
      | c_HOL_Oinverse(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4684]) ).

fof(c_0_7622,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X5)
      | ~ class_Ring__and__Field_Ofield(X5)
      | c_HOL_Oinverse(c_1,X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4685]) ).

fof(c_0_7623,plain,
    ! [X23] : c_Binomial_Obinomial(c_Suc(X23),X23) = c_Suc(X23),
    inference(variable_rename,[status(thm)],[c_0_4686]) ).

fof(c_0_7624,plain,
    ! [X25,X26] :
      ( c_List_Oset(X25,X26) != c_emptyset
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4687])])]) ).

fof(c_0_7625,plain,
    ! [X25,X26] :
      ( c_emptyset != c_List_Oset(X25,X26)
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4688])])]) ).

fof(c_0_7626,plain,
    ! [X25,X26] :
      ( c_List_Orotate1(X25,X26) != c_List_Olist_ONil
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4689])])]) ).

fof(c_0_7627,plain,
    ! [X25,X26] :
      ( c_List_Orev(X25,X26) != c_List_Olist_ONil
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4690])])]) ).

fof(c_0_7628,plain,
    ! [X5,X6] :
      ( c_List_Olist_ONil != c_List_Oremdups(X5,X6)
      | X5 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4691])])]) ).

fof(c_0_7629,plain,
    ! [X5,X6] :
      ( c_List_Oremdups(X5,X6) != c_List_Olist_ONil
      | X5 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4692])])]) ).

fof(c_0_7630,plain,
    ! [X25,X26] :
      ( c_List_Olist_ONil != c_List_Orev(X25,X26)
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4693])])]) ).

fof(c_0_7631,plain,
    ! [X42,X43] :
      ( c_Datatype_Oo2s(X42,X43) != c_emptyset
      | X42 = c_Datatype_Ooption_ONone ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_4694])])]) ).

fof(c_0_7632,plain,
    ! [X34] : c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X34))) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4695]) ).

fof(c_0_7633,plain,
    ! [X17] : c_HOL_Oabs(c_IntDef_Oint(X17),tc_IntDef_Oint) = c_IntDef_Oint(X17),
    inference(variable_rename,[status(thm)],[c_0_4696]) ).

fof(c_0_7634,plain,
    ! [X44,X45] : c_Datatype_Ooption_OSome(X44,X45) != c_Datatype_Ooption_ONone,
    inference(variable_rename,[status(thm)],[c_0_4697]) ).

fof(c_0_7635,plain,
    ! [X44,X45] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X44,X45),
    inference(variable_rename,[status(thm)],[c_0_4698]) ).

fof(c_0_7636,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_HOL_Oabs(c_1,X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4699]) ).

fof(c_0_7637,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X5)
      | c_OrderedGroup_Opprt(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4700]) ).

fof(c_0_7638,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X5)
      | c_OrderedGroup_Onprt(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4701]) ).

fof(c_0_7639,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X5)
      | c_uminus(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4702]) ).

fof(c_0_7640,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X5)
      | c_0 = c_uminus(c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4703]) ).

fof(c_0_7641,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
      | c_HOL_Oabs(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4704]) ).

fof(c_0_7642,plain,
    ! [X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
      | c_0 = c_HOL_Oabs(c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4705]) ).

fof(c_0_7643,plain,
    ! [X5] :
      ( ~ class_Numeral_Onumber__ring(X5)
      | c_Numeral_Onumber__of(c_Numeral_OPls,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4706]) ).

fof(c_0_7644,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | c_NatArith_Oof__nat(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4707]) ).

fof(c_0_7645,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
      | c_NatArith_Oof__nat(c_1,X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4708]) ).

fof(c_0_7646,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X5)
      | c_0 = c_NatArith_Oof__nat(c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4709]) ).

fof(c_0_7647,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_IntDef_Oof__int(c_0,X5) = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_4710]) ).

fof(c_0_7648,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
      | c_IntDef_Oof__int(c_1,X5) = c_1 ),
    inference(variable_rename,[status(thm)],[c_0_4711]) ).

fof(c_0_7649,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_0 = c_IntDef_Oof__int(c_0,X5) ),
    inference(variable_rename,[status(thm)],[c_0_4712]) ).

fof(c_0_7650,plain,
    ! [X92] : c_Nat_Osize(c_Message_Omsg_OKey(X92),tc_Message_Omsg) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4713]) ).

fof(c_0_7651,plain,
    ! [X92] : c_Nat_Osize(c_Message_Omsg_ONonce(X92),tc_Message_Omsg) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4714]) ).

fof(c_0_7652,plain,
    ! [X92] : c_Nat_Osize(c_Message_Omsg_ONumber(X92),tc_Message_Omsg) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4715]) ).

fof(c_0_7653,plain,
    ! [X97] : c_Nat_Osize(c_Message_Omsg_OAgent(X97),tc_Message_Omsg) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4716]) ).

fof(c_0_7654,plain,
    ! [X92] : c_Nat_Osize(c_Message_Oagent_OFriend(X92),tc_Message_Oagent) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4717]) ).

fof(c_0_7655,plain,
    ! [X5] : c_uminus(c_emptyset,tc_set(X5)) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4718]) ).

fof(c_0_7656,plain,
    ! [X5] : c_uminus(c_UNIV,tc_set(X5)) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4719]) ).

fof(c_0_7657,plain,
    ! [X5] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4720]) ).

fof(c_0_7658,plain,
    ! [X5] : c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X5)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4721]) ).

fof(c_0_7659,plain,
    ! [X18] : c_Binomial_Obinomial(c_0,c_Suc(X18)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4722]) ).

fof(c_0_7660,axiom,
    c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
    c_0_4723 ).

fof(c_0_7661,plain,
    ! [X2] : c_Binomial_Obinomial(X2,c_Suc(c_0)) = X2,
    inference(variable_rename,[status(thm)],[c_0_4724]) ).

fof(c_0_7662,plain,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    c_0_4725 ).

fof(c_0_7663,plain,
    ! [X39] :
      ( class_Finite__Set_Ofinite(tc_set(X39))
      | ~ class_Finite__Set_Ofinite(X39) ),
    inference(variable_rename,[status(thm)],[c_0_4726]) ).

fof(c_0_7664,plain,
    ! [X39] :
      ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X39))
      | ~ class_Finite__Set_Ofinite(X39) ),
    inference(variable_rename,[status(thm)],[c_0_4727]) ).

fof(c_0_7665,plain,
    ! [X15] : c_Event_Oknows(X15,c_List_Olist_ONil) = c_Event_OinitState(X15),
    inference(variable_rename,[status(thm)],[c_0_4728]) ).

fof(c_0_7666,plain,
    ! [X13] : c_Numeral_Obin__mult(c_Numeral_OMin,X13) = c_Numeral_Obin__minus(X13),
    inference(variable_rename,[status(thm)],[c_0_4729]) ).

fof(c_0_7667,plain,
    ! [X13] : c_Numeral_Obin__add(X13,c_Numeral_OMin) = c_Numeral_Obin__pred(X13),
    inference(variable_rename,[status(thm)],[c_0_4730]) ).

fof(c_0_7668,plain,
    ! [X13] : c_Numeral_Obin__add(c_Numeral_OMin,X13) = c_Numeral_Obin__pred(X13),
    inference(variable_rename,[status(thm)],[c_0_4731]) ).

fof(c_0_7669,plain,
    ! [X3,X4] :
      ( c_Public_OshrK(X4) != c_Public_OshrK(X3)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_4732]) ).

fof(c_0_7670,plain,
    ! [X99,X100] :
      ( c_Message_Omsg_OHash(X100) != c_Message_Omsg_OHash(X99)
      | X100 = X99 ),
    inference(variable_rename,[status(thm)],[c_0_4733]) ).

fof(c_0_7671,plain,
    ! [X92,X93] :
      ( c_Message_Omsg_OKey(X93) != c_Message_Omsg_OKey(X92)
      | X93 = X92 ),
    inference(variable_rename,[status(thm)],[c_0_4734]) ).

fof(c_0_7672,plain,
    ! [X92,X93] :
      ( c_Message_Omsg_ONonce(X93) != c_Message_Omsg_ONonce(X92)
      | X93 = X92 ),
    inference(variable_rename,[status(thm)],[c_0_4735]) ).

fof(c_0_7673,plain,
    ! [X92,X93] :
      ( c_Message_Omsg_ONumber(X93) != c_Message_Omsg_ONumber(X92)
      | X93 = X92 ),
    inference(variable_rename,[status(thm)],[c_0_4736]) ).

fof(c_0_7674,plain,
    ! [X97,X98] :
      ( c_Message_Omsg_OAgent(X98) != c_Message_Omsg_OAgent(X97)
      | X98 = X97 ),
    inference(variable_rename,[status(thm)],[c_0_4737]) ).

fof(c_0_7675,plain,
    ! [X94,X95] :
      ( c_Message_OinvKey(X95) != c_Message_OinvKey(X94)
      | X95 = X94 ),
    inference(variable_rename,[status(thm)],[c_0_4738]) ).

fof(c_0_7676,plain,
    ! [X92,X93] :
      ( c_Message_Oagent_OFriend(X93) != c_Message_Oagent_OFriend(X92)
      | X93 = X92 ),
    inference(variable_rename,[status(thm)],[c_0_4739]) ).

fof(c_0_7677,plain,
    ! [X23,X24] :
      ( c_Suc(X24) != c_Suc(X23)
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_4740]) ).

fof(c_0_7678,plain,
    ! [X23,X24] :
      ( c_IntDef_Oint(X24) != c_IntDef_Oint(X23)
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_4741]) ).

fof(c_0_7679,plain,
    ! [X5,X6] : c_Fun_Oid(X5,X6) = X5,
    inference(variable_rename,[status(thm)],[c_0_4742]) ).

fof(c_0_7680,plain,
    ! [X15] : c_Message_OinvKey(c_Public_OshrK(X15)) = c_Public_OshrK(X15),
    inference(variable_rename,[status(thm)],[c_0_4743]) ).

fof(c_0_7681,plain,
    ! [X90] : c_Message_Oparts(c_Message_Oparts(X90)) = c_Message_Oparts(X90),
    inference(variable_rename,[status(thm)],[c_0_4744]) ).

fof(c_0_7682,plain,
    ! [X90] : c_Message_Oparts(c_Message_Oanalz(X90)) = c_Message_Oparts(X90),
    inference(variable_rename,[status(thm)],[c_0_4745]) ).

fof(c_0_7683,plain,
    ! [X90] : c_Message_Oanalz(c_Message_Oparts(X90)) = c_Message_Oparts(X90),
    inference(variable_rename,[status(thm)],[c_0_4746]) ).

fof(c_0_7684,plain,
    ! [X90] : c_Message_Oanalz(c_Message_Oanalz(X90)) = c_Message_Oanalz(X90),
    inference(variable_rename,[status(thm)],[c_0_4747]) ).

fof(c_0_7685,plain,
    ! [X23] : c_Binomial_Obinomial(X23,X23) = c_1,
    inference(variable_rename,[status(thm)],[c_0_4748]) ).

fof(c_0_7686,axiom,
    c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    c_0_4749 ).

fof(c_0_7687,axiom,
    c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
    c_0_4750 ).

fof(c_0_7688,axiom,
    c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    c_0_4751 ).

fof(c_0_7689,plain,
    ! [X2] : c_Numeral_Obin__add(X2,c_Numeral_OPls) = X2,
    inference(variable_rename,[status(thm)],[c_0_4752]) ).

fof(c_0_7690,plain,
    ! [X2] : c_Numeral_Obin__add(c_Numeral_OPls,X2) = X2,
    inference(variable_rename,[status(thm)],[c_0_4753]) ).

fof(c_0_7691,plain,
    ! [X2] : c_NatArith_Oof__nat(X2,tc_nat) = X2,
    inference(variable_rename,[status(thm)],[c_0_4754]) ).

fof(c_0_7692,plain,
    ! [X5] : c_Transitive__Closure_Otrancl(c_emptyset,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4755]) ).

fof(c_0_7693,plain,
    ! [X5] : c_Transitive__Closure_Ortrancl(c_emptyset,X5) = c_Relation_OId,
    inference(variable_rename,[status(thm)],[c_0_4756]) ).

fof(c_0_7694,plain,
    ! [X5] : c_Union(c_emptyset,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4757]) ).

fof(c_0_7695,plain,
    ! [X5] : c_Union(c_UNIV,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4758]) ).

fof(c_0_7696,plain,
    ! [X5] : c_Pow(c_UNIV,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4759]) ).

fof(c_0_7697,plain,
    ! [X5] : c_Inter(c_emptyset,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4760]) ).

fof(c_0_7698,plain,
    ! [X5] : c_Inter(c_UNIV,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4761]) ).

fof(c_0_7699,plain,
    ! [X5] : c_Relation_Odiag(c_emptyset,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4762]) ).

fof(c_0_7700,plain,
    ! [X13] : c_Numeral_Obin__mult(c_Numeral_OPls,X13) = c_Numeral_OPls,
    inference(variable_rename,[status(thm)],[c_0_4763]) ).

fof(c_0_7701,plain,
    ! [X45] : c_List_Oupt(X45,c_0) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4764]) ).

fof(c_0_7702,plain,
    ! [X43] : c_List_Otl(c_List_Olist_ONil,X43) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4765]) ).

fof(c_0_7703,plain,
    ! [X5] : c_List_Oset(c_List_Olist_ONil,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4766]) ).

fof(c_0_7704,plain,
    ! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5),
    inference(variable_rename,[status(thm)],[c_0_4767]) ).

fof(c_0_7705,plain,
    ! [X5] : c_List_Orotate1(c_List_Olist_ONil,X5) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4768]) ).

fof(c_0_7706,plain,
    ! [X5] : c_List_Orev(c_List_Olist_ONil,X5) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4769]) ).

fof(c_0_7707,plain,
    ! [X5] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X5),
    inference(variable_rename,[status(thm)],[c_0_4770]) ).

fof(c_0_7708,plain,
    ! [X5] : c_List_Oremdups(c_List_Olist_ONil,X5) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4771]) ).

fof(c_0_7709,plain,
    ! [X43] : c_List_Onull(c_List_Olist_ONil,X43),
    inference(variable_rename,[status(thm)],[c_0_4772]) ).

fof(c_0_7710,plain,
    ! [X5] : c_List_Olists(c_UNIV,X5) = c_UNIV,
    inference(variable_rename,[status(thm)],[c_0_4773]) ).

fof(c_0_7711,plain,
    ! [X43] : c_List_Odistinct(c_List_Olist_ONil,X43),
    inference(variable_rename,[status(thm)],[c_0_4774]) ).

fof(c_0_7712,plain,
    ! [X43] : c_List_Oconcat(c_List_Olist_ONil,X43) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4775]) ).

fof(c_0_7713,plain,
    ! [X43] : c_List_Obutlast(c_List_Olist_ONil,X43) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_4776]) ).

fof(c_0_7714,plain,
    ! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5),
    inference(variable_rename,[status(thm)],[c_0_4777]) ).

fof(c_0_7715,plain,
    ! [X5] : c_Finite__Set_Ocard(c_emptyset,X5) = c_0,
    inference(variable_rename,[status(thm)],[c_0_4778]) ).

fof(c_0_7716,plain,
    ! [X5] : c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X5) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_4779]) ).

fof(c_0_7717,plain,
    ! [X23] : c_Binomial_Obinomial(X23,c_0) = c_1,
    inference(variable_rename,[status(thm)],[c_0_4780]) ).

fof(c_0_7718,plain,
    ! [X5] : c_Wellfounded__Recursion_Owf(c_emptyset,X5),
    inference(variable_rename,[status(thm)],[c_0_4781]) ).

fof(c_0_7719,plain,
    ! [X41] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4782]) ).

fof(c_0_7720,plain,
    ! [X41] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4783]) ).

fof(c_0_7721,plain,
    ! [X41] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4784]) ).

fof(c_0_7722,plain,
    ! [X41] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4785]) ).

fof(c_0_7723,plain,
    ! [X41] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4786]) ).

fof(c_0_7724,plain,
    ! [X41] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4787]) ).

fof(c_0_7725,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4788]) ).

fof(c_0_7726,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4789]) ).

fof(c_0_7727,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4790]) ).

fof(c_0_7728,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4791]) ).

fof(c_0_7729,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4792]) ).

fof(c_0_7730,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4793]) ).

fof(c_0_7731,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4794]) ).

fof(c_0_7732,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4795]) ).

fof(c_0_7733,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4796]) ).

fof(c_0_7734,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4797]) ).

fof(c_0_7735,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4798]) ).

fof(c_0_7736,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4799]) ).

fof(c_0_7737,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4800]) ).

fof(c_0_7738,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4801]) ).

fof(c_0_7739,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4802]) ).

fof(c_0_7740,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4803]) ).

fof(c_0_7741,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4804]) ).

fof(c_0_7742,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4805]) ).

fof(c_0_7743,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4806]) ).

fof(c_0_7744,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4807]) ).

fof(c_0_7745,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4808]) ).

fof(c_0_7746,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4809]) ).

fof(c_0_7747,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4810]) ).

fof(c_0_7748,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4811]) ).

fof(c_0_7749,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4812]) ).

fof(c_0_7750,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4813]) ).

fof(c_0_7751,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4814]) ).

fof(c_0_7752,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__1(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4815]) ).

fof(c_0_7753,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4816]) ).

fof(c_0_7754,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4817]) ).

fof(c_0_7755,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4818]) ).

fof(c_0_7756,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4819]) ).

fof(c_0_7757,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4820]) ).

fof(c_0_7758,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4821]) ).

fof(c_0_7759,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4822]) ).

fof(c_0_7760,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4823]) ).

fof(c_0_7761,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4824]) ).

fof(c_0_7762,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4825]) ).

fof(c_0_7763,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4826]) ).

fof(c_0_7764,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4827]) ).

fof(c_0_7765,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4828]) ).

fof(c_0_7766,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4829]) ).

fof(c_0_7767,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4830]) ).

fof(c_0_7768,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4831]) ).

fof(c_0_7769,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4832]) ).

fof(c_0_7770,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4833]) ).

fof(c_0_7771,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring__0(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4834]) ).

fof(c_0_7772,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4835]) ).

fof(c_0_7773,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4836]) ).

fof(c_0_7774,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4837]) ).

fof(c_0_7775,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4838]) ).

fof(c_0_7776,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Osemiring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4839]) ).

fof(c_0_7777,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4840]) ).

fof(c_0_7778,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4841]) ).

fof(c_0_7779,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4842]) ).

fof(c_0_7780,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4843]) ).

fof(c_0_7781,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4844]) ).

fof(c_0_7782,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4845]) ).

fof(c_0_7783,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4846]) ).

fof(c_0_7784,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4847]) ).

fof(c_0_7785,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4848]) ).

fof(c_0_7786,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4849]) ).

fof(c_0_7787,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4850]) ).

fof(c_0_7788,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4851]) ).

fof(c_0_7789,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4852]) ).

fof(c_0_7790,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4853]) ).

fof(c_0_7791,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4854]) ).

fof(c_0_7792,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4855]) ).

fof(c_0_7793,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4856]) ).

fof(c_0_7794,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4857]) ).

fof(c_0_7795,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4858]) ).

fof(c_0_7796,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring__1(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4859]) ).

fof(c_0_7797,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4860]) ).

fof(c_0_7798,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4861]) ).

fof(c_0_7799,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4862]) ).

fof(c_0_7800,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4863]) ).

fof(c_0_7801,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4864]) ).

fof(c_0_7802,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4865]) ).

fof(c_0_7803,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4866]) ).

fof(c_0_7804,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4867]) ).

fof(c_0_7805,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4868]) ).

fof(c_0_7806,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4869]) ).

fof(c_0_7807,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4870]) ).

fof(c_0_7808,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4871]) ).

fof(c_0_7809,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4872]) ).

fof(c_0_7810,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4873]) ).

fof(c_0_7811,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4874]) ).

fof(c_0_7812,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4875]) ).

fof(c_0_7813,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4876]) ).

fof(c_0_7814,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4877]) ).

fof(c_0_7815,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4878]) ).

fof(c_0_7816,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4879]) ).

fof(c_0_7817,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4880]) ).

fof(c_0_7818,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4881]) ).

fof(c_0_7819,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4882]) ).

fof(c_0_7820,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4883]) ).

fof(c_0_7821,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4884]) ).

fof(c_0_7822,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4885]) ).

fof(c_0_7823,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4886]) ).

fof(c_0_7824,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4887]) ).

fof(c_0_7825,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4888]) ).

fof(c_0_7826,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4889]) ).

fof(c_0_7827,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4890]) ).

fof(c_0_7828,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4891]) ).

fof(c_0_7829,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4892]) ).

fof(c_0_7830,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4893]) ).

fof(c_0_7831,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4894]) ).

fof(c_0_7832,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4895]) ).

fof(c_0_7833,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4896]) ).

fof(c_0_7834,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4897]) ).

fof(c_0_7835,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4898]) ).

fof(c_0_7836,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4899]) ).

fof(c_0_7837,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4900]) ).

fof(c_0_7838,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4901]) ).

fof(c_0_7839,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4902]) ).

fof(c_0_7840,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4903]) ).

fof(c_0_7841,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4904]) ).

fof(c_0_7842,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4905]) ).

fof(c_0_7843,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4906]) ).

fof(c_0_7844,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4907]) ).

fof(c_0_7845,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__ring(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4908]) ).

fof(c_0_7846,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4909]) ).

fof(c_0_7847,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4910]) ).

fof(c_0_7848,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4911]) ).

fof(c_0_7849,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4912]) ).

fof(c_0_7850,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4913]) ).

fof(c_0_7851,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4914]) ).

fof(c_0_7852,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4915]) ).

fof(c_0_7853,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4916]) ).

fof(c_0_7854,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4917]) ).

fof(c_0_7855,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4918]) ).

fof(c_0_7856,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4919]) ).

fof(c_0_7857,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4920]) ).

fof(c_0_7858,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4921]) ).

fof(c_0_7859,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4922]) ).

fof(c_0_7860,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4923]) ).

fof(c_0_7861,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4924]) ).

fof(c_0_7862,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4925]) ).

fof(c_0_7863,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4926]) ).

fof(c_0_7864,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4927]) ).

fof(c_0_7865,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4928]) ).

fof(c_0_7866,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4929]) ).

fof(c_0_7867,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4930]) ).

fof(c_0_7868,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4931]) ).

fof(c_0_7869,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4932]) ).

fof(c_0_7870,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4933]) ).

fof(c_0_7871,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4934]) ).

fof(c_0_7872,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4935]) ).

fof(c_0_7873,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Opordered__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4936]) ).

fof(c_0_7874,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4937]) ).

fof(c_0_7875,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4938]) ).

fof(c_0_7876,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4939]) ).

fof(c_0_7877,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4940]) ).

fof(c_0_7878,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4941]) ).

fof(c_0_7879,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4942]) ).

fof(c_0_7880,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4943]) ).

fof(c_0_7881,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4944]) ).

fof(c_0_7882,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4945]) ).

fof(c_0_7883,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4946]) ).

fof(c_0_7884,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4947]) ).

fof(c_0_7885,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4948]) ).

fof(c_0_7886,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4949]) ).

fof(c_0_7887,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4950]) ).

fof(c_0_7888,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4951]) ).

fof(c_0_7889,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4952]) ).

fof(c_0_7890,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4953]) ).

fof(c_0_7891,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4954]) ).

fof(c_0_7892,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4955]) ).

fof(c_0_7893,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4956]) ).

fof(c_0_7894,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4957]) ).

fof(c_0_7895,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4958]) ).

fof(c_0_7896,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4959]) ).

fof(c_0_7897,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4960]) ).

fof(c_0_7898,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4961]) ).

fof(c_0_7899,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4962]) ).

fof(c_0_7900,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4963]) ).

fof(c_0_7901,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4964]) ).

fof(c_0_7902,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4965]) ).

fof(c_0_7903,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4966]) ).

fof(c_0_7904,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4967]) ).

fof(c_0_7905,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4968]) ).

fof(c_0_7906,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4969]) ).

fof(c_0_7907,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4970]) ).

fof(c_0_7908,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4971]) ).

fof(c_0_7909,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4972]) ).

fof(c_0_7910,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4973]) ).

fof(c_0_7911,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4974]) ).

fof(c_0_7912,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4975]) ).

fof(c_0_7913,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4976]) ).

fof(c_0_7914,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4977]) ).

fof(c_0_7915,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4978]) ).

fof(c_0_7916,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4979]) ).

fof(c_0_7917,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4980]) ).

fof(c_0_7918,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4981]) ).

fof(c_0_7919,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4982]) ).

fof(c_0_7920,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4983]) ).

fof(c_0_7921,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4984]) ).

fof(c_0_7922,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4985]) ).

fof(c_0_7923,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X41)
      | class_Ring__and__Field_Opordered__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4986]) ).

fof(c_0_7924,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4987]) ).

fof(c_0_7925,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4988]) ).

fof(c_0_7926,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4989]) ).

fof(c_0_7927,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4990]) ).

fof(c_0_7928,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4991]) ).

fof(c_0_7929,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4992]) ).

fof(c_0_7930,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4993]) ).

fof(c_0_7931,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4994]) ).

fof(c_0_7932,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4995]) ).

fof(c_0_7933,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4996]) ).

fof(c_0_7934,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4997]) ).

fof(c_0_7935,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4998]) ).

fof(c_0_7936,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_4999]) ).

fof(c_0_7937,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5000]) ).

fof(c_0_7938,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5001]) ).

fof(c_0_7939,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5002]) ).

fof(c_0_7940,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5003]) ).

fof(c_0_7941,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5004]) ).

fof(c_0_7942,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5005]) ).

fof(c_0_7943,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5006]) ).

fof(c_0_7944,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5007]) ).

fof(c_0_7945,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5008]) ).

fof(c_0_7946,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5009]) ).

fof(c_0_7947,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5010]) ).

fof(c_0_7948,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5011]) ).

fof(c_0_7949,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5012]) ).

fof(c_0_7950,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5013]) ).

fof(c_0_7951,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5014]) ).

fof(c_0_7952,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5015]) ).

fof(c_0_7953,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5016]) ).

fof(c_0_7954,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5017]) ).

fof(c_0_7955,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5018]) ).

fof(c_0_7956,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5019]) ).

fof(c_0_7957,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5020]) ).

fof(c_0_7958,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Opordered__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5021]) ).

fof(c_0_7959,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5022]) ).

fof(c_0_7960,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5023]) ).

fof(c_0_7961,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5024]) ).

fof(c_0_7962,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5025]) ).

fof(c_0_7963,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5026]) ).

fof(c_0_7964,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5027]) ).

fof(c_0_7965,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5028]) ).

fof(c_0_7966,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5029]) ).

fof(c_0_7967,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5030]) ).

fof(c_0_7968,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5031]) ).

fof(c_0_7969,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Oordered__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5032]) ).

fof(c_0_7970,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5033]) ).

fof(c_0_7971,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5034]) ).

fof(c_0_7972,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5035]) ).

fof(c_0_7973,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5036]) ).

fof(c_0_7974,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5037]) ).

fof(c_0_7975,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5038]) ).

fof(c_0_7976,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5039]) ).

fof(c_0_7977,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5040]) ).

fof(c_0_7978,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5041]) ).

fof(c_0_7979,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5042]) ).

fof(c_0_7980,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5043]) ).

fof(c_0_7981,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5044]) ).

fof(c_0_7982,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5045]) ).

fof(c_0_7983,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5046]) ).

fof(c_0_7984,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5047]) ).

fof(c_0_7985,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5048]) ).

fof(c_0_7986,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5049]) ).

fof(c_0_7987,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5050]) ).

fof(c_0_7988,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5051]) ).

fof(c_0_7989,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5052]) ).

fof(c_0_7990,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5053]) ).

fof(c_0_7991,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5054]) ).

fof(c_0_7992,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5055]) ).

fof(c_0_7993,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5056]) ).

fof(c_0_7994,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5057]) ).

fof(c_0_7995,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Olordered__ab__group__join(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5058]) ).

fof(c_0_7996,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Olordered__ab__group__meet(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5059]) ).

fof(c_0_7997,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Olordered__ab__group__abs(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5060]) ).

fof(c_0_7998,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Opordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5061]) ).

fof(c_0_7999,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Olordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5062]) ).

fof(c_0_8000,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5063]) ).

fof(c_0_8001,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5064]) ).

fof(c_0_8002,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5065]) ).

fof(c_0_8003,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Oaxclass__abs__if(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5066]) ).

fof(c_0_8004,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5067]) ).

fof(c_0_8005,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5068]) ).

fof(c_0_8006,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5069]) ).

fof(c_0_8007,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5070]) ).

fof(c_0_8008,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5071]) ).

fof(c_0_8009,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5072]) ).

fof(c_0_8010,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5073]) ).

fof(c_0_8011,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5074]) ).

fof(c_0_8012,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5075]) ).

fof(c_0_8013,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5076]) ).

fof(c_0_8014,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5077]) ).

fof(c_0_8015,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5078]) ).

fof(c_0_8016,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5079]) ).

fof(c_0_8017,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Oordered__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5080]) ).

fof(c_0_8018,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5081]) ).

fof(c_0_8019,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5082]) ).

fof(c_0_8020,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5083]) ).

fof(c_0_8021,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5084]) ).

fof(c_0_8022,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5085]) ).

fof(c_0_8023,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5086]) ).

fof(c_0_8024,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5087]) ).

fof(c_0_8025,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5088]) ).

fof(c_0_8026,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5089]) ).

fof(c_0_8027,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5090]) ).

fof(c_0_8028,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5091]) ).

fof(c_0_8029,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oidom(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5092]) ).

fof(c_0_8030,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5093]) ).

fof(c_0_8031,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oordered__semidom(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5094]) ).

fof(c_0_8032,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5095]) ).

fof(c_0_8033,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5096]) ).

fof(c_0_8034,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Olordered__ab__group__join(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5097]) ).

fof(c_0_8035,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Olordered__ab__group__meet(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5098]) ).

fof(c_0_8036,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Olordered__ab__group__abs(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5099]) ).

fof(c_0_8037,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5100]) ).

fof(c_0_8038,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Opordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5101]) ).

fof(c_0_8039,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Olordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5102]) ).

fof(c_0_8040,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oordered__ring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5103]) ).

fof(c_0_8041,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oaxclass__abs__if(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5104]) ).

fof(c_0_8042,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5105]) ).

fof(c_0_8043,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5106]) ).

fof(c_0_8044,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5107]) ).

fof(c_0_8045,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5108]) ).

fof(c_0_8046,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Opordered__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5109]) ).

fof(c_0_8047,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5110]) ).

fof(c_0_8048,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5111]) ).

fof(c_0_8049,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5112]) ).

fof(c_0_8050,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5113]) ).

fof(c_0_8051,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5114]) ).

fof(c_0_8052,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5115]) ).

fof(c_0_8053,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5116]) ).

fof(c_0_8054,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5117]) ).

fof(c_0_8055,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5118]) ).

fof(c_0_8056,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5119]) ).

fof(c_0_8057,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oordered__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5120]) ).

fof(c_0_8058,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5121]) ).

fof(c_0_8059,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5122]) ).

fof(c_0_8060,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5123]) ).

fof(c_0_8061,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5124]) ).

fof(c_0_8062,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5125]) ).

fof(c_0_8063,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5126]) ).

fof(c_0_8064,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5127]) ).

fof(c_0_8065,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5128]) ).

fof(c_0_8066,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5129]) ).

fof(c_0_8067,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5130]) ).

fof(c_0_8068,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5131]) ).

fof(c_0_8069,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5132]) ).

fof(c_0_8070,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5133]) ).

fof(c_0_8071,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5134]) ).

fof(c_0_8072,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5135]) ).

fof(c_0_8073,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5136]) ).

fof(c_0_8074,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5137]) ).

fof(c_0_8075,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5138]) ).

fof(c_0_8076,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5139]) ).

fof(c_0_8077,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5140]) ).

fof(c_0_8078,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5141]) ).

fof(c_0_8079,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5142]) ).

fof(c_0_8080,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5143]) ).

fof(c_0_8081,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5144]) ).

fof(c_0_8082,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__idom(X41)
      | class_Ring__and__Field_Ocomm__ring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5145]) ).

fof(c_0_8083,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5146]) ).

fof(c_0_8084,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5147]) ).

fof(c_0_8085,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5148]) ).

fof(c_0_8086,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oordered__semidom(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5149]) ).

fof(c_0_8087,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5150]) ).

fof(c_0_8088,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5151]) ).

fof(c_0_8089,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5152]) ).

fof(c_0_8090,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5153]) ).

fof(c_0_8091,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5154]) ).

fof(c_0_8092,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5155]) ).

fof(c_0_8093,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5156]) ).

fof(c_0_8094,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5157]) ).

fof(c_0_8095,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5158]) ).

fof(c_0_8096,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5159]) ).

fof(c_0_8097,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5160]) ).

fof(c_0_8098,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5161]) ).

fof(c_0_8099,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Olordered__ab__group__join(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5162]) ).

fof(c_0_8100,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Olordered__ab__group__meet(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5163]) ).

fof(c_0_8101,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Olordered__ab__group__abs(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5164]) ).

fof(c_0_8102,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5165]) ).

fof(c_0_8103,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5166]) ).

fof(c_0_8104,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Opordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5167]) ).

fof(c_0_8105,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Olordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5168]) ).

fof(c_0_8106,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oaxclass__abs__if(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5169]) ).

fof(c_0_8107,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5170]) ).

fof(c_0_8108,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5171]) ).

fof(c_0_8109,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5172]) ).

fof(c_0_8110,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oordered__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5173]) ).

fof(c_0_8111,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oordered__ring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5174]) ).

fof(c_0_8112,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Opordered__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5175]) ).

fof(c_0_8113,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5176]) ).

fof(c_0_8114,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5177]) ).

fof(c_0_8115,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oordered__idom(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5178]) ).

fof(c_0_8116,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5179]) ).

fof(c_0_8117,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5180]) ).

fof(c_0_8118,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5181]) ).

fof(c_0_8119,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5182]) ).

fof(c_0_8120,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__ring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5183]) ).

fof(c_0_8121,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5184]) ).

fof(c_0_8122,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5185]) ).

fof(c_0_8123,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5186]) ).

fof(c_0_8124,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5187]) ).

fof(c_0_8125,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5188]) ).

fof(c_0_8126,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5189]) ).

fof(c_0_8127,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5190]) ).

fof(c_0_8128,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5191]) ).

fof(c_0_8129,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5192]) ).

fof(c_0_8130,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5193]) ).

fof(c_0_8131,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oidom(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5194]) ).

fof(c_0_8132,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5195]) ).

fof(c_0_8133,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5196]) ).

fof(c_0_8134,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5197]) ).

fof(c_0_8135,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5198]) ).

fof(c_0_8136,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5199]) ).

fof(c_0_8137,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5200]) ).

fof(c_0_8138,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5201]) ).

fof(c_0_8139,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5202]) ).

fof(c_0_8140,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5203]) ).

fof(c_0_8141,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5204]) ).

fof(c_0_8142,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_HOL_Oinverse(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5205]) ).

fof(c_0_8143,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__field(X41)
      | class_Ring__and__Field_Ofield(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5206]) ).

fof(c_0_8144,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5207]) ).

fof(c_0_8145,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5208]) ).

fof(c_0_8146,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5209]) ).

fof(c_0_8147,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5210]) ).

fof(c_0_8148,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5211]) ).

fof(c_0_8149,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5212]) ).

fof(c_0_8150,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5213]) ).

fof(c_0_8151,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Opordered__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5214]) ).

fof(c_0_8152,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5215]) ).

fof(c_0_8153,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5216]) ).

fof(c_0_8154,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5217]) ).

fof(c_0_8155,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5218]) ).

fof(c_0_8156,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Oordered__semiring__strict(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5219]) ).

fof(c_0_8157,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5220]) ).

fof(c_0_8158,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5221]) ).

fof(c_0_8159,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5222]) ).

fof(c_0_8160,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5223]) ).

fof(c_0_8161,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5224]) ).

fof(c_0_8162,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5225]) ).

fof(c_0_8163,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5226]) ).

fof(c_0_8164,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5227]) ).

fof(c_0_8165,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5228]) ).

fof(c_0_8166,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5229]) ).

fof(c_0_8167,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5230]) ).

fof(c_0_8168,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5231]) ).

fof(c_0_8169,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5232]) ).

fof(c_0_8170,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5233]) ).

fof(c_0_8171,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5234]) ).

fof(c_0_8172,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5235]) ).

fof(c_0_8173,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5236]) ).

fof(c_0_8174,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5237]) ).

fof(c_0_8175,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Opordered__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5238]) ).

fof(c_0_8176,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Opordered__cancel__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5239]) ).

fof(c_0_8177,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5240]) ).

fof(c_0_8178,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5241]) ).

fof(c_0_8179,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5242]) ).

fof(c_0_8180,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Olordered__ab__group__join(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5243]) ).

fof(c_0_8181,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5244]) ).

fof(c_0_8182,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Olordered__ab__group__meet(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5245]) ).

fof(c_0_8183,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5246]) ).

fof(c_0_8184,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5247]) ).

fof(c_0_8185,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5248]) ).

fof(c_0_8186,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5249]) ).

fof(c_0_8187,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Olordered__ab__group__abs(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5250]) ).

fof(c_0_8188,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5251]) ).

fof(c_0_8189,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5252]) ).

fof(c_0_8190,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5253]) ).

fof(c_0_8191,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5254]) ).

fof(c_0_8192,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5255]) ).

fof(c_0_8193,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5256]) ).

fof(c_0_8194,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5257]) ).

fof(c_0_8195,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5258]) ).

fof(c_0_8196,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5259]) ).

fof(c_0_8197,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5260]) ).

fof(c_0_8198,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5261]) ).

fof(c_0_8199,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5262]) ).

fof(c_0_8200,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5263]) ).

fof(c_0_8201,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5264]) ).

fof(c_0_8202,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5265]) ).

fof(c_0_8203,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5266]) ).

fof(c_0_8204,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Olordered__ring(X41)
      | class_Ring__and__Field_Opordered__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5267]) ).

fof(c_0_8205,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5268]) ).

fof(c_0_8206,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5269]) ).

fof(c_0_8207,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5270]) ).

fof(c_0_8208,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5271]) ).

fof(c_0_8209,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5272]) ).

fof(c_0_8210,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5273]) ).

fof(c_0_8211,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5274]) ).

fof(c_0_8212,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5275]) ).

fof(c_0_8213,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5276]) ).

fof(c_0_8214,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5277]) ).

fof(c_0_8215,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5278]) ).

fof(c_0_8216,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5279]) ).

fof(c_0_8217,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5280]) ).

fof(c_0_8218,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5281]) ).

fof(c_0_8219,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5282]) ).

fof(c_0_8220,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5283]) ).

fof(c_0_8221,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5284]) ).

fof(c_0_8222,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5285]) ).

fof(c_0_8223,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Oring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5286]) ).

fof(c_0_8224,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5287]) ).

fof(c_0_8225,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5288]) ).

fof(c_0_8226,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5289]) ).

fof(c_0_8227,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5290]) ).

fof(c_0_8228,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5291]) ).

fof(c_0_8229,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5292]) ).

fof(c_0_8230,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5293]) ).

fof(c_0_8231,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5294]) ).

fof(c_0_8232,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5295]) ).

fof(c_0_8233,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5296]) ).

fof(c_0_8234,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5297]) ).

fof(c_0_8235,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | class_Ring__and__Field_Ocomm__ring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5298]) ).

fof(c_0_8236,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5299]) ).

fof(c_0_8237,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5300]) ).

fof(c_0_8238,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5301]) ).

fof(c_0_8239,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5302]) ).

fof(c_0_8240,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5303]) ).

fof(c_0_8241,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5304]) ).

fof(c_0_8242,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5305]) ).

fof(c_0_8243,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Oidom(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5306]) ).

fof(c_0_8244,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_HOL_Oinverse(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5307]) ).

fof(c_0_8245,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5308]) ).

fof(c_0_8246,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5309]) ).

fof(c_0_8247,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5310]) ).

fof(c_0_8248,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5311]) ).

fof(c_0_8249,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5312]) ).

fof(c_0_8250,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5313]) ).

fof(c_0_8251,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5314]) ).

fof(c_0_8252,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5315]) ).

fof(c_0_8253,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5316]) ).

fof(c_0_8254,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5317]) ).

fof(c_0_8255,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5318]) ).

fof(c_0_8256,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Oring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5319]) ).

fof(c_0_8257,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5320]) ).

fof(c_0_8258,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5321]) ).

fof(c_0_8259,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5322]) ).

fof(c_0_8260,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5323]) ).

fof(c_0_8261,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5324]) ).

fof(c_0_8262,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5325]) ).

fof(c_0_8263,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5326]) ).

fof(c_0_8264,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5327]) ).

fof(c_0_8265,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5328]) ).

fof(c_0_8266,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5329]) ).

fof(c_0_8267,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5330]) ).

fof(c_0_8268,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ofield(X41)
      | class_Ring__and__Field_Ocomm__ring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5331]) ).

fof(c_0_8269,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X41)
      | class_HOL_Oinverse(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5332]) ).

fof(c_0_8270,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5333]) ).

fof(c_0_8271,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5334]) ).

fof(c_0_8272,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5335]) ).

fof(c_0_8273,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5336]) ).

fof(c_0_8274,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5337]) ).

fof(c_0_8275,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5338]) ).

fof(c_0_8276,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5339]) ).

fof(c_0_8277,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5340]) ).

fof(c_0_8278,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5341]) ).

fof(c_0_8279,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5342]) ).

fof(c_0_8280,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5343]) ).

fof(c_0_8281,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5344]) ).

fof(c_0_8282,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5345]) ).

fof(c_0_8283,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5346]) ).

fof(c_0_8284,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5347]) ).

fof(c_0_8285,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5348]) ).

fof(c_0_8286,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5349]) ).

fof(c_0_8287,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5350]) ).

fof(c_0_8288,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5351]) ).

fof(c_0_8289,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5352]) ).

fof(c_0_8290,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5353]) ).

fof(c_0_8291,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5354]) ).

fof(c_0_8292,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5355]) ).

fof(c_0_8293,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5356]) ).

fof(c_0_8294,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5357]) ).

fof(c_0_8295,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5358]) ).

fof(c_0_8296,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5359]) ).

fof(c_0_8297,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5360]) ).

fof(c_0_8298,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5361]) ).

fof(c_0_8299,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5362]) ).

fof(c_0_8300,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5363]) ).

fof(c_0_8301,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5364]) ).

fof(c_0_8302,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5365]) ).

fof(c_0_8303,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5366]) ).

fof(c_0_8304,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5367]) ).

fof(c_0_8305,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5368]) ).

fof(c_0_8306,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5369]) ).

fof(c_0_8307,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5370]) ).

fof(c_0_8308,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5371]) ).

fof(c_0_8309,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5372]) ).

fof(c_0_8310,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5373]) ).

fof(c_0_8311,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5374]) ).

fof(c_0_8312,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5375]) ).

fof(c_0_8313,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5376]) ).

fof(c_0_8314,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5377]) ).

fof(c_0_8315,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5378]) ).

fof(c_0_8316,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5379]) ).

fof(c_0_8317,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5380]) ).

fof(c_0_8318,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5381]) ).

fof(c_0_8319,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5382]) ).

fof(c_0_8320,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5383]) ).

fof(c_0_8321,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5384]) ).

fof(c_0_8322,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5385]) ).

fof(c_0_8323,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5386]) ).

fof(c_0_8324,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5387]) ).

fof(c_0_8325,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5388]) ).

fof(c_0_8326,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5389]) ).

fof(c_0_8327,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5390]) ).

fof(c_0_8328,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5391]) ).

fof(c_0_8329,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5392]) ).

fof(c_0_8330,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5393]) ).

fof(c_0_8331,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5394]) ).

fof(c_0_8332,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5395]) ).

fof(c_0_8333,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5396]) ).

fof(c_0_8334,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5397]) ).

fof(c_0_8335,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5398]) ).

fof(c_0_8336,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5399]) ).

fof(c_0_8337,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5400]) ).

fof(c_0_8338,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5401]) ).

fof(c_0_8339,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5402]) ).

fof(c_0_8340,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5403]) ).

fof(c_0_8341,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5404]) ).

fof(c_0_8342,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5405]) ).

fof(c_0_8343,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5406]) ).

fof(c_0_8344,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5407]) ).

fof(c_0_8345,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5408]) ).

fof(c_0_8346,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5409]) ).

fof(c_0_8347,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5410]) ).

fof(c_0_8348,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5411]) ).

fof(c_0_8349,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5412]) ).

fof(c_0_8350,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5413]) ).

fof(c_0_8351,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5414]) ).

fof(c_0_8352,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5415]) ).

fof(c_0_8353,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Oring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5416]) ).

fof(c_0_8354,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5417]) ).

fof(c_0_8355,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5418]) ).

fof(c_0_8356,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5419]) ).

fof(c_0_8357,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5420]) ).

fof(c_0_8358,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5421]) ).

fof(c_0_8359,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5422]) ).

fof(c_0_8360,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5423]) ).

fof(c_0_8361,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5424]) ).

fof(c_0_8362,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5425]) ).

fof(c_0_8363,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5426]) ).

fof(c_0_8364,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5427]) ).

fof(c_0_8365,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5428]) ).

fof(c_0_8366,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5429]) ).

fof(c_0_8367,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5430]) ).

fof(c_0_8368,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5431]) ).

fof(c_0_8369,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5432]) ).

fof(c_0_8370,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5433]) ).

fof(c_0_8371,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5434]) ).

fof(c_0_8372,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5435]) ).

fof(c_0_8373,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5436]) ).

fof(c_0_8374,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5437]) ).

fof(c_0_8375,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5438]) ).

fof(c_0_8376,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5439]) ).

fof(c_0_8377,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5440]) ).

fof(c_0_8378,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5441]) ).

fof(c_0_8379,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5442]) ).

fof(c_0_8380,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5443]) ).

fof(c_0_8381,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5444]) ).

fof(c_0_8382,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5445]) ).

fof(c_0_8383,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5446]) ).

fof(c_0_8384,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5447]) ).

fof(c_0_8385,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5448]) ).

fof(c_0_8386,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5449]) ).

fof(c_0_8387,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5450]) ).

fof(c_0_8388,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5451]) ).

fof(c_0_8389,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5452]) ).

fof(c_0_8390,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5453]) ).

fof(c_0_8391,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5454]) ).

fof(c_0_8392,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5455]) ).

fof(c_0_8393,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5456]) ).

fof(c_0_8394,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5457]) ).

fof(c_0_8395,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5458]) ).

fof(c_0_8396,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5459]) ).

fof(c_0_8397,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5460]) ).

fof(c_0_8398,plain,
    ! [X41] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5461]) ).

fof(c_0_8399,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5462]) ).

fof(c_0_8400,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5463]) ).

fof(c_0_8401,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5464]) ).

fof(c_0_8402,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5465]) ).

fof(c_0_8403,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5466]) ).

fof(c_0_8404,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5467]) ).

fof(c_0_8405,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5468]) ).

fof(c_0_8406,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5469]) ).

fof(c_0_8407,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5470]) ).

fof(c_0_8408,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5471]) ).

fof(c_0_8409,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5472]) ).

fof(c_0_8410,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5473]) ).

fof(c_0_8411,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5474]) ).

fof(c_0_8412,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5475]) ).

fof(c_0_8413,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5476]) ).

fof(c_0_8414,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5477]) ).

fof(c_0_8415,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5478]) ).

fof(c_0_8416,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5479]) ).

fof(c_0_8417,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5480]) ).

fof(c_0_8418,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5481]) ).

fof(c_0_8419,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5482]) ).

fof(c_0_8420,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5483]) ).

fof(c_0_8421,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5484]) ).

fof(c_0_8422,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5485]) ).

fof(c_0_8423,plain,
    ! [X41] :
      ( ~ class_Power_Orecpower(X41)
      | class_Nat_Opower(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5486]) ).

fof(c_0_8424,plain,
    ! [X41] :
      ( ~ class_Orderings_Oorder(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5487]) ).

fof(c_0_8425,plain,
    ! [X41] :
      ( ~ class_Orderings_Olinorder(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5488]) ).

fof(c_0_8426,plain,
    ! [X41] :
      ( ~ class_Orderings_Olinorder(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5489]) ).

fof(c_0_8427,plain,
    ! [X41] :
      ( ~ class_Orderings_Olinorder(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5490]) ).

fof(c_0_8428,plain,
    ! [X41] :
      ( ~ class_Orderings_Olinorder(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5491]) ).

fof(c_0_8429,plain,
    ! [X41] :
      ( ~ class_Orderings_Olinorder(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5492]) ).

fof(c_0_8430,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5493]) ).

fof(c_0_8431,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Osemigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5494]) ).

fof(c_0_8432,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5495]) ).

fof(c_0_8433,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5496]) ).

fof(c_0_8434,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5497]) ).

fof(c_0_8435,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5498]) ).

fof(c_0_8436,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5499]) ).

fof(c_0_8437,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5500]) ).

fof(c_0_8438,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5501]) ).

fof(c_0_8439,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5502]) ).

fof(c_0_8440,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5503]) ).

fof(c_0_8441,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5504]) ).

fof(c_0_8442,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5505]) ).

fof(c_0_8443,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5506]) ).

fof(c_0_8444,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5507]) ).

fof(c_0_8445,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5508]) ).

fof(c_0_8446,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5509]) ).

fof(c_0_8447,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5510]) ).

fof(c_0_8448,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5511]) ).

fof(c_0_8449,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5512]) ).

fof(c_0_8450,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5513]) ).

fof(c_0_8451,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5514]) ).

fof(c_0_8452,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5515]) ).

fof(c_0_8453,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5516]) ).

fof(c_0_8454,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5517]) ).

fof(c_0_8455,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5518]) ).

fof(c_0_8456,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5519]) ).

fof(c_0_8457,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5520]) ).

fof(c_0_8458,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5521]) ).

fof(c_0_8459,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5522]) ).

fof(c_0_8460,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5523]) ).

fof(c_0_8461,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5524]) ).

fof(c_0_8462,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5525]) ).

fof(c_0_8463,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5526]) ).

fof(c_0_8464,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5527]) ).

fof(c_0_8465,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5528]) ).

fof(c_0_8466,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5529]) ).

fof(c_0_8467,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5530]) ).

fof(c_0_8468,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_Orderings_Olinorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5531]) ).

fof(c_0_8469,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5532]) ).

fof(c_0_8470,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5533]) ).

fof(c_0_8471,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5534]) ).

fof(c_0_8472,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5535]) ).

fof(c_0_8473,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5536]) ).

fof(c_0_8474,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5537]) ).

fof(c_0_8475,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5538]) ).

fof(c_0_8476,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5539]) ).

fof(c_0_8477,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5540]) ).

fof(c_0_8478,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5541]) ).

fof(c_0_8479,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5542]) ).

fof(c_0_8480,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5543]) ).

fof(c_0_8481,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5544]) ).

fof(c_0_8482,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Omonoid__mult(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5545]) ).

fof(c_0_8483,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Omonoid__mult(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5546]) ).

fof(c_0_8484,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Omonoid__mult(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5547]) ).

fof(c_0_8485,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5548]) ).

fof(c_0_8486,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5549]) ).

fof(c_0_8487,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5550]) ).

fof(c_0_8488,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5551]) ).

fof(c_0_8489,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5552]) ).

fof(c_0_8490,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5553]) ).

fof(c_0_8491,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5554]) ).

fof(c_0_8492,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5555]) ).

fof(c_0_8493,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5556]) ).

fof(c_0_8494,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5557]) ).

fof(c_0_8495,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5558]) ).

fof(c_0_8496,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5559]) ).

fof(c_0_8497,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5560]) ).

fof(c_0_8498,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5561]) ).

fof(c_0_8499,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5562]) ).

fof(c_0_8500,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5563]) ).

fof(c_0_8501,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5564]) ).

fof(c_0_8502,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5565]) ).

fof(c_0_8503,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5566]) ).

fof(c_0_8504,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5567]) ).

fof(c_0_8505,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5568]) ).

fof(c_0_8506,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5569]) ).

fof(c_0_8507,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5570]) ).

fof(c_0_8508,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5571]) ).

fof(c_0_8509,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5572]) ).

fof(c_0_8510,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5573]) ).

fof(c_0_8511,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5574]) ).

fof(c_0_8512,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5575]) ).

fof(c_0_8513,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5576]) ).

fof(c_0_8514,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5577]) ).

fof(c_0_8515,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5578]) ).

fof(c_0_8516,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5579]) ).

fof(c_0_8517,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5580]) ).

fof(c_0_8518,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5581]) ).

fof(c_0_8519,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5582]) ).

fof(c_0_8520,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5583]) ).

fof(c_0_8521,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5584]) ).

fof(c_0_8522,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5585]) ).

fof(c_0_8523,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5586]) ).

fof(c_0_8524,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5587]) ).

fof(c_0_8525,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5588]) ).

fof(c_0_8526,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5589]) ).

fof(c_0_8527,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5590]) ).

fof(c_0_8528,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5591]) ).

fof(c_0_8529,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5592]) ).

fof(c_0_8530,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5593]) ).

fof(c_0_8531,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5594]) ).

fof(c_0_8532,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5595]) ).

fof(c_0_8533,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5596]) ).

fof(c_0_8534,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5597]) ).

fof(c_0_8535,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5598]) ).

fof(c_0_8536,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5599]) ).

fof(c_0_8537,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5600]) ).

fof(c_0_8538,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5601]) ).

fof(c_0_8539,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5602]) ).

fof(c_0_8540,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5603]) ).

fof(c_0_8541,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X41)
      | class_OrderedGroup_Olordered__ab__group(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5604]) ).

fof(c_0_8542,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5605]) ).

fof(c_0_8543,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5606]) ).

fof(c_0_8544,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5607]) ).

fof(c_0_8545,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5608]) ).

fof(c_0_8546,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5609]) ).

fof(c_0_8547,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5610]) ).

fof(c_0_8548,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5611]) ).

fof(c_0_8549,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5612]) ).

fof(c_0_8550,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5613]) ).

fof(c_0_8551,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5614]) ).

fof(c_0_8552,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_LOrder_Olorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5615]) ).

fof(c_0_8553,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5616]) ).

fof(c_0_8554,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5617]) ).

fof(c_0_8555,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5618]) ).

fof(c_0_8556,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5619]) ).

fof(c_0_8557,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5620]) ).

fof(c_0_8558,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5621]) ).

fof(c_0_8559,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X41)
      | class_OrderedGroup_Opordered__ab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5622]) ).

fof(c_0_8560,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5623]) ).

fof(c_0_8561,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5624]) ).

fof(c_0_8562,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5625]) ).

fof(c_0_8563,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5626]) ).

fof(c_0_8564,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5627]) ).

fof(c_0_8565,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5628]) ).

fof(c_0_8566,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5629]) ).

fof(c_0_8567,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5630]) ).

fof(c_0_8568,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5631]) ).

fof(c_0_8569,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5632]) ).

fof(c_0_8570,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5633]) ).

fof(c_0_8571,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5634]) ).

fof(c_0_8572,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5635]) ).

fof(c_0_8573,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5636]) ).

fof(c_0_8574,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5637]) ).

fof(c_0_8575,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5638]) ).

fof(c_0_8576,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5639]) ).

fof(c_0_8577,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5640]) ).

fof(c_0_8578,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5641]) ).

fof(c_0_8579,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5642]) ).

fof(c_0_8580,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5643]) ).

fof(c_0_8581,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5644]) ).

fof(c_0_8582,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5645]) ).

fof(c_0_8583,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5646]) ).

fof(c_0_8584,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5647]) ).

fof(c_0_8585,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5648]) ).

fof(c_0_8586,plain,
    ! [X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5649]) ).

fof(c_0_8587,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Ocomm__monoid__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5650]) ).

fof(c_0_8588,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_HOL_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5651]) ).

fof(c_0_8589,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5652]) ).

fof(c_0_8590,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Osemiring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5653]) ).

fof(c_0_8591,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Oab__semigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5654]) ).

fof(c_0_8592,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Osemigroup__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5655]) ).

fof(c_0_8593,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Numeral_Onumber(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5656]) ).

fof(c_0_8594,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_HOL_Otimes(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5657]) ).

fof(c_0_8595,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__ring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5658]) ).

fof(c_0_8596,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5659]) ).

fof(c_0_8597,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Oring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5660]) ).

fof(c_0_8598,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Osemiring__1__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5661]) ).

fof(c_0_8599,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5662]) ).

fof(c_0_8600,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Osemiring__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5663]) ).

fof(c_0_8601,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Ocomm__monoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5664]) ).

fof(c_0_8602,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Omonoid__mult(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5665]) ).

fof(c_0_8603,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5666]) ).

fof(c_0_8604,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_HOL_Oone(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5667]) ).

fof(c_0_8605,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Oab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5668]) ).

fof(c_0_8606,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__ring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5669]) ).

fof(c_0_8607,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5670]) ).

fof(c_0_8608,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Oring(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5671]) ).

fof(c_0_8609,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Osemiring__0__cancel(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5672]) ).

fof(c_0_8610,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Oab__group__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5673]) ).

fof(c_0_8611,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5674]) ).

fof(c_0_8612,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Ocancel__semigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5675]) ).

fof(c_0_8613,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_HOL_Ominus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5676]) ).

fof(c_0_8614,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Ocomm__semiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5677]) ).

fof(c_0_8615,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_Ring__and__Field_Osemiring__0(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5678]) ).

fof(c_0_8616,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_OrderedGroup_Osemigroup__add(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5679]) ).

fof(c_0_8617,plain,
    ! [X41] :
      ( ~ class_Numeral_Onumber__ring(X41)
      | class_HOL_Oplus(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5680]) ).

fof(c_0_8618,plain,
    ! [X41] :
      ( ~ class_LOrder_Omeet__semilorder(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5681]) ).

fof(c_0_8619,plain,
    ! [X41] :
      ( ~ class_LOrder_Omeet__semilorder(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5682]) ).

fof(c_0_8620,plain,
    ! [X41] :
      ( ~ class_LOrder_Olorder(X41)
      | class_LOrder_Ojoin__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5683]) ).

fof(c_0_8621,plain,
    ! [X41] :
      ( ~ class_LOrder_Olorder(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5684]) ).

fof(c_0_8622,plain,
    ! [X41] :
      ( ~ class_LOrder_Olorder(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5685]) ).

fof(c_0_8623,plain,
    ! [X41] :
      ( ~ class_LOrder_Olorder(X41)
      | class_LOrder_Omeet__semilorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5686]) ).

fof(c_0_8624,plain,
    ! [X41] :
      ( ~ class_LOrder_Ojoin__semilorder(X41)
      | class_Orderings_Oorder(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5687]) ).

fof(c_0_8625,plain,
    ! [X41] :
      ( ~ class_LOrder_Ojoin__semilorder(X41)
      | class_Orderings_Oord(X41) ),
    inference(variable_rename,[status(thm)],[c_0_5688]) ).

fof(c_0_8626,axiom,
    c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
    c_0_5689 ).

fof(c_0_8627,axiom,
    c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
    c_0_5690 ).

fof(c_0_8628,plain,
    ! [X2] : c_Message_OinvKey(c_Message_OinvKey(X2)) = X2,
    inference(variable_rename,[status(thm)],[c_0_5691]) ).

fof(c_0_8629,axiom,
    c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
    c_0_5692 ).

fof(c_0_8630,axiom,
    c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
    c_0_5693 ).

fof(c_0_8631,axiom,
    c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
    c_0_5694 ).

fof(c_0_8632,axiom,
    c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
    c_0_5695 ).

fof(c_0_8633,axiom,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    c_0_5696 ).

fof(c_0_8634,axiom,
    c_Parity_Oeven(c_0,tc_nat),
    c_0_5697 ).

fof(c_0_8635,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
    c_0_5698 ).

fof(c_0_8636,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
    c_0_5699 ).

fof(c_0_8637,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
    c_0_5700 ).

fof(c_0_8638,axiom,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
    c_0_5701 ).

fof(c_0_8639,axiom,
    c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
    c_0_5702 ).

fof(c_0_8640,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
    c_0_5703 ).

fof(c_0_8641,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
    c_0_5704 ).

fof(c_0_8642,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
    c_0_5705 ).

fof(c_0_8643,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
    c_0_5706 ).

fof(c_0_8644,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
    c_0_5707 ).

fof(c_0_8645,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
    c_0_5708 ).

fof(c_0_8646,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
    c_0_5709 ).

fof(c_0_8647,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
    c_0_5710 ).

fof(c_0_8648,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
    c_0_5711 ).

fof(c_0_8649,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
    c_0_5712 ).

fof(c_0_8650,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
    c_0_5713 ).

fof(c_0_8651,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
    c_0_5714 ).

fof(c_0_8652,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
    c_0_5715 ).

fof(c_0_8653,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
    c_0_5716 ).

fof(c_0_8654,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
    c_0_5717 ).

fof(c_0_8655,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
    c_0_5718 ).

fof(c_0_8656,plain,
    ! [X2] : c_IntDef_Onat(c_IntDef_Oint(X2)) = X2,
    inference(variable_rename,[status(thm)],[c_0_5719]) ).

fof(c_0_8657,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
    c_0_5720 ).

fof(c_0_8658,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
    c_0_5721 ).

fof(c_0_8659,axiom,
    c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
    c_0_5722 ).

fof(c_0_8660,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_5723 ).

fof(c_0_8661,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_5724 ).

fof(c_0_8662,plain,
    ! [X39] : class_Nat_Opower(tc_set(X39)),
    inference(variable_rename,[status(thm)],[c_0_5725]) ).

fof(c_0_8663,plain,
    ! [X39] : class_Orderings_Oorder(tc_set(X39)),
    inference(variable_rename,[status(thm)],[c_0_5726]) ).

fof(c_0_8664,plain,
    ! [X39] : class_Orderings_Oord(tc_set(X39)),
    inference(variable_rename,[status(thm)],[c_0_5727]) ).

fof(c_0_8665,plain,
    ! [X39] : class_HOL_Ominus(tc_set(X39)),
    inference(variable_rename,[status(thm)],[c_0_5728]) ).

fof(c_0_8666,plain,
    ! [X23] :
      ( c_IntDef_Oint(X23) != c_0
      | X23 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_5729]) ).

fof(c_0_8667,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X5)
      | c_1 != c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_5730])])]) ).

fof(c_0_8668,plain,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X5)
      | c_0 != c_1 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_5731])])]) ).

fof(c_0_8669,plain,
    ! [X92] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X92),
    inference(variable_rename,[status(thm)],[c_0_5732]) ).

fof(c_0_8670,plain,
    ! [X92] : c_Message_Oagent_OFriend(X92) != c_Message_Oagent_OSpy,
    inference(variable_rename,[status(thm)],[c_0_5733]) ).

fof(c_0_8671,plain,
    ! [X91] : c_Message_Oagent_OFriend(X91) != c_Message_Oagent_OServer,
    inference(variable_rename,[status(thm)],[c_0_5734]) ).

fof(c_0_8672,plain,
    ! [X91] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X91),
    inference(variable_rename,[status(thm)],[c_0_5735]) ).

fof(c_0_8673,plain,
    ! [X17] : c_0 != c_Suc(X17),
    inference(variable_rename,[status(thm)],[c_0_5736]) ).

fof(c_0_8674,plain,
    ! [X17] : c_Suc(X17) != c_0,
    inference(variable_rename,[status(thm)],[c_0_5737]) ).

fof(c_0_8675,axiom,
    c_IntDef_Onat(c_1) = c_Suc(c_0),
    c_0_5738 ).

fof(c_0_8676,axiom,
    c_Message_Oanalz(c_emptyset) = c_emptyset,
    c_0_5739 ).

fof(c_0_8677,axiom,
    c_Message_Oparts(c_emptyset) = c_emptyset,
    c_0_5740 ).

fof(c_0_8678,axiom,
    c_Message_OkeysFor(c_emptyset) = c_emptyset,
    c_0_5741 ).

fof(c_0_8679,axiom,
    c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
    c_0_5742 ).

fof(c_0_8680,axiom,
    c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
    c_0_5743 ).

fof(c_0_8681,axiom,
    c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
    c_0_5744 ).

fof(c_0_8682,axiom,
    c_1 = c_Suc(c_0),
    c_0_5745 ).

fof(c_0_8683,axiom,
    c_IntDef_Onat(c_0) = c_0,
    c_0_5746 ).

fof(c_0_8684,axiom,
    c_IntDef_Oint(c_0) = c_0,
    c_0_5747 ).

fof(c_0_8685,axiom,
    c_IntDef_Oint(c_1) = c_1,
    c_0_5748 ).

fof(c_0_8686,axiom,
    class_HOL_Ominus(tc_nat),
    c_0_5749 ).

fof(c_0_8687,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    c_0_5750 ).

fof(c_0_8688,axiom,
    class_Orderings_Olinorder(tc_nat),
    c_0_5751 ).

fof(c_0_8689,axiom,
    class_LOrder_Olorder(tc_nat),
    c_0_5752 ).

fof(c_0_8690,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    c_0_5753 ).

fof(c_0_8691,axiom,
    class_Parity_Oeven__odd(tc_nat),
    c_0_5754 ).

fof(c_0_8692,axiom,
    class_Numeral_Onumber(tc_nat),
    c_0_5755 ).

fof(c_0_8693,axiom,
    class_Power_Orecpower(tc_nat),
    c_0_5756 ).

fof(c_0_8694,axiom,
    class_Divides_Odiv(tc_nat),
    c_0_5757 ).

fof(c_0_8695,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_5758 ).

fof(c_0_8696,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_5759 ).

fof(c_0_8697,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    c_0_5760 ).

fof(c_0_8698,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    c_0_5761 ).

fof(c_0_8699,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    c_0_5762 ).

fof(c_0_8700,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_5763 ).

fof(c_0_8701,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_5764 ).

fof(c_0_8702,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_5765 ).

fof(c_0_8703,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    c_0_5766 ).

fof(c_0_8704,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_5767 ).

fof(c_0_8705,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_5768 ).

fof(c_0_8706,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_5769 ).

fof(c_0_8707,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    c_0_5770 ).

fof(c_0_8708,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    c_0_5771 ).

fof(c_0_8709,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    c_0_5772 ).

fof(c_0_8710,axiom,
    class_Orderings_Oorder(tc_nat),
    c_0_5773 ).

fof(c_0_8711,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    c_0_5774 ).

fof(c_0_8712,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_5775 ).

fof(c_0_8713,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_5776 ).

fof(c_0_8714,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_5777 ).

fof(c_0_8715,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_5778 ).

fof(c_0_8716,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    c_0_5779 ).

fof(c_0_8717,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    c_0_5780 ).

fof(c_0_8718,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    c_0_5781 ).

fof(c_0_8719,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    c_0_5782 ).

fof(c_0_8720,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_5783 ).

fof(c_0_8721,axiom,
    class_Orderings_Oord(tc_nat),
    c_0_5784 ).

fof(c_0_8722,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_5785 ).

fof(c_0_8723,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_5786 ).

fof(c_0_8724,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_5787 ).

fof(c_0_8725,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    c_0_5788 ).

fof(c_0_8726,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_5789 ).

fof(c_0_8727,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    c_0_5790 ).

fof(c_0_8728,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    c_0_5791 ).

fof(c_0_8729,axiom,
    class_Nat_Opower(tc_nat),
    c_0_5792 ).

fof(c_0_8730,axiom,
    class_HOL_Otimes(tc_nat),
    c_0_5793 ).

fof(c_0_8731,axiom,
    class_HOL_Oplus(tc_nat),
    c_0_5794 ).

fof(c_0_8732,axiom,
    class_HOL_Ozero(tc_nat),
    c_0_5795 ).

fof(c_0_8733,axiom,
    class_HOL_Oone(tc_nat),
    c_0_5796 ).

fof(c_0_8734,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    c_0_5797 ).

fof(c_0_8735,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    c_0_5798 ).

fof(c_0_8736,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    c_0_5799 ).

fof(c_0_8737,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    c_0_5800 ).

fof(c_0_8738,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    c_0_5801 ).

fof(c_0_8739,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    c_0_5802 ).

fof(c_0_8740,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    c_0_5803 ).

fof(c_0_8741,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    c_0_5804 ).

fof(c_0_8742,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    c_0_5805 ).

fof(c_0_8743,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    c_0_5806 ).

fof(c_0_8744,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    c_0_5807 ).

fof(c_0_8745,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    c_0_5808 ).

fof(c_0_8746,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    c_0_5809 ).

fof(c_0_8747,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    c_0_5810 ).

fof(c_0_8748,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    c_0_5811 ).

fof(c_0_8749,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    c_0_5812 ).

fof(c_0_8750,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    c_0_5813 ).

fof(c_0_8751,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    c_0_5814 ).

fof(c_0_8752,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    c_0_5815 ).

fof(c_0_8753,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    c_0_5816 ).

fof(c_0_8754,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    c_0_5817 ).

fof(c_0_8755,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    c_0_5818 ).

fof(c_0_8756,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    c_0_5819 ).

fof(c_0_8757,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    c_0_5820 ).

fof(c_0_8758,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    c_0_5821 ).

fof(c_0_8759,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    c_0_5822 ).

fof(c_0_8760,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    c_0_5823 ).

fof(c_0_8761,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    c_0_5824 ).

fof(c_0_8762,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    c_0_5825 ).

fof(c_0_8763,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    c_0_5826 ).

fof(c_0_8764,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    c_0_5827 ).

fof(c_0_8765,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    c_0_5828 ).

fof(c_0_8766,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    c_0_5829 ).

fof(c_0_8767,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5830 ).

fof(c_0_8768,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    c_0_5831 ).

fof(c_0_8769,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5832 ).

fof(c_0_8770,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5833 ).

fof(c_0_8771,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    c_0_5834 ).

fof(c_0_8772,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    c_0_5835 ).

fof(c_0_8773,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    c_0_5836 ).

fof(c_0_8774,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    c_0_5837 ).

fof(c_0_8775,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    c_0_5838 ).

fof(c_0_8776,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    c_0_5839 ).

fof(c_0_8777,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    c_0_5840 ).

fof(c_0_8778,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    c_0_5841 ).

fof(c_0_8779,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    c_0_5842 ).

fof(c_0_8780,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    c_0_5843 ).

fof(c_0_8781,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    c_0_5844 ).

fof(c_0_8782,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    c_0_5845 ).

fof(c_0_8783,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    c_0_5846 ).

fof(c_0_8784,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    c_0_5847 ).

fof(c_0_8785,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    c_0_5848 ).

fof(c_0_8786,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    c_0_5849 ).

fof(c_0_8787,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    c_0_5850 ).

fof(c_0_8788,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    c_0_5851 ).

fof(c_0_8789,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    c_0_5852 ).

fof(c_0_8790,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    c_0_5853 ).

fof(c_0_8791,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    c_0_5854 ).

fof(c_0_8792,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5855 ).

fof(c_0_8793,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    c_0_5856 ).

fof(c_0_8794,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    c_0_5857 ).

fof(c_0_8795,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    c_0_5858 ).

fof(c_0_8796,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    c_0_5859 ).

fof(c_0_8797,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    c_0_5860 ).

fof(c_0_8798,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    c_0_5861 ).

fof(c_0_8799,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    c_0_5862 ).

fof(c_0_8800,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    c_0_5863 ).

fof(c_0_8801,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    c_0_5864 ).

fof(c_0_8802,axiom,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    c_0_5865 ).

fof(c_0_8803,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    c_0_5866 ).

fof(c_0_8804,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    c_0_5867 ).

fof(c_0_8805,axiom,
    c_UNIV != c_emptyset,
    c_0_5868 ).

fof(c_0_8806,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    c_0_5869 ).

fof(c_0_8807,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    c_0_5870 ).

fof(c_0_8808,axiom,
    c_0 != c_1,
    c_0_5871 ).

fof(c_0_8809,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_5872 ).

fof(c_0_8810,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    c_0_5873 ).

cnf(c_0_8811,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble8,X17) = X9,
    inference(split_conjunct,[status(thm)],[c_0_5874]) ).

cnf(c_0_8812,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble7,X17) = X8,
    inference(split_conjunct,[status(thm)],[c_0_5875]) ).

cnf(c_0_8813,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble6,X17) = X7,
    inference(split_conjunct,[status(thm)],[c_0_5876]) ).

cnf(c_0_8814,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble5,X17) = X6,
    inference(split_conjunct,[status(thm)],[c_0_5877]) ).

cnf(c_0_8815,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble4,X17) = X5,
    inference(split_conjunct,[status(thm)],[c_0_5878]) ).

cnf(c_0_8816,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble3,X17) = X4,
    inference(split_conjunct,[status(thm)],[c_0_5879]) ).

cnf(c_0_8817,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble2,X17) = X3,
    inference(split_conjunct,[status(thm)],[c_0_5880]) ).

cnf(c_0_8818,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble1,X17) = X2,
    inference(split_conjunct,[status(thm)],[c_0_5881]) ).

cnf(c_0_8819,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble0,X17) = X1,
    inference(split_conjunct,[status(thm)],[c_0_5882]) ).

cnf(c_0_8820,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleF,X17) = X16,
    inference(split_conjunct,[status(thm)],[c_0_5883]) ).

cnf(c_0_8821,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleE,X17) = X15,
    inference(split_conjunct,[status(thm)],[c_0_5884]) ).

cnf(c_0_8822,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleD,X17) = X14,
    inference(split_conjunct,[status(thm)],[c_0_5885]) ).

cnf(c_0_8823,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleC,X17) = X13,
    inference(split_conjunct,[status(thm)],[c_0_5886]) ).

cnf(c_0_8824,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleB,X17) = X12,
    inference(split_conjunct,[status(thm)],[c_0_5887]) ).

cnf(c_0_8825,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleA,X17) = X11,
    inference(split_conjunct,[status(thm)],[c_0_5888]) ).

cnf(c_0_8826,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble9,X17) = X10,
    inference(split_conjunct,[status(thm)],[c_0_5889]) ).

cnf(c_0_8827,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble8,X17) = X9,
    inference(split_conjunct,[status(thm)],[c_0_5890]) ).

cnf(c_0_8828,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble7,X17) = X8,
    inference(split_conjunct,[status(thm)],[c_0_5891]) ).

cnf(c_0_8829,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble6,X17) = X7,
    inference(split_conjunct,[status(thm)],[c_0_5892]) ).

cnf(c_0_8830,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble5,X17) = X6,
    inference(split_conjunct,[status(thm)],[c_0_5893]) ).

cnf(c_0_8831,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble4,X17) = X5,
    inference(split_conjunct,[status(thm)],[c_0_5894]) ).

cnf(c_0_8832,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble3,X17) = X4,
    inference(split_conjunct,[status(thm)],[c_0_5895]) ).

cnf(c_0_8833,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble2,X17) = X3,
    inference(split_conjunct,[status(thm)],[c_0_5896]) ).

cnf(c_0_8834,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble1,X17) = X2,
    inference(split_conjunct,[status(thm)],[c_0_5897]) ).

cnf(c_0_8835,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble0,X17) = X1,
    inference(split_conjunct,[status(thm)],[c_0_5898]) ).

cnf(c_0_8836,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleF,X17) = X16,
    inference(split_conjunct,[status(thm)],[c_0_5899]) ).

cnf(c_0_8837,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleE,X17) = X15,
    inference(split_conjunct,[status(thm)],[c_0_5900]) ).

cnf(c_0_8838,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleD,X17) = X14,
    inference(split_conjunct,[status(thm)],[c_0_5901]) ).

cnf(c_0_8839,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleC,X17) = X13,
    inference(split_conjunct,[status(thm)],[c_0_5902]) ).

cnf(c_0_8840,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleB,X17) = X12,
    inference(split_conjunct,[status(thm)],[c_0_5903]) ).

cnf(c_0_8841,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleA,X17) = X11,
    inference(split_conjunct,[status(thm)],[c_0_5904]) ).

cnf(c_0_8842,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble9,X17) = X10,
    inference(split_conjunct,[status(thm)],[c_0_5905]) ).

cnf(c_0_8843,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_5906]) ).

cnf(c_0_8844,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_5907]) ).

cnf(c_0_8845,plain,
    ( X1 = c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5)
    | ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_5908]) ).

cnf(c_0_8846,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5909]) ).

cnf(c_0_8847,plain,
    ( c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5910]) ).

cnf(c_0_8848,plain,
    ( c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5911]) ).

cnf(c_0_8849,plain,
    ( c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5912]) ).

cnf(c_0_8850,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5913]) ).

cnf(c_0_8851,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5914]) ).

cnf(c_0_8852,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5915]) ).

cnf(c_0_8853,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5916]) ).

cnf(c_0_8854,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5917]) ).

cnf(c_0_8855,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5918]) ).

cnf(c_0_8856,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5919]) ).

cnf(c_0_8857,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | X1 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5920]) ).

cnf(c_0_8858,plain,
    ( c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5921]) ).

cnf(c_0_8859,plain,
    ( X1 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5922]) ).

cnf(c_0_8860,plain,
    ( X1 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5)
    | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5923]) ).

cnf(c_0_8861,plain,
    ( X1 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5)
    | ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5924]) ).

cnf(c_0_8862,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_5925]) ).

cnf(c_0_8863,plain,
    ( c_plus(X1,X2,tc_nat) = c_plus(X3,X4,tc_nat)
    | ~ c_in(c_Pair(c_Pair(X1,X4,tc_nat,tc_nat),c_Pair(X3,X2,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_5926]) ).

cnf(c_0_8864,plain,
    ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
    | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5927]) ).

cnf(c_0_8865,plain,
    ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
    | c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5928]) ).

cnf(c_0_8866,plain,
    ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
    | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5929]) ).

cnf(c_0_8867,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5930]) ).

cnf(c_0_8868,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_5931]) ).

cnf(c_0_8869,plain,
    ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
    | c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5932]) ).

cnf(c_0_8870,plain,
    ( c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5933]) ).

cnf(c_0_8871,plain,
    ( c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5934]) ).

cnf(c_0_8872,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5935]) ).

cnf(c_0_8873,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5936]) ).

cnf(c_0_8874,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5937]) ).

cnf(c_0_8875,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5938]) ).

cnf(c_0_8876,plain,
    ( c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_5939]) ).

cnf(c_0_8877,plain,
    ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5940]) ).

cnf(c_0_8878,plain,
    ( c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5941]) ).

cnf(c_0_8879,plain,
    ( c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_5942]) ).

cnf(c_0_8880,plain,
    ( c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_5943]) ).

cnf(c_0_8881,plain,
    c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X1,X2,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(split_conjunct,[status(thm)],[c_0_5944]) ).

cnf(c_0_8882,plain,
    ( c_in(c_Pair(c_Pair(X1,X2,tc_nat,tc_nat),c_Pair(X3,X4,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_plus(X1,X4,tc_nat) != c_plus(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_5945]) ).

cnf(c_0_8883,plain,
    ( c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5946]) ).

cnf(c_0_8884,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5947]) ).

cnf(c_0_8885,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5948]) ).

cnf(c_0_8886,plain,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | c_in(c_Pair(X1,X3,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X2),c_List_Olist_OCons(X6,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_5949]) ).

cnf(c_0_8887,plain,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_5950]) ).

cnf(c_0_8888,plain,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_5951]) ).

cnf(c_0_8889,plain,
    ( c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_5952]) ).

cnf(c_0_8890,plain,
    ( X1 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_5953]) ).

cnf(c_0_8891,plain,
    ( X1 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_5954]) ).

cnf(c_0_8892,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_5955]) ).

cnf(c_0_8893,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_5956]) ).

cnf(c_0_8894,plain,
    ( c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_5957]) ).

cnf(c_0_8895,plain,
    ( X1 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4)
    | X1 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4)
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_5958]) ).

cnf(c_0_8896,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X3))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5959]) ).

cnf(c_0_8897,plain,
    ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_5960]) ).

cnf(c_0_8898,plain,
    ( X1 = c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4)
    | X1 = c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5961]) ).

cnf(c_0_8899,plain,
    ( X1 = c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5962]) ).

cnf(c_0_8900,plain,
    ( X1 = c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_5963]) ).

cnf(c_0_8901,plain,
    ( c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5964]) ).

cnf(c_0_8902,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OScons(X2,X3,X4,X5),X4,X5) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X1,X2,X4,X5),c_Datatype__Universe_Ontrunc(X1,X3,X4,X5),X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_5965]) ).

cnf(c_0_8903,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5966]) ).

cnf(c_0_8904,plain,
    ( c_Wellfounded__Recursion_Owf(X1,X2)
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5967]) ).

cnf(c_0_8905,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5968]) ).

cnf(c_0_8906,plain,
    ( c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
    | ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5969]) ).

cnf(c_0_8907,plain,
    ( c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
    | ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5970]) ).

cnf(c_0_8908,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5971]) ).

cnf(c_0_8909,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5972]) ).

cnf(c_0_8910,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_5973]) ).

cnf(c_0_8911,plain,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | X4 = X5
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X2),c_List_Olist_OCons(X5,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X6,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_5974]) ).

cnf(c_0_8912,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_5975]) ).

cnf(c_0_8913,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_5976]) ).

cnf(c_0_8914,plain,
    ( c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5)
    | ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_5977]) ).

cnf(c_0_8915,plain,
    ( c_List_Ozip(c_append(X1,X2,X3),c_append(X4,X5,X6),X3,X6) = c_append(c_List_Ozip(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6))
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X4,tc_List_Olist(X6))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_5978]) ).

cnf(c_0_8916,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5979]) ).

cnf(c_0_8917,plain,
    c_Relation_ODomain(c_Datatype__Universe_Odsum(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Relation_ODomain(X2,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_5980]) ).

cnf(c_0_8918,plain,
    c_Relation_ODomain(c_Datatype__Universe_Odprod(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Relation_ODomain(X2,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_5981]) ).

cnf(c_0_8919,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5982]) ).

cnf(c_0_8920,plain,
    ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5983]) ).

cnf(c_0_8921,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5984]) ).

cnf(c_0_8922,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5985]) ).

cnf(c_0_8923,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5986]) ).

cnf(c_0_8924,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5987]) ).

cnf(c_0_8925,plain,
    c_Nat_Opower(X1,c_Suc(X2),tc_set(tc_prod(X3,X3))) = c_Relation_Orel__comp(X1,c_Nat_Opower(X1,X2,tc_set(tc_prod(X3,X3))),X3,X3,X3),
    inference(split_conjunct,[status(thm)],[c_0_5988]) ).

cnf(c_0_8926,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5989]) ).

cnf(c_0_8927,plain,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_5990]) ).

cnf(c_0_8928,plain,
    ( X1 = c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3)
    | ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5991]) ).

cnf(c_0_8929,plain,
    c_List_Ozip(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X6),X3,X6) = c_List_Olist_OCons(c_Pair(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)),
    inference(split_conjunct,[status(thm)],[c_0_5992]) ).

cnf(c_0_8930,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5993]) ).

cnf(c_0_8931,plain,
    ( c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_5994]) ).

cnf(c_0_8932,plain,
    ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5995]) ).

cnf(c_0_8933,plain,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) != c_Nat_Osize(X3,tc_List_Olist(X4))
    | c_Map_Omap__of(c_List_Ozip(X1,X3,X2,X4),X5,X2,X4) != c_Datatype_Ooption_ONone
    | ~ c_in(X5,c_List_Oset(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5996]) ).

cnf(c_0_8934,plain,
    ( c_List_Onth(c_List_Ozip(X1,X2,X3,X4),X5,tc_prod(X3,X4)) = c_Pair(c_List_Onth(X1,X5,X3),c_List_Onth(X2,X5,X4),X3,X4)
    | ~ c_less(X5,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_less(X5,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_5997]) ).

cnf(c_0_8935,plain,
    ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5998]) ).

cnf(c_0_8936,plain,
    ( c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_5999]) ).

cnf(c_0_8937,plain,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_6000]) ).

cnf(c_0_8938,plain,
    c_Relation_Orel__comp(X1,c_Relation_OId,X2,X3,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6001]) ).

cnf(c_0_8939,plain,
    c_Relation_Orel__comp(c_Relation_OId,X1,X2,X2,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6002]) ).

cnf(c_0_8940,plain,
    ( c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6003]) ).

cnf(c_0_8941,plain,
    c_GCD_Ogcd(c_Pair(X1,c_plus(X2,X1,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6004]) ).

cnf(c_0_8942,plain,
    c_GCD_Ogcd(c_Pair(X1,c_plus(X1,X2,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6005]) ).

cnf(c_0_8943,plain,
    c_GCD_Ogcd(c_Pair(c_plus(X1,X2,tc_nat),X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6006]) ).

cnf(c_0_8944,plain,
    c_List_Ozip(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X5,X6),X3,X6) = c_List_Oreplicate(c_Orderings_Omin(X1,X4,tc_nat),c_Pair(X2,X5,X3,X6),tc_prod(X3,X6)),
    inference(split_conjunct,[status(thm)],[c_0_6007]) ).

cnf(c_0_8945,plain,
    ( c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4) = c_List_Olist__update(X1,X2,X5,X4)
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6008]) ).

cnf(c_0_8946,plain,
    ( X1 = c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X2),c_Main_Olexord__Nil__left__2(X1,X2),X2)
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6009]) ).

cnf(c_0_8947,plain,
    ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6010]) ).

cnf(c_0_8948,plain,
    ( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
    | ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6011]) ).

cnf(c_0_8949,plain,
    ( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6012]) ).

cnf(c_0_8950,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6013]) ).

cnf(c_0_8951,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6014]) ).

cnf(c_0_8952,plain,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6015]) ).

cnf(c_0_8953,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6016]) ).

cnf(c_0_8954,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6017]) ).

cnf(c_0_8955,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6018]) ).

cnf(c_0_8956,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6019]) ).

cnf(c_0_8957,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6020]) ).

cnf(c_0_8958,plain,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(split_conjunct,[status(thm)],[c_0_6021]) ).

cnf(c_0_8959,plain,
    ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(split_conjunct,[status(thm)],[c_0_6022]) ).

cnf(c_0_8960,plain,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(split_conjunct,[status(thm)],[c_0_6023]) ).

cnf(c_0_8961,plain,
    ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6024]) ).

cnf(c_0_8962,plain,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6025]) ).

cnf(c_0_8963,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6026]) ).

cnf(c_0_8964,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6027]) ).

cnf(c_0_8965,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6028]) ).

cnf(c_0_8966,plain,
    ( c_Nat_Opower(c_uminus(X1,X2),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2) = c_Nat_Opower(X1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6029]) ).

cnf(c_0_8967,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_6030]) ).

cnf(c_0_8968,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X1)),c_Datatype__Universe_OIn1(X2,X3,X4),X3,X4) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X1),X2,X3,X4),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6031]) ).

cnf(c_0_8969,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X1)),c_Datatype__Universe_OIn0(X2,X3,X4),X3,X4) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X1),X2,X3,X4),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6032]) ).

cnf(c_0_8970,plain,
    ( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
    | ~ c_Wellfounded__Recursion_Owf(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6033]) ).

cnf(c_0_8971,plain,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1
    | ~ c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6034]) ).

cnf(c_0_8972,plain,
    ( X1 = X2
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6035]) ).

cnf(c_0_8973,plain,
    c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6036]) ).

cnf(c_0_8974,plain,
    ( c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_6037]) ).

cnf(c_0_8975,plain,
    ( c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_6038]) ).

cnf(c_0_8976,plain,
    c_Message_Oparts(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X1,X2),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oparts(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6039]) ).

cnf(c_0_8977,plain,
    c_Message_Oanalz(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_OHPair(X1,X2),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6040]) ).

cnf(c_0_8978,plain,
    ( c_Map_Omap__of(c_List_Ozip(X1,X2,X3,X4),X5,X3,X4) = c_Datatype_Ooption_ONone
    | c_in(X5,c_List_Oset(X1,X3),X3)
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6041]) ).

cnf(c_0_8979,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X1,X2),c_Message_Oparts(c_insert(X1,c_insert(X2,X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6042]) ).

cnf(c_0_8980,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X1,X2),c_Message_Oanalz(c_insert(X1,c_insert(X2,X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6043]) ).

cnf(c_0_8981,plain,
    c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    inference(split_conjunct,[status(thm)],[c_0_6044]) ).

cnf(c_0_8982,plain,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6045]) ).

cnf(c_0_8983,plain,
    c_List_Otake(X1,c_append(X2,X3,X4),X4) = c_append(c_List_Otake(X1,X2,X4),c_List_Otake(c_minus(X1,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4),
    inference(split_conjunct,[status(thm)],[c_0_6046]) ).

cnf(c_0_8984,plain,
    c_List_Odrop(X1,c_append(X2,X3,X4),X4) = c_append(c_List_Odrop(X1,X2,X4),c_List_Odrop(c_minus(X1,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4),
    inference(split_conjunct,[status(thm)],[c_0_6047]) ).

cnf(c_0_8985,plain,
    ( X1 = X2
    | c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_6048]) ).

cnf(c_0_8986,plain,
    ( X1 = X2
    | c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_6049]) ).

cnf(c_0_8987,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_6050]) ).

cnf(c_0_8988,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_6051]) ).

cnf(c_0_8989,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6052]) ).

cnf(c_0_8990,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6053]) ).

cnf(c_0_8991,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6054]) ).

cnf(c_0_8992,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6055]) ).

cnf(c_0_8993,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6056]) ).

cnf(c_0_8994,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6057]) ).

cnf(c_0_8995,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6058]) ).

cnf(c_0_8996,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6059]) ).

cnf(c_0_8997,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6060]) ).

cnf(c_0_8998,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6061]) ).

cnf(c_0_8999,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6062]) ).

cnf(c_0_9000,plain,
    ( c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6063]) ).

cnf(c_0_9001,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6064]) ).

cnf(c_0_9002,plain,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6065]) ).

cnf(c_0_9003,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6066]) ).

cnf(c_0_9004,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6067]) ).

cnf(c_0_9005,plain,
    ( c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1 ),
    inference(split_conjunct,[status(thm)],[c_0_6068]) ).

cnf(c_0_9006,plain,
    c_List_Olist__update(c_append(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize(X1,tc_List_Olist(X4)),X5,X4) = c_append(X1,c_List_Olist_OCons(X5,X3,X4),X4),
    inference(split_conjunct,[status(thm)],[c_0_6069]) ).

cnf(c_0_9007,plain,
    ( c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2))
    | ~ c_in(X1,X5,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6070]) ).

cnf(c_0_9008,plain,
    ( c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3))
    | ~ c_in(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6071]) ).

cnf(c_0_9009,plain,
    c_IntDiv_OnegateSnd(c_Pair(X1,X2,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6072]) ).

cnf(c_0_9010,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6073]) ).

cnf(c_0_9011,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6074]) ).

cnf(c_0_9012,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6075]) ).

cnf(c_0_9013,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6076]) ).

cnf(c_0_9014,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6077]) ).

cnf(c_0_9015,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6078]) ).

cnf(c_0_9016,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6079]) ).

cnf(c_0_9017,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6080]) ).

cnf(c_0_9018,plain,
    c_IntDiv_OposDivAlg(c_Pair(c_0,X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6081]) ).

cnf(c_0_9019,plain,
    c_GCD_Ogcd(c_Pair(X1,c_times(X1,X2,tc_nat),tc_nat,tc_nat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6082]) ).

cnf(c_0_9020,plain,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6083]) ).

cnf(c_0_9021,plain,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6084]) ).

cnf(c_0_9022,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6085]) ).

cnf(c_0_9023,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6086]) ).

cnf(c_0_9024,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6087]) ).

cnf(c_0_9025,plain,
    ( c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6088]) ).

cnf(c_0_9026,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6089]) ).

cnf(c_0_9027,plain,
    ( c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6090]) ).

cnf(c_0_9028,plain,
    c_Nat_Osize(c_List_Ozip(X1,X2,X3,X4),tc_List_Olist(tc_prod(X3,X4))) = c_Orderings_Omin(c_Nat_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6091]) ).

cnf(c_0_9029,plain,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X2,X4) = X3
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6092]) ).

cnf(c_0_9030,plain,
    ( c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2))
    | ~ c_in(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6093]) ).

cnf(c_0_9031,plain,
    ( c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6094]) ).

cnf(c_0_9032,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6095]) ).

cnf(c_0_9033,plain,
    ( c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6096]) ).

cnf(c_0_9034,plain,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6097]) ).

cnf(c_0_9035,plain,
    ( X1 = c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3)
    | ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6098]) ).

cnf(c_0_9036,plain,
    ( c_List_Onth(c_List_Odrop(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_plus(X1,X4,tc_nat),X3)
    | ~ c_lessequals(c_plus(X1,X4,tc_nat),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6099]) ).

cnf(c_0_9037,plain,
    c_div(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6100]) ).

cnf(c_0_9038,plain,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5 ),
    inference(split_conjunct,[status(thm)],[c_0_6101]) ).

cnf(c_0_9039,plain,
    ( c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_plus(X3,c_div(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6102]) ).

cnf(c_0_9040,plain,
    ( c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_plus(X2,c_div(X1,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6103]) ).

cnf(c_0_9041,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
    inference(split_conjunct,[status(thm)],[c_0_6104]) ).

cnf(c_0_9042,plain,
    c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X1))),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6105]) ).

cnf(c_0_9043,plain,
    c_div(c_Suc(c_Suc(c_Suc(X1))),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6106]) ).

cnf(c_0_9044,plain,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X1,X2,X3),X4,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X3,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X4),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6107]) ).

cnf(c_0_9045,plain,
    ( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6108]) ).

cnf(c_0_9046,plain,
    ( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X1,X3)
    | ~ c_Relation_Otrans(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6109]) ).

cnf(c_0_9047,plain,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6110]) ).

cnf(c_0_9048,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6111]) ).

cnf(c_0_9049,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6112]) ).

cnf(c_0_9050,plain,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_plus(X3,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Osemiring(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6113]) ).

cnf(c_0_9051,plain,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_minus(X3,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oring(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6114]) ).

cnf(c_0_9052,plain,
    ( c_times(c_plus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3) = c_plus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Osemiring(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6115]) ).

cnf(c_0_9053,plain,
    ( c_times(c_minus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3) = c_minus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oring(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6116]) ).

cnf(c_0_9054,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
    inference(split_conjunct,[status(thm)],[c_0_6117]) ).

cnf(c_0_9055,plain,
    ( ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6118]) ).

cnf(c_0_9056,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6119]) ).

cnf(c_0_9057,plain,
    ( c_lessequals(X1,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6120]) ).

cnf(c_0_9058,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6121]) ).

cnf(c_0_9059,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6122]) ).

cnf(c_0_9060,plain,
    ( c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6123]) ).

cnf(c_0_9061,plain,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(X1,X4,X3)
    | ~ c_less(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6124]) ).

cnf(c_0_9062,plain,
    ( c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6125]) ).

cnf(c_0_9063,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6126]) ).

cnf(c_0_9064,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6127]) ).

cnf(c_0_9065,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6128]) ).

cnf(c_0_9066,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6129]) ).

cnf(c_0_9067,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6130]) ).

cnf(c_0_9068,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6131]) ).

cnf(c_0_9069,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6132]) ).

cnf(c_0_9070,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6133]) ).

cnf(c_0_9071,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6134]) ).

cnf(c_0_9072,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6135]) ).

cnf(c_0_9073,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X5,X4,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6136]) ).

cnf(c_0_9074,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6137]) ).

cnf(c_0_9075,plain,
    c_snd(c_Pair(X1,X2,X3,X4),X3,X4) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6138]) ).

cnf(c_0_9076,plain,
    c_fst(c_Pair(X1,X2,X3,X4),X3,X4) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6139]) ).

cnf(c_0_9077,plain,
    c_Divides_Oop_Amod(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat) = c_Divides_Oop_Amod(X1,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6140]) ).

cnf(c_0_9078,plain,
    c_div(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat) = c_div(X1,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6141]) ).

cnf(c_0_9079,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6142]) ).

cnf(c_0_9080,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6143]) ).

cnf(c_0_9081,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6144]) ).

cnf(c_0_9082,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6145]) ).

cnf(c_0_9083,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6146]) ).

cnf(c_0_9084,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6147]) ).

cnf(c_0_9085,plain,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(c_List_Osublist(X2,X4,X3),X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6148]) ).

cnf(c_0_9086,plain,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(c_List_Oremove1(X4,X2,X3),X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6149]) ).

cnf(c_0_9087,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6150]) ).

cnf(c_0_9088,plain,
    c_Nat_Osize(c_List_Olist__update(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize(X1,tc_List_Olist(X4)),
    inference(split_conjunct,[status(thm)],[c_0_6151]) ).

cnf(c_0_9089,plain,
    c_Nat_Osize(c_Pair(X1,X2,X3,X4),tc_prod(X3,X4)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_6152]) ).

cnf(c_0_9090,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6153]) ).

cnf(c_0_9091,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6154]) ).

cnf(c_0_9092,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6155]) ).

cnf(c_0_9093,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6156]) ).

cnf(c_0_9094,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6157]) ).

cnf(c_0_9095,plain,
    ( c_minus(c_Suc(c_minus(X1,X2,tc_nat)),X3,tc_nat) = c_minus(c_Suc(X1),c_plus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6158]) ).

cnf(c_0_9096,plain,
    ( c_minus(X1,c_Suc(c_minus(X2,X3,tc_nat)),tc_nat) = c_minus(c_plus(X1,X3,tc_nat),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6159]) ).

cnf(c_0_9097,plain,
    ( X1 = X2
    | c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6160]) ).

cnf(c_0_9098,plain,
    ( X1 = X2
    | c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6161]) ).

cnf(c_0_9099,plain,
    ( c_List_Olist__update(X1,X2,c_List_Onth(X1,X2,X3),X3) = X1
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6162]) ).

cnf(c_0_9100,plain,
    c_GCD_Ogcd(c_Pair(c_Suc(c_0),X1,tc_nat,tc_nat)) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_6163]) ).

cnf(c_0_9101,plain,
    c_GCD_Ogcd(c_Pair(X1,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_6164]) ).

cnf(c_0_9102,plain,
    ( c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | X2 = c_Numeral_Obit_OB0
    | c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6165]) ).

cnf(c_0_9103,plain,
    c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6166]) ).

cnf(c_0_9104,plain,
    c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6167]) ).

cnf(c_0_9105,plain,
    c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6168]) ).

cnf(c_0_9106,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6169]) ).

cnf(c_0_9107,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6170]) ).

cnf(c_0_9108,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6171]) ).

cnf(c_0_9109,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6172]) ).

cnf(c_0_9110,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6173]) ).

cnf(c_0_9111,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6174]) ).

cnf(c_0_9112,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6175]) ).

cnf(c_0_9113,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6176]) ).

cnf(c_0_9114,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6177]) ).

cnf(c_0_9115,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6178]) ).

cnf(c_0_9116,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6179]) ).

cnf(c_0_9117,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6180]) ).

cnf(c_0_9118,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6181]) ).

cnf(c_0_9119,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6182]) ).

cnf(c_0_9120,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6183]) ).

cnf(c_0_9121,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6184]) ).

cnf(c_0_9122,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_ONumb(X5,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6185]) ).

cnf(c_0_9123,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OLeaf(X5,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6186]) ).

cnf(c_0_9124,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OAtom(X5,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6187]) ).

cnf(c_0_9125,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6188]) ).

cnf(c_0_9126,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6189]) ).

cnf(c_0_9127,plain,
    c_Datatype__Universe_OAtom(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6190]) ).

cnf(c_0_9128,plain,
    ( c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6191]) ).

cnf(c_0_9129,plain,
    ( c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6192]) ).

cnf(c_0_9130,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6193]) ).

cnf(c_0_9131,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6194]) ).

cnf(c_0_9132,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6195]) ).

cnf(c_0_9133,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6196]) ).

cnf(c_0_9134,plain,
    X1 = c_Pair(c_Main_Osurj__pair__1(X1,X2,X3),c_Main_Osurj__pair__2(X1,X2,X3),X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6197]) ).

cnf(c_0_9135,plain,
    c_Pair(c_fst(X1,X2,X3),c_snd(X1,X2,X3),X2,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6198]) ).

cnf(c_0_9136,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_times(X2,X1,tc_nat),c_times(X3,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6199]) ).

cnf(c_0_9137,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6200]) ).

cnf(c_0_9138,plain,
    ( c_less(c_0,X1,X2)
    | c_less(X1,c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6201]) ).

cnf(c_0_9139,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6202]) ).

cnf(c_0_9140,plain,
    ( c_less(c_0,X1,X2)
    | c_less(X1,c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6203]) ).

cnf(c_0_9141,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6204]) ).

cnf(c_0_9142,plain,
    c_Relation_OImage(c_List_Olistrel(X1,X2),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X2)),tc_List_Olist(X2),tc_List_Olist(X2)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X2)),
    inference(split_conjunct,[status(thm)],[c_0_6205]) ).

cnf(c_0_9143,plain,
    ( c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X2,X5,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6206]) ).

cnf(c_0_9144,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6207]) ).

cnf(c_0_9145,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6208]) ).

cnf(c_0_9146,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oparts(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6209]) ).

cnf(c_0_9147,plain,
    ( c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_less(c_1,X1,X3)
    | ~ c_less(X2,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6210]) ).

cnf(c_0_9148,plain,
    ( c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_less(c_1,X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6211]) ).

cnf(c_0_9149,plain,
    ( c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Olist__inter(X2,X4,X3),X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6212]) ).

cnf(c_0_9150,plain,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6213]) ).

cnf(c_0_9151,plain,
    ( c_List_Otake(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(X2,c_plus(X2,X1,tc_nat))
    | ~ c_lessequals(c_plus(X2,X1,tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6214]) ).

cnf(c_0_9152,plain,
    ( c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6215]) ).

cnf(c_0_9153,plain,
    ( c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6216]) ).

cnf(c_0_9154,plain,
    ( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6217]) ).

cnf(c_0_9155,plain,
    ( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6218]) ).

cnf(c_0_9156,plain,
    ( c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6219]) ).

cnf(c_0_9157,plain,
    ( c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6220]) ).

cnf(c_0_9158,plain,
    ( c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6221]) ).

cnf(c_0_9159,plain,
    ( c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6222]) ).

cnf(c_0_9160,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,X2,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6223]) ).

cnf(c_0_9161,plain,
    ( X1 = c_emptyset
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6224]) ).

cnf(c_0_9162,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6225]) ).

cnf(c_0_9163,plain,
    ( X1 = c_emptyset
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6226]) ).

cnf(c_0_9164,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6227]) ).

cnf(c_0_9165,plain,
    c_insert(X1,c_minus(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)),X3) = c_insert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6228]) ).

cnf(c_0_9166,plain,
    c_List_Orev(c_append(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil,X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_6229]) ).

cnf(c_0_9167,plain,
    c_inter(c_insert(X1,X2,X3),c_insert(X1,X4,X3),X3) = c_insert(X1,c_inter(X2,X4,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6230]) ).

cnf(c_0_9168,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6231]) ).

cnf(c_0_9169,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6232]) ).

cnf(c_0_9170,plain,
    ( c_lessequals(X1,c_0,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6233]) ).

cnf(c_0_9171,plain,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X2,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X3),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6234]) ).

cnf(c_0_9172,plain,
    ( c_less(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6235]) ).

cnf(c_0_9173,plain,
    ( c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6236]) ).

cnf(c_0_9174,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6237]) ).

cnf(c_0_9175,plain,
    ( X1 = c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2)
    | ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6238]) ).

cnf(c_0_9176,plain,
    ( c_minus(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X1,X4,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X4,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6239]) ).

cnf(c_0_9177,plain,
    c_Divides_Oop_Amod(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6240]) ).

cnf(c_0_9178,plain,
    c_Divides_Oop_Amod(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6241]) ).

cnf(c_0_9179,plain,
    c_Divides_Oop_Amod(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_Divides_Oop_Amod(X1,X3,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6242]) ).

cnf(c_0_9180,plain,
    ( c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6243]) ).

cnf(c_0_9181,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_ONumb(X2,X3,X4),X3,X4) = c_Datatype__Universe_ONumb(X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6244]) ).

cnf(c_0_9182,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OLeaf(X2,X3,X4),X3,X4) = c_Datatype__Universe_OLeaf(X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6245]) ).

cnf(c_0_9183,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OAtom(X2,X3,X4),X3,X4) = c_Datatype__Universe_OAtom(X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6246]) ).

cnf(c_0_9184,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6247]) ).

cnf(c_0_9185,plain,
    c_List_Onth(c_append(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize(X1,tc_List_Olist(X4)),X4) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6248]) ).

cnf(c_0_9186,plain,
    ( c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6249]) ).

cnf(c_0_9187,plain,
    c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X1,X2,X3),X4,tc_Event_Oevent)) = c_insert(X3,c_Event_Oknows(c_Message_Oagent_OSpy,X4),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6250]) ).

cnf(c_0_9188,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6251]) ).

cnf(c_0_9189,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6252]) ).

cnf(c_0_9190,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6253]) ).

cnf(c_0_9191,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6254]) ).

cnf(c_0_9192,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6255]) ).

cnf(c_0_9193,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6256]) ).

cnf(c_0_9194,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6257]) ).

cnf(c_0_9195,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6258]) ).

cnf(c_0_9196,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_minus(X3,c_Numeral_Onumber__of(X4,X2),X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X4)),X2),X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6259]) ).

cnf(c_0_9197,plain,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6260]) ).

cnf(c_0_9198,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6261]) ).

cnf(c_0_9199,plain,
    ( c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6262]) ).

cnf(c_0_9200,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Onth(c_List_Olist_OCons(X2,X3,X4),c_Numeral_Onumber__of(X1,tc_nat),X4) = c_List_Onth(X3,c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6263]) ).

cnf(c_0_9201,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6264]) ).

cnf(c_0_9202,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,c_0,X2)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6265]) ).

cnf(c_0_9203,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6266]) ).

cnf(c_0_9204,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6267]) ).

cnf(c_0_9205,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6268]) ).

cnf(c_0_9206,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6269]) ).

cnf(c_0_9207,plain,
    ( c_minus(X1,c_minus(X2,X3,tc_nat),tc_nat) = c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6270]) ).

cnf(c_0_9208,plain,
    ( c_plus(X1,c_minus(X2,X3,tc_nat),tc_nat) = c_minus(c_plus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6271]) ).

cnf(c_0_9209,plain,
    ( c_plus(c_minus(X1,X2,tc_nat),X3,tc_nat) = c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6272]) ).

cnf(c_0_9210,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6273]) ).

cnf(c_0_9211,plain,
    c_List_Onth(c_append(X1,X2,X3),c_plus(c_Nat_Osize(X1,tc_List_Olist(X3)),X4,tc_nat),X3) = c_List_Onth(X2,X4,X3),
    inference(split_conjunct,[status(thm)],[c_0_6274]) ).

cnf(c_0_9212,plain,
    ( c_div(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) = c_div(X1,X3,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6275]) ).

cnf(c_0_9213,plain,
    ( c_div(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) = c_div(X2,X3,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6276]) ).

cnf(c_0_9214,plain,
    ( ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6277]) ).

cnf(c_0_9215,plain,
    ( c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_6278]) ).

cnf(c_0_9216,plain,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6279]) ).

cnf(c_0_9217,plain,
    ( X1 = c_0
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6280]) ).

cnf(c_0_9218,plain,
    c_Message_Oanalz(c_union(c_Message_Osynth(X1),X2,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X1,X2,tc_Message_Omsg)),c_Message_Osynth(X1),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6281]) ).

cnf(c_0_9219,plain,
    ( c_List_Olist__update(X1,X2,X3,X4) = X1
    | ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6282]) ).

cnf(c_0_9220,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6283]) ).

cnf(c_0_9221,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6284]) ).

cnf(c_0_9222,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6285]) ).

cnf(c_0_9223,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6286]) ).

cnf(c_0_9224,plain,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6287]) ).

cnf(c_0_9225,plain,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6288]) ).

cnf(c_0_9226,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6289]) ).

cnf(c_0_9227,plain,
    ( c_List_Onth(c_List_Oupt(X1,X2),X3,tc_nat) = c_plus(X1,X3,tc_nat)
    | ~ c_less(c_plus(X1,X3,tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6290]) ).

cnf(c_0_9228,plain,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_times(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2),X4,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6291]) ).

cnf(c_0_9229,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_plus(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2),X4,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6292]) ).

cnf(c_0_9230,plain,
    ( X1 = c_emptyset
    | c_less(X2,X3,X4)
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6293]) ).

cnf(c_0_9231,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,X3,X4)
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6294]) ).

cnf(c_0_9232,plain,
    ( X1 = c_emptyset
    | c_less(X2,X3,X4)
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6295]) ).

cnf(c_0_9233,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,X3,X4)
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6296]) ).

cnf(c_0_9234,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint))
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6297]) ).

cnf(c_0_9235,plain,
    ( c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6298]) ).

cnf(c_0_9236,plain,
    ( c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6299]) ).

cnf(c_0_9237,plain,
    ( c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6300]) ).

cnf(c_0_9238,plain,
    ( c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6301]) ).

cnf(c_0_9239,plain,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6302]) ).

cnf(c_0_9240,plain,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6303]) ).

cnf(c_0_9241,plain,
    ( c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3)
    | ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6304]) ).

cnf(c_0_9242,plain,
    ( c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2)
    | ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6305]) ).

cnf(c_0_9243,plain,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6306]) ).

cnf(c_0_9244,plain,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6307]) ).

cnf(c_0_9245,plain,
    ( c_less(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ c_less(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6308]) ).

cnf(c_0_9246,plain,
    ( c_less(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6309]) ).

cnf(c_0_9247,plain,
    ( c_lessequals(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6310]) ).

cnf(c_0_9248,plain,
    ( c_lessequals(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6311]) ).

cnf(c_0_9249,plain,
    ( c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X1,X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6312]) ).

cnf(c_0_9250,plain,
    ( c_lessequals(X1,c_inter(X2,X3,X4),tc_set(X4))
    | ~ c_lessequals(X1,X2,tc_set(X4))
    | ~ c_lessequals(X1,X3,tc_set(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6313]) ).

cnf(c_0_9251,plain,
    ( ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6314]) ).

cnf(c_0_9252,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6315]) ).

cnf(c_0_9253,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6316]) ).

cnf(c_0_9254,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X1,X2,X3),X2,X3) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_6317]) ).

cnf(c_0_9255,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X1,X2,X3),X2,X3) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_6318]) ).

cnf(c_0_9256,plain,
    ( c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6319]) ).

cnf(c_0_9257,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_lessequals(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6320]) ).

cnf(c_0_9258,plain,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6321]) ).

cnf(c_0_9259,plain,
    ( c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6322]) ).

cnf(c_0_9260,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Power_Orecpower(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6323]) ).

cnf(c_0_9261,plain,
    ( c_less(c_0,X1,tc_nat)
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6324]) ).

cnf(c_0_9262,plain,
    ( c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6325]) ).

cnf(c_0_9263,plain,
    ( c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6326]) ).

cnf(c_0_9264,plain,
    ( c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6327]) ).

cnf(c_0_9265,plain,
    ( c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6328]) ).

cnf(c_0_9266,plain,
    ( c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6329]) ).

cnf(c_0_9267,plain,
    ( c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6330]) ).

cnf(c_0_9268,plain,
    ( c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6331]) ).

cnf(c_0_9269,plain,
    ( c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6332]) ).

cnf(c_0_9270,plain,
    ( c_less(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6333]) ).

cnf(c_0_9271,plain,
    ( c_lessequals(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6334]) ).

cnf(c_0_9272,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6335]) ).

cnf(c_0_9273,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6336]) ).

cnf(c_0_9274,plain,
    ( X1 = c_emptyset
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6337]) ).

cnf(c_0_9275,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6338]) ).

cnf(c_0_9276,plain,
    ( X1 = c_emptyset
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6339]) ).

cnf(c_0_9277,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6340]) ).

cnf(c_0_9278,plain,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6341]) ).

cnf(c_0_9279,plain,
    ( c_in(X1,c_SetInterval_OgreaterThanLessThan(X2,X3,X4),X4)
    | ~ c_less(X2,X1,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6342]) ).

cnf(c_0_9280,plain,
    ( c_in(X1,c_SetInterval_OgreaterThanAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ c_less(X2,X1,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6343]) ).

cnf(c_0_9281,plain,
    ( c_in(X1,c_SetInterval_OatLeastLessThan(X2,X3,X4),X4)
    | ~ c_lessequals(X2,X1,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6344]) ).

cnf(c_0_9282,plain,
    ( c_in(X1,c_SetInterval_OatLeastAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X2,X1,X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6345]) ).

cnf(c_0_9283,plain,
    ( c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6346]) ).

cnf(c_0_9284,plain,
    ( c_lessequals(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6347]) ).

cnf(c_0_9285,plain,
    ( c_less(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_less(X1,X2,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6348]) ).

cnf(c_0_9286,plain,
    ( c_less(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_less(X1,X4,X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6349]) ).

cnf(c_0_9287,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6350]) ).

cnf(c_0_9288,plain,
    ( c_Message_Osynth(c_Message_Oanalz(c_insert(X1,X2,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X2))
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6351]) ).

cnf(c_0_9289,plain,
    ( c_emptyset != c_inter(c_insert(X1,X2,X3),X4,X3)
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6352]) ).

cnf(c_0_9290,plain,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6353]) ).

cnf(c_0_9291,plain,
    ( c_emptyset != c_inter(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X2,X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6354]) ).

cnf(c_0_9292,plain,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset
    | ~ c_in(X2,X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6355]) ).

cnf(c_0_9293,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6356]) ).

cnf(c_0_9294,plain,
    ( c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6357]) ).

cnf(c_0_9295,plain,
    ( c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6358]) ).

cnf(c_0_9296,plain,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6359]) ).

cnf(c_0_9297,plain,
    ( c_divide(c_times(X1,X2,X3),c_times(X4,X2,X3),X3) = c_divide(X1,X4,X3)
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6360]) ).

cnf(c_0_9298,plain,
    ( c_divide(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) = c_divide(X2,X4,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6361]) ).

cnf(c_0_9299,plain,
    ( c_HOL_Oabs(c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2),X2) = c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6362]) ).

cnf(c_0_9300,plain,
    ( c_divide(X1,c_divide(X2,X3,X4),X4) = c_divide(c_times(X1,X3,X4),X2,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6363]) ).

cnf(c_0_9301,plain,
    ( c_divide(c_divide(X1,X2,X3),X4,X3) = c_divide(X1,c_times(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6364]) ).

cnf(c_0_9302,plain,
    ( c_in(c_times(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6365]) ).

cnf(c_0_9303,plain,
    ( c_in(c_plus(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6366]) ).

cnf(c_0_9304,plain,
    ( c_in(c_times(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6367]) ).

cnf(c_0_9305,plain,
    ( c_in(c_minus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6368]) ).

cnf(c_0_9306,plain,
    ( c_in(c_plus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6369]) ).

cnf(c_0_9307,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6370]) ).

cnf(c_0_9308,plain,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInter__iff__1(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6371]) ).

cnf(c_0_9309,plain,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6372]) ).

cnf(c_0_9310,plain,
    ( c_List_Odistinct(c_append(X1,X2,X3),X3)
    | c_inter(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) != c_emptyset
    | ~ c_List_Odistinct(X1,X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6373]) ).

cnf(c_0_9311,plain,
    ( c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6374]) ).

cnf(c_0_9312,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_nat),tc_IntDef_Oint))
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6375]) ).

cnf(c_0_9313,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint))
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6376]) ).

cnf(c_0_9314,plain,
    ( c_List_Oset(c_List_Oremove1(X1,X2,X3),X3) = c_minus(c_List_Oset(X2,X3),c_insert(X1,c_emptyset,X3),tc_set(X3))
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6377]) ).

cnf(c_0_9315,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6378]) ).

cnf(c_0_9316,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6379]) ).

cnf(c_0_9317,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6380]) ).

cnf(c_0_9318,plain,
    c_minus(c_minus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_minus(c_minus(X1,X2,tc_nat),X3,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6381]) ).

cnf(c_0_9319,plain,
    ( c_in(c_List_Onth(X1,X2,X3),c_List_Oset(X1,X3),X3)
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6382]) ).

cnf(c_0_9320,plain,
    ( c_times(c_divide(X1,X2,X3),X4,X3) = c_divide(c_times(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6383]) ).

cnf(c_0_9321,plain,
    ( c_times(X1,c_divide(X2,X3,X4),X4) = c_divide(c_times(X1,X2,X4),X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6384]) ).

cnf(c_0_9322,plain,
    ( c_less(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_less(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6385]) ).

cnf(c_0_9323,plain,
    ( c_lessequals(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6386]) ).

cnf(c_0_9324,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_less(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6387]) ).

cnf(c_0_9325,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_lessequals(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6388]) ).

cnf(c_0_9326,plain,
    ( c_1 = c_Numeral_Onumber__of(X1,X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6389]) ).

cnf(c_0_9327,plain,
    c_List_Olast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3),X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6390]) ).

cnf(c_0_9328,plain,
    c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3),X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6391]) ).

cnf(c_0_9329,plain,
    ( c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3)
    | ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6392]) ).

cnf(c_0_9330,plain,
    c_List_Otake(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X1,X3,X4),X4),
    inference(split_conjunct,[status(thm)],[c_0_6393]) ).

cnf(c_0_9331,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6394]) ).

cnf(c_0_9332,plain,
    c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_inter(X1,X3,X2),
    inference(split_conjunct,[status(thm)],[c_0_6395]) ).

cnf(c_0_9333,plain,
    ( X1 = X2
    | c_IntDef_OAbs__Integ(X1) != c_IntDef_OAbs__Integ(X2)
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_6396]) ).

cnf(c_0_9334,plain,
    ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_insert(X2,c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    inference(split_conjunct,[status(thm)],[c_0_6397]) ).

cnf(c_0_9335,plain,
    ( c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_6398]) ).

cnf(c_0_9336,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_insert(X4,X1,X3),X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6399]) ).

cnf(c_0_9337,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6400]) ).

cnf(c_0_9338,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_union(X1,X4,X3),X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6401]) ).

cnf(c_0_9339,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,c_inter(X4,X2,X3),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6402]) ).

cnf(c_0_9340,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,c_inter(X2,X4,X3),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6403]) ).

cnf(c_0_9341,plain,
    ( c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6404]) ).

cnf(c_0_9342,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6405]) ).

cnf(c_0_9343,plain,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6406]) ).

cnf(c_0_9344,plain,
    c_union(X1,c_insert(X2,X3,X4),X4) = c_insert(X2,c_union(X1,X3,X4),X4),
    inference(split_conjunct,[status(thm)],[c_0_6407]) ).

cnf(c_0_9345,plain,
    c_union(c_insert(X1,X2,X3),X4,X3) = c_insert(X1,c_union(X2,X4,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6408]) ).

cnf(c_0_9346,plain,
    c_append(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_append(X2,X4,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6409]) ).

cnf(c_0_9347,plain,
    c_List_Oitrev(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Oitrev(X2,c_List_Olist_OCons(X1,X4,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6410]) ).

cnf(c_0_9348,plain,
    c_append(c_append(X1,X2,X3),X4,X3) = c_append(X1,c_append(X2,X4,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6411]) ).

cnf(c_0_9349,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_insert(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6412]) ).

cnf(c_0_9350,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6413]) ).

cnf(c_0_9351,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6414]) ).

cnf(c_0_9352,plain,
    ( c_less(c_minus(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6415]) ).

cnf(c_0_9353,plain,
    ( c_less(c_div(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_1,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6416]) ).

cnf(c_0_9354,plain,
    c_List_Otake(X1,c_List_Otake(X2,X3,X4),X4) = c_List_Otake(c_Orderings_Omin(X1,X2,tc_nat),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6417]) ).

cnf(c_0_9355,plain,
    c_List_Otake(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_Orderings_Omin(X1,X2,tc_nat),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6418]) ).

cnf(c_0_9356,plain,
    c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_minus(X2,X1,tc_nat),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6419]) ).

cnf(c_0_9357,plain,
    c_List_Odrop(X1,c_List_Odrop(X2,X3,X4),X4) = c_List_Odrop(c_plus(X1,X2,tc_nat),X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6420]) ).

cnf(c_0_9358,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6421]) ).

cnf(c_0_9359,plain,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_insert(X1,X4,X3),X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6422]) ).

cnf(c_0_9360,plain,
    ( c_less(c_0,c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6423]) ).

cnf(c_0_9361,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6424]) ).

cnf(c_0_9362,plain,
    ( ~ c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6425]) ).

cnf(c_0_9363,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanLessThan(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6426]) ).

cnf(c_0_9364,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanLessThan(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6427]) ).

cnf(c_0_9365,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanAtMost(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6428]) ).

cnf(c_0_9366,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanAtMost(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6429]) ).

cnf(c_0_9367,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatLeastLessThan(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6430]) ).

cnf(c_0_9368,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeastLessThan(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6431]) ).

cnf(c_0_9369,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatLeastAtMost(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6432]) ).

cnf(c_0_9370,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeastAtMost(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6433]) ).

cnf(c_0_9371,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6434]) ).

cnf(c_0_9372,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6435]) ).

cnf(c_0_9373,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6436]) ).

cnf(c_0_9374,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6437]) ).

cnf(c_0_9375,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6438]) ).

cnf(c_0_9376,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6439]) ).

cnf(c_0_9377,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6440]) ).

cnf(c_0_9378,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6441]) ).

cnf(c_0_9379,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X3)),c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6442]) ).

cnf(c_0_9380,plain,
    ( c_NatArith_Oof__nat(c_minus(X1,X2,tc_nat),X3) = c_minus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6443]) ).

cnf(c_0_9381,plain,
    ( c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6444]) ).

cnf(c_0_9382,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6445]) ).

cnf(c_0_9383,plain,
    ( c_less(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ c_less(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6446]) ).

cnf(c_0_9384,plain,
    ( c_lessequals(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ c_lessequals(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6447]) ).

cnf(c_0_9385,plain,
    ( c_less(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6448]) ).

cnf(c_0_9386,plain,
    ( c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6449]) ).

cnf(c_0_9387,plain,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6450]) ).

cnf(c_0_9388,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6451]) ).

cnf(c_0_9389,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6452]) ).

cnf(c_0_9390,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6453]) ).

cnf(c_0_9391,plain,
    ( c_minus(c_insert(X1,X2,X3),X4,tc_set(X3)) = c_minus(X2,X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6454]) ).

cnf(c_0_9392,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6455]) ).

cnf(c_0_9393,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6456]) ).

cnf(c_0_9394,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6457]) ).

cnf(c_0_9395,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6458]) ).

cnf(c_0_9396,plain,
    c_minus(c_minus(X1,X2,tc_nat),X3,tc_nat) = c_minus(X1,c_plus(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6459]) ).

cnf(c_0_9397,plain,
    ( c_div(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_plus(c_div(X1,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X2 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6460]) ).

cnf(c_0_9398,plain,
    ( c_div(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_plus(c_div(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6461]) ).

cnf(c_0_9399,plain,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6462]) ).

cnf(c_0_9400,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6463]) ).

cnf(c_0_9401,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6464]) ).

cnf(c_0_9402,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6465]) ).

cnf(c_0_9403,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6466]) ).

cnf(c_0_9404,plain,
    ( X1 = X2
    | c_in(X1,X3,X4)
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6467]) ).

cnf(c_0_9405,plain,
    ( X1 = X2
    | c_List_Oop_Amem(X2,X3,X4)
    | ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6468]) ).

cnf(c_0_9406,plain,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6469]) ).

cnf(c_0_9407,plain,
    ( c_emptyset = c_inter(X1,X2,X3)
    | c_emptyset != c_inter(c_insert(X4,X1,X3),X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6470]) ).

cnf(c_0_9408,plain,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_6471]) ).

cnf(c_0_9409,plain,
    ( c_emptyset = c_inter(X1,X2,X3)
    | c_emptyset != c_inter(X1,c_insert(X4,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6472]) ).

cnf(c_0_9410,plain,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_6473]) ).

cnf(c_0_9411,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X4,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6474]) ).

cnf(c_0_9412,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6475]) ).

cnf(c_0_9413,plain,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6476]) ).

cnf(c_0_9414,plain,
    c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6477]) ).

cnf(c_0_9415,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6478]) ).

cnf(c_0_9416,plain,
    c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6479]) ).

cnf(c_0_9417,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6480]) ).

cnf(c_0_9418,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6481]) ).

cnf(c_0_9419,plain,
    ( c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_0),c_times(X2,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6482]) ).

cnf(c_0_9420,plain,
    ( c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6483]) ).

cnf(c_0_9421,plain,
    ( c_Finite__Set_OMin(c_insert(X1,X2,X3),X3) = c_Orderings_Omin(X1,c_Finite__Set_OMin(X2,X3),X3)
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6484]) ).

cnf(c_0_9422,plain,
    ( c_Finite__Set_OMax(c_insert(X1,X2,X3),X3) = c_Orderings_Omax(X1,c_Finite__Set_OMax(X2,X3),X3)
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6485]) ).

cnf(c_0_9423,plain,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6486]) ).

cnf(c_0_9424,plain,
    ( c_emptyset = c_inter(c_insert(X1,X2,X3),X4,X3)
    | c_in(X1,X4,X3)
    | c_emptyset != c_inter(X2,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6487]) ).

cnf(c_0_9425,plain,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(X2,X4,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_6488]) ).

cnf(c_0_9426,plain,
    ( c_emptyset = c_inter(X1,c_insert(X2,X3,X4),X4)
    | c_in(X2,X1,X4)
    | c_emptyset != c_inter(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6489]) ).

cnf(c_0_9427,plain,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,X3,X4) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_6490]) ).

cnf(c_0_9428,plain,
    ( c_List_Onth(c_List_Otake(X1,X2,X3),X4,X3) = c_List_Onth(X2,X4,X3)
    | ~ c_less(X4,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6491]) ).

cnf(c_0_9429,plain,
    ( c_Finite__Set_Ocard(c_insert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6492]) ).

cnf(c_0_9430,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X1,X3),c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6493]) ).

cnf(c_0_9431,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_0,c_minus(X2,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6494]) ).

cnf(c_0_9432,plain,
    ( c_inter(c_List_Oset(X1,X2),c_List_Oset(X3,X2),X2) = c_emptyset
    | ~ c_List_Odistinct(c_append(X1,X3,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6495]) ).

cnf(c_0_9433,plain,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X3,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6496]) ).

cnf(c_0_9434,plain,
    ( c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist__inter(X2,X4,X3)
    | c_in(X1,c_List_Oset(X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6497]) ).

cnf(c_0_9435,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_times(X2,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6498]) ).

cnf(c_0_9436,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_times(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6499]) ).

cnf(c_0_9437,plain,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6500]) ).

cnf(c_0_9438,plain,
    ( c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6501]) ).

cnf(c_0_9439,plain,
    ( c_in(c_Main_OUnion__iff__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6502]) ).

cnf(c_0_9440,plain,
    ( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6503]) ).

cnf(c_0_9441,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6504]) ).

cnf(c_0_9442,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6505]) ).

cnf(c_0_9443,plain,
    ( X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6506]) ).

cnf(c_0_9444,plain,
    ( c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2)
    | ~ c_in(c_0,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6507]) ).

cnf(c_0_9445,plain,
    c_Nat_Osize(c_Message_Omsg_OMPair(X1,X2),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X1,tc_Message_Omsg),c_Nat_Osize(X2,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6508]) ).

cnf(c_0_9446,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6509]) ).

cnf(c_0_9447,plain,
    c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X2,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6510]) ).

cnf(c_0_9448,plain,
    ( c_in(X1,c_Main_OUnion__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6511]) ).

cnf(c_0_9449,plain,
    ( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6512]) ).

cnf(c_0_9450,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6513]) ).

cnf(c_0_9451,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6514]) ).

cnf(c_0_9452,plain,
    ( c_List_Oupt(X1,c_Suc(X2)) = c_append(c_List_Oupt(X1,X2),c_List_Olist_OCons(X2,c_List_Olist_ONil,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6515]) ).

cnf(c_0_9453,plain,
    ( c_in(c_Message_Omsg_OKey(v_sko__uhi(X1,X2)),X1,tc_Message_Omsg)
    | c_in(X2,c_Message_OkeysFor(X1),tc_nat)
    | ~ c_in(X2,c_Message_OkeysFor(c_Message_Osynth(X1)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6516]) ).

cnf(c_0_9454,plain,
    ( c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)) = c_minus(X1,X3,tc_set(X4))
    | c_in(X2,X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6517]) ).

cnf(c_0_9455,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6518]) ).

cnf(c_0_9456,plain,
    ( c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,c_List_Oremdups(X2,X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6519]) ).

cnf(c_0_9457,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6520]) ).

cnf(c_0_9458,plain,
    ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Event_Obad,tc_Message_Oagent) ),
    inference(split_conjunct,[status(thm)],[c_0_6521]) ).

cnf(c_0_9459,plain,
    ( c_List_Olast(c_List_Odrop(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | ~ c_less(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6522]) ).

cnf(c_0_9460,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6523]) ).

cnf(c_0_9461,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6524]) ).

cnf(c_0_9462,plain,
    ( c_List_Otl(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_minus(X1,c_1,tc_nat),X2,X3)
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6525]) ).

cnf(c_0_9463,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6526]) ).

cnf(c_0_9464,plain,
    ( c_divide(c_times(X1,c_0,X2),c_times(X3,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6527]) ).

cnf(c_0_9465,plain,
    ( c_divide(c_times(c_0,X1,X2),c_times(c_0,X3,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6528]) ).

cnf(c_0_9466,plain,
    ( c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6529]) ).

cnf(c_0_9467,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | X3 = c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6530]) ).

cnf(c_0_9468,plain,
    ( c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6531]) ).

cnf(c_0_9469,plain,
    ( c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6532]) ).

cnf(c_0_9470,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | X3 = c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6533]) ).

cnf(c_0_9471,plain,
    ( c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
    | c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6534]) ).

cnf(c_0_9472,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6535]) ).

cnf(c_0_9473,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6536]) ).

cnf(c_0_9474,plain,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6537]) ).

cnf(c_0_9475,plain,
    ( c_in(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6538]) ).

cnf(c_0_9476,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6539]) ).

cnf(c_0_9477,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6540]) ).

cnf(c_0_9478,plain,
    ( c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X3,tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6541]) ).

cnf(c_0_9479,plain,
    ( X1 = X2
    | c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6542]) ).

cnf(c_0_9480,plain,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6543]) ).

cnf(c_0_9481,plain,
    ( c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6544]) ).

cnf(c_0_9482,plain,
    ( c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6545]) ).

cnf(c_0_9483,plain,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6546]) ).

cnf(c_0_9484,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6547]) ).

cnf(c_0_9485,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6548]) ).

cnf(c_0_9486,plain,
    c_append(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6549]) ).

cnf(c_0_9487,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6550]) ).

cnf(c_0_9488,plain,
    ( c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint))
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6551]) ).

cnf(c_0_9489,plain,
    ( c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6552]) ).

cnf(c_0_9490,plain,
    ( c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oremdups(X2,X3)
    | ~ c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6553]) ).

cnf(c_0_9491,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6554]) ).

cnf(c_0_9492,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6555]) ).

cnf(c_0_9493,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6556]) ).

cnf(c_0_9494,plain,
    ( c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6557]) ).

cnf(c_0_9495,plain,
    ( c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,X3,X4)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6558]) ).

cnf(c_0_9496,plain,
    ( c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6559]) ).

cnf(c_0_9497,plain,
    ( c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6560]) ).

cnf(c_0_9498,plain,
    ( c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6561]) ).

cnf(c_0_9499,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6562]) ).

cnf(c_0_9500,plain,
    c_uminus(c_union(X1,X2,X3),tc_set(X3)) = c_inter(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3),
    inference(split_conjunct,[status(thm)],[c_0_6563]) ).

cnf(c_0_9501,plain,
    c_uminus(c_inter(X1,X2,X3),tc_set(X3)) = c_union(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3),
    inference(split_conjunct,[status(thm)],[c_0_6564]) ).

cnf(c_0_9502,plain,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_OkeysFor(c_Message_Oanalz(X2)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6565]) ).

cnf(c_0_9503,plain,
    c_Nat_Osize(c_append(X1,X2,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6566]) ).

cnf(c_0_9504,plain,
    ( c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6567]) ).

cnf(c_0_9505,plain,
    ( c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6568]) ).

cnf(c_0_9506,plain,
    ( c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6569]) ).

cnf(c_0_9507,plain,
    ( c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6570]) ).

cnf(c_0_9508,plain,
    ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6571]) ).

cnf(c_0_9509,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6572]) ).

cnf(c_0_9510,plain,
    ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6573]) ).

cnf(c_0_9511,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6574]) ).

cnf(c_0_9512,plain,
    ( c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6575]) ).

cnf(c_0_9513,plain,
    ( c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6576]) ).

cnf(c_0_9514,plain,
    ( X1 = X2
    | ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6577]) ).

cnf(c_0_9515,plain,
    ( c_Nat_Opower(c_HOL_Oabs(X1,X2),c_Numeral_Onumber__of(X3,tc_nat),X2) = c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6578]) ).

cnf(c_0_9516,plain,
    ( c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6579]) ).

cnf(c_0_9517,plain,
    ( c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6580]) ).

cnf(c_0_9518,plain,
    ( c_less(c_minus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6581]) ).

cnf(c_0_9519,plain,
    ( c_minus(c_insert(X1,c_emptyset,X2),c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_insert(X1,c_emptyset,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6582]) ).

cnf(c_0_9520,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6583]) ).

cnf(c_0_9521,plain,
    ( c_in(c_Main_OInter__iff__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6584]) ).

cnf(c_0_9522,plain,
    ( c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6585]) ).

cnf(c_0_9523,plain,
    ( c_in(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6586]) ).

cnf(c_0_9524,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6587]) ).

cnf(c_0_9525,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6588]) ).

cnf(c_0_9526,plain,
    ( c_List_Oop_Amem(X1,c_List_Olist_OCons(X2,X3,X4),X4)
    | ~ c_List_Oop_Amem(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6589]) ).

cnf(c_0_9527,plain,
    c_Public_Okeymode_Okeymode__rec(X1,X2,c_Public_Okeymode_OEncryption,X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6590]) ).

cnf(c_0_9528,plain,
    c_Public_Okeymode_Okeymode__rec(X1,X2,c_Public_Okeymode_OSignature,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6591]) ).

cnf(c_0_9529,plain,
    c_Public_Okeymode_Okeymode__case(X1,X2,c_Public_Okeymode_OEncryption,X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6592]) ).

cnf(c_0_9530,plain,
    c_Public_Okeymode_Okeymode__case(X1,X2,c_Public_Okeymode_OSignature,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6593]) ).

cnf(c_0_9531,plain,
    c_Relation_OImage(c_Relation_OId,X1,X2,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6594]) ).

cnf(c_0_9532,plain,
    c_Numeral_Obit_Obit__rec(X1,X2,c_Numeral_Obit_OB1,X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6595]) ).

cnf(c_0_9533,plain,
    c_Numeral_Obit_Obit__rec(X1,X2,c_Numeral_Obit_OB0,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6596]) ).

cnf(c_0_9534,plain,
    c_Numeral_Obit_Obit__case(X1,X2,c_Numeral_Obit_OB1,X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6597]) ).

cnf(c_0_9535,plain,
    c_Numeral_Obit_Obit__case(X1,X2,c_Numeral_Obit_OB0,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6598]) ).

cnf(c_0_9536,plain,
    c_Extraction_Osumbool_Osumbool__rec(X1,X2,c_Extraction_Osumbool_ORight,X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6599]) ).

cnf(c_0_9537,plain,
    c_Extraction_Osumbool_Osumbool__rec(X1,X2,c_Extraction_Osumbool_OLeft,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6600]) ).

cnf(c_0_9538,plain,
    c_Extraction_Osumbool_Osumbool__case(X1,X2,c_Extraction_Osumbool_ORight,X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6601]) ).

cnf(c_0_9539,plain,
    c_Extraction_Osumbool_Osumbool__case(X1,X2,c_Extraction_Osumbool_OLeft,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6602]) ).

cnf(c_0_9540,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6603]) ).

cnf(c_0_9541,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6604]) ).

cnf(c_0_9542,plain,
    c_Relation_OImage(X1,c_emptyset,X2,X3) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_6605]) ).

cnf(c_0_9543,plain,
    c_List_Ozip(c_List_Olist_ONil,X1,X2,X3) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_6606]) ).

cnf(c_0_9544,plain,
    c_List_Ozip(X1,c_List_Olist_ONil,X2,X3) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_6607]) ).

cnf(c_0_9545,plain,
    ( c_List_Onth(c_List_Oreplicate(X1,X2,X3),X4,X3) = X2
    | ~ c_less(X4,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6608]) ).

cnf(c_0_9546,plain,
    c_List_Olist__update(c_List_Olist_ONil,X1,X2,X3) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_6609]) ).

cnf(c_0_9547,plain,
    c_Datatype__Universe_Ontrunc(c_0,X1,X2,X3) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_6610]) ).

cnf(c_0_9548,plain,
    c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_6611]) ).

cnf(c_0_9549,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6612]) ).

cnf(c_0_9550,plain,
    ( c_plus(X1,c_minus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6613]) ).

cnf(c_0_9551,plain,
    ( c_plus(c_minus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6614]) ).

cnf(c_0_9552,plain,
    ( c_minus(X1,c_minus(X1,X2,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6615]) ).

cnf(c_0_9553,plain,
    ( c_HOL_Oinverse(c_times(X1,X2,X3),X3) = c_times(c_HOL_Oinverse(X1,X3),c_HOL_Oinverse(X2,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6616]) ).

cnf(c_0_9554,plain,
    ( c_HOL_Oabs(c_divide(X1,X2,X3),X3) = c_divide(c_HOL_Oabs(X1,X3),c_HOL_Oabs(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6617]) ).

cnf(c_0_9555,plain,
    ( c_lessequals(c_Suc(c_0),c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6618]) ).

cnf(c_0_9556,plain,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6619]) ).

cnf(c_0_9557,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6620]) ).

cnf(c_0_9558,plain,
    c_minus(c_minus(X1,X2,tc_set(X3)),X2,tc_set(X3)) = c_minus(X1,X2,tc_set(X3)),
    inference(split_conjunct,[status(thm)],[c_0_6621]) ).

cnf(c_0_9559,plain,
    c_Union(c_union(X1,X2,tc_set(X3)),X3) = c_union(c_Union(X1,X3),c_Union(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6622]) ).

cnf(c_0_9560,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6623]) ).

cnf(c_0_9561,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6624]) ).

cnf(c_0_9562,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6625]) ).

cnf(c_0_9563,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6626]) ).

cnf(c_0_9564,plain,
    ( c_less(c_0,c_minus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6627]) ).

cnf(c_0_9565,plain,
    c_List_Oconcat(c_append(X1,X2,tc_List_Olist(X3)),X3) = c_append(c_List_Oconcat(X1,X3),c_List_Oconcat(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6628]) ).

cnf(c_0_9566,plain,
    ( c_div(c_times(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6629]) ).

cnf(c_0_9567,plain,
    ( c_div(c_times(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6630]) ).

cnf(c_0_9568,plain,
    ( c_append(c_List_Obutlast(X1,X2),c_List_Olist_OCons(c_List_Olast(X1,X2),c_List_Olist_ONil,X2),X2) = X1
    | X1 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_6631]) ).

cnf(c_0_9569,plain,
    ( c_less(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6632]) ).

cnf(c_0_9570,plain,
    ( c_less(X1,c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(X1,c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6633]) ).

cnf(c_0_9571,plain,
    ( c_less(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6634]) ).

cnf(c_0_9572,plain,
    ( c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6635]) ).

cnf(c_0_9573,plain,
    ( c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6636]) ).

cnf(c_0_9574,plain,
    ( c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6637]) ).

cnf(c_0_9575,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6638]) ).

cnf(c_0_9576,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6639]) ).

cnf(c_0_9577,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6640]) ).

cnf(c_0_9578,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6641]) ).

cnf(c_0_9579,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6642]) ).

cnf(c_0_9580,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6643]) ).

cnf(c_0_9581,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6644]) ).

cnf(c_0_9582,plain,
    ( c_lessequals(c_0,c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6645]) ).

cnf(c_0_9583,plain,
    ( c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(X2,c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6646]) ).

cnf(c_0_9584,plain,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6647]) ).

cnf(c_0_9585,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6648]) ).

cnf(c_0_9586,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6649]) ).

cnf(c_0_9587,plain,
    ( c_uminus(c_LOrder_Omeet(X1,X2,X3),X3) = c_LOrder_Ojoin(c_uminus(X1,X3),c_uminus(X2,X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6650]) ).

cnf(c_0_9588,plain,
    ( c_uminus(c_LOrder_Ojoin(X1,X2,X3),X3) = c_LOrder_Omeet(c_uminus(X1,X3),c_uminus(X2,X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6651]) ).

cnf(c_0_9589,plain,
    ( c_uminus(c_plus(X1,X2,X3),X3) = c_plus(c_uminus(X1,X3),c_uminus(X2,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6652]) ).

cnf(c_0_9590,plain,
    ( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
    | ~ c_in(X1,X2,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6653]) ).

cnf(c_0_9591,plain,
    c_Pow(c_inter(X1,X2,X3),X3) = c_inter(c_Pow(X1,X3),c_Pow(X2,X3),tc_set(X3)),
    inference(split_conjunct,[status(thm)],[c_0_6654]) ).

cnf(c_0_9592,plain,
    c_List_Olists(c_inter(X1,X2,X3),X3) = c_inter(c_List_Olists(X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)),
    inference(split_conjunct,[status(thm)],[c_0_6655]) ).

cnf(c_0_9593,plain,
    ( c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2))
    | ~ c_lessequals(X3,X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6656]) ).

cnf(c_0_9594,plain,
    ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3)
    | c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    inference(split_conjunct,[status(thm)],[c_0_6657]) ).

cnf(c_0_9595,plain,
    ( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | ~ c_in(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6658]) ).

cnf(c_0_9596,plain,
    ( c_times(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2),X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6659]) ).

cnf(c_0_9597,plain,
    c_uminus(c_minus(X1,X2,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X1,tc_set(X3)),X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6660]) ).

cnf(c_0_9598,plain,
    ( c_NatArith_Oof__nat(c_times(X1,X2,tc_nat),X3) = c_times(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6661]) ).

cnf(c_0_9599,plain,
    ( c_NatArith_Oof__nat(c_plus(X1,X2,tc_nat),X3) = c_plus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6662]) ).

cnf(c_0_9600,plain,
    ( c_IntDef_Oof__int(c_times(X1,X2,tc_IntDef_Oint),X3) = c_times(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6663]) ).

cnf(c_0_9601,plain,
    ( c_IntDef_Oof__int(c_minus(X1,X2,tc_IntDef_Oint),X3) = c_minus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6664]) ).

cnf(c_0_9602,plain,
    ( c_IntDef_Oof__int(c_plus(X1,X2,tc_IntDef_Oint),X3) = c_plus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6665]) ).

cnf(c_0_9603,plain,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6666]) ).

cnf(c_0_9604,plain,
    ( c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
    | ~ c_less(c_0,X2,tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6667]) ).

cnf(c_0_9605,plain,
    ( c_divide(X1,c_times(X2,X1,X3),X3) = c_divide(c_1,X2,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6668]) ).

cnf(c_0_9606,plain,
    ( c_divide(X1,c_times(X1,X2,X3),X3) = c_divide(c_1,X2,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6669]) ).

cnf(c_0_9607,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6670]) ).

cnf(c_0_9608,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6671]) ).

cnf(c_0_9609,plain,
    c_div(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6672]) ).

cnf(c_0_9610,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6673]) ).

cnf(c_0_9611,plain,
    ( c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_uminus(c_Nat_Opower(X1,X3,X2),X2)
    | c_Parity_Oeven(X3,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6674]) ).

cnf(c_0_9612,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6675]) ).

cnf(c_0_9613,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6676]) ).

cnf(c_0_9614,plain,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6677]) ).

cnf(c_0_9615,plain,
    ( c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6678]) ).

cnf(c_0_9616,plain,
    c_Message_Oanalz(c_union(c_Message_Oanalz(X1),X2,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X1,X2,tc_Message_Omsg)),
    inference(split_conjunct,[status(thm)],[c_0_6679]) ).

cnf(c_0_9617,plain,
    c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6680]) ).

cnf(c_0_9618,plain,
    c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6681]) ).

cnf(c_0_9619,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6682]) ).

cnf(c_0_9620,plain,
    c_List_Oset(c_append(X1,X2,X3),X3) = c_union(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6683]) ).

cnf(c_0_9621,plain,
    c_List_Orev(c_append(X1,X2,X3),X3) = c_append(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6684]) ).

cnf(c_0_9622,plain,
    ( c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6685]) ).

cnf(c_0_9623,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_1 != c_Numeral_Onumber__of(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6686]) ).

cnf(c_0_9624,plain,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6687]) ).

cnf(c_0_9625,plain,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6688]) ).

cnf(c_0_9626,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X1),c_Message_OkeysFor(X3),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6689]) ).

cnf(c_0_9627,plain,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6690]) ).

cnf(c_0_9628,plain,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6691]) ).

cnf(c_0_9629,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,X1,tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6692]) ).

cnf(c_0_9630,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,X1,tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6693]) ).

cnf(c_0_9631,plain,
    ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),c_0,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6694]) ).

cnf(c_0_9632,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6695]) ).

cnf(c_0_9633,plain,
    ( c_Orderings_Omax(X1,c_Orderings_Omax(X1,X2,X3),X3) = c_Orderings_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6696]) ).

cnf(c_0_9634,plain,
    ( c_Orderings_Omin(X1,c_Orderings_Omin(X1,X2,X3),X3) = c_Orderings_Omin(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6697]) ).

cnf(c_0_9635,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6698]) ).

cnf(c_0_9636,plain,
    ( c_in(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6699]) ).

cnf(c_0_9637,plain,
    c_List_Oreplicate(c_Suc(X1),X2,X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6700]) ).

cnf(c_0_9638,plain,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X3) = c_List_Onth(X2,X4,X3),
    inference(split_conjunct,[status(thm)],[c_0_6701]) ).

cnf(c_0_9639,plain,
    c_List_Odrop(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(X1,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_6702]) ).

cnf(c_0_9640,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6703]) ).

cnf(c_0_9641,plain,
    c_Nat_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X2,tc_List_Olist(X3)),c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6704]) ).

cnf(c_0_9642,plain,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_uminus(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6705]) ).

cnf(c_0_9643,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_Numeral_Onumber__of(X3,X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6706]) ).

cnf(c_0_9644,plain,
    ( c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6707]) ).

cnf(c_0_9645,plain,
    ( c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6708]) ).

cnf(c_0_9646,plain,
    c_Nat_Osize(c_List_Otake(X1,X2,X3),tc_List_Olist(X3)) = c_Orderings_Omin(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6709]) ).

cnf(c_0_9647,plain,
    c_Nat_Osize(c_List_Odrop(X1,X2,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6710]) ).

cnf(c_0_9648,plain,
    ( c_minus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6711]) ).

cnf(c_0_9649,plain,
    ( c_less(c_uminus(c_1,X1),X2,X1)
    | ~ c_less(c_uminus(X2,X1),c_1,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6712]) ).

cnf(c_0_9650,plain,
    ( c_lessequals(c_uminus(c_1,X1),X2,X1)
    | ~ c_lessequals(c_uminus(X2,X1),c_1,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6713]) ).

cnf(c_0_9651,plain,
    ( c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(c_divide(c_1,X2,X1),X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6714]) ).

cnf(c_0_9652,plain,
    ( c_less(X1,c_uminus(c_1,X2),X2)
    | ~ c_less(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6715]) ).

cnf(c_0_9653,plain,
    ( c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6716]) ).

cnf(c_0_9654,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6717]) ).

cnf(c_0_9655,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6718]) ).

cnf(c_0_9656,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6719]) ).

cnf(c_0_9657,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6720]) ).

cnf(c_0_9658,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6721]) ).

cnf(c_0_9659,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6722]) ).

cnf(c_0_9660,plain,
    ( c_less(c_uminus(X1,X2),c_1,X2)
    | ~ c_less(c_uminus(c_1,X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6723]) ).

cnf(c_0_9661,plain,
    ( c_lessequals(c_uminus(X1,X2),c_1,X2)
    | ~ c_lessequals(c_uminus(c_1,X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6724]) ).

cnf(c_0_9662,plain,
    ( c_less(c_1,c_uminus(X1,X2),X2)
    | ~ c_less(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6725]) ).

cnf(c_0_9663,plain,
    ( c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6726]) ).

cnf(c_0_9664,plain,
    c_union(X1,c_union(X2,X1,X3),X3) = c_union(X2,X1,X3),
    inference(split_conjunct,[status(thm)],[c_0_6727]) ).

cnf(c_0_9665,plain,
    c_insert(X1,c_insert(X1,X2,X3),X3) = c_insert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6728]) ).

cnf(c_0_9666,plain,
    c_Nat_Opower(X1,c_Suc(X2),tc_nat) = c_times(X1,c_Nat_Opower(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6729]) ).

cnf(c_0_9667,plain,
    c_times(c_Suc(X1),X2,tc_nat) = c_plus(X2,c_times(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6730]) ).

cnf(c_0_9668,plain,
    c_times(X1,c_Suc(X2),tc_nat) = c_plus(X1,c_times(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6731]) ).

cnf(c_0_9669,plain,
    c_Nat_Opower(X1,c_Suc(X2),tc_IntDef_Oint) = c_times(X1,c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6732]) ).

cnf(c_0_9670,plain,
    ( c_divide(X1,c_uminus(X2,X3),X3) = c_uminus(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6733]) ).

cnf(c_0_9671,plain,
    c_Divides_Oop_Amod(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6734]) ).

cnf(c_0_9672,plain,
    c_Union(c_insert(X1,X2,tc_set(X3)),X3) = c_union(X1,c_Union(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6735]) ).

cnf(c_0_9673,plain,
    c_Inter(c_insert(X1,X2,tc_set(X3)),X3) = c_inter(X1,c_Inter(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6736]) ).

cnf(c_0_9674,plain,
    c_List_Olistset(c_List_Olist_OCons(X1,X2,tc_set(X3)),X3) = c_List_Oset__Cons(X1,c_List_Olistset(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6737]) ).

cnf(c_0_9675,plain,
    c_List_Oconcat(c_List_Olist_OCons(X1,X2,tc_List_Olist(X3)),X3) = c_append(X1,c_List_Oconcat(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6738]) ).

cnf(c_0_9676,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_6739]) ).

cnf(c_0_9677,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6740]) ).

cnf(c_0_9678,plain,
    c_plus(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6741]) ).

cnf(c_0_9679,plain,
    c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1,tc_nat) = c_Suc(c_Suc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6742]) ).

cnf(c_0_9680,plain,
    ( c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_ONil
    | c_in(c_0,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6743]) ).

cnf(c_0_9681,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6744]) ).

cnf(c_0_9682,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6745]) ).

cnf(c_0_9683,plain,
    c_Divides_Oop_Amod(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6746]) ).

cnf(c_0_9684,plain,
    c_Divides_Oop_Amod(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6747]) ).

cnf(c_0_9685,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6748]) ).

cnf(c_0_9686,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_nat),X1,tc_nat) = c_Divides_Oop_Amod(X2,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6749]) ).

cnf(c_0_9687,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6750]) ).

cnf(c_0_9688,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6751]) ).

cnf(c_0_9689,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6752]) ).

cnf(c_0_9690,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMin(X1,X2),c_Finite__Set_OMax(X1,X2),X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6753]) ).

cnf(c_0_9691,plain,
    ( c_times(X1,c_uminus(X2,X3),X3) = c_uminus(c_times(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6754]) ).

cnf(c_0_9692,plain,
    ( c_times(c_uminus(X1,X2),X3,X2) = c_uminus(c_times(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Oring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6755]) ).

cnf(c_0_9693,plain,
    ( c_divide(c_uminus(X1,X2),X3,X2) = c_uminus(c_divide(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6756]) ).

cnf(c_0_9694,plain,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_0
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6757]) ).

cnf(c_0_9695,plain,
    ( c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_1
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6758]) ).

cnf(c_0_9696,plain,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6759]) ).

cnf(c_0_9697,plain,
    ( c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6760]) ).

cnf(c_0_9698,plain,
    ( c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6761]) ).

cnf(c_0_9699,plain,
    ( c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6762]) ).

cnf(c_0_9700,plain,
    ( c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6763]) ).

cnf(c_0_9701,plain,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Numeral_Onumber__of(X4,tc_nat),X3) = X1
    | c_Numeral_Onumber__of(X4,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6764]) ).

cnf(c_0_9702,plain,
    ( c_Message_Oparts(c_insert(X1,X2,tc_Message_Omsg)) = c_Message_Oparts(X2)
    | ~ c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6765]) ).

cnf(c_0_9703,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6766]) ).

cnf(c_0_9704,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate(X3,X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6767]) ).

cnf(c_0_9705,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_append(X3,X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6768]) ).

cnf(c_0_9706,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_append(X1,X3,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6769]) ).

cnf(c_0_9707,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X3,X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6770]) ).

cnf(c_0_9708,plain,
    ( c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_ONil
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6771]) ).

cnf(c_0_9709,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6772]) ).

cnf(c_0_9710,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6773]) ).

cnf(c_0_9711,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6774]) ).

cnf(c_0_9712,plain,
    ( X1 = c_Message_OinvKey(v_sko__uhi(X2,X1))
    | c_in(X1,c_Message_OkeysFor(X2),tc_nat)
    | ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6775]) ).

cnf(c_0_9713,plain,
    ( c_List_Otl(c_append(X1,X2,X3),X3) = c_append(c_List_Otl(X1,X3),X2,X3)
    | X1 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_6776]) ).

cnf(c_0_9714,plain,
    ( c_List_Obutlast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,c_List_Obutlast(X2,X3),X3)
    | X2 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_6777]) ).

cnf(c_0_9715,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6778]) ).

cnf(c_0_9716,plain,
    c_List_Oset(c_List_Olist_OCons(X1,X2,X3),X3) = c_insert(X1,c_List_Oset(X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6779]) ).

cnf(c_0_9717,plain,
    c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6780]) ).

cnf(c_0_9718,plain,
    ( c_lessequals(c_OrderedGroup_Opprt(X1,X2),c_OrderedGroup_Opprt(X3,X2),X2)
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6781]) ).

cnf(c_0_9719,plain,
    ( c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_OrderedGroup_Onprt(X3,X2),X2)
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6782]) ).

cnf(c_0_9720,plain,
    ( c_less(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6783]) ).

cnf(c_0_9721,plain,
    ( c_lessequals(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6784]) ).

cnf(c_0_9722,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X3),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6785]) ).

cnf(c_0_9723,plain,
    ( c_List_Otake(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6786]) ).

cnf(c_0_9724,plain,
    ( c_List_Orotate(X1,X2,X3) = X2
    | c_Divides_Oop_Amod(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6787]) ).

cnf(c_0_9725,plain,
    ( c_List_Odrop(X1,X2,X3) = c_List_Olist_ONil
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6788]) ).

cnf(c_0_9726,plain,
    c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6789]) ).

cnf(c_0_9727,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6790]) ).

cnf(c_0_9728,plain,
    ( c_less(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ c_less(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6791]) ).

cnf(c_0_9729,plain,
    ( c_lessequals(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6792]) ).

cnf(c_0_9730,plain,
    ( c_less(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ c_less(X1,X3,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6793]) ).

cnf(c_0_9731,plain,
    ( c_lessequals(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ c_lessequals(X1,X3,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6794]) ).

cnf(c_0_9732,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6795]) ).

cnf(c_0_9733,plain,
    ( X1 = X2
    | ~ c_in(X2,X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6796]) ).

cnf(c_0_9734,plain,
    ( c_List_Orotate(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),c_1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6797]) ).

cnf(c_0_9735,plain,
    c_List_Odrop(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(c_plus(X2,X1,tc_nat),X3),
    inference(split_conjunct,[status(thm)],[c_0_6798]) ).

cnf(c_0_9736,plain,
    ( c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6799]) ).

cnf(c_0_9737,plain,
    ( ~ c_lessequals(v_sko__urX(X1),X2,tc_nat)
    | ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(X1),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6800]) ).

cnf(c_0_9738,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6801]) ).

cnf(c_0_9739,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6802]) ).

cnf(c_0_9740,plain,
    ( c_0 = c_Numeral_Onumber__of(X1,X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6803]) ).

cnf(c_0_9741,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6804]) ).

cnf(c_0_9742,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6805]) ).

cnf(c_0_9743,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6806]) ).

cnf(c_0_9744,plain,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6807]) ).

cnf(c_0_9745,plain,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6808]) ).

cnf(c_0_9746,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6809]) ).

cnf(c_0_9747,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6810]) ).

cnf(c_0_9748,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6811]) ).

cnf(c_0_9749,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6812]) ).

cnf(c_0_9750,plain,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6813]) ).

cnf(c_0_9751,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6814]) ).

cnf(c_0_9752,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6815]) ).

cnf(c_0_9753,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6816]) ).

cnf(c_0_9754,plain,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X2,X1,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6817]) ).

cnf(c_0_9755,plain,
    ( c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6818]) ).

cnf(c_0_9756,plain,
    ~ c_List_Onull(c_List_Olist_OCons(X1,X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6819]) ).

cnf(c_0_9757,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6820]) ).

cnf(c_0_9758,plain,
    ( c_HOL_Oinverse(c_divide(X1,X2,X3),X3) = c_divide(X2,X1,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6821]) ).

cnf(c_0_9759,plain,
    ( X1 = c_0
    | X2 = X3
    | c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6822]) ).

cnf(c_0_9760,plain,
    ( X1 = c_0
    | X2 = X3
    | c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6823]) ).

cnf(c_0_9761,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6824]) ).

cnf(c_0_9762,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6825]) ).

cnf(c_0_9763,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6826]) ).

cnf(c_0_9764,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6827]) ).

cnf(c_0_9765,plain,
    ( c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1),X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6828]) ).

cnf(c_0_9766,plain,
    ( c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6829]) ).

cnf(c_0_9767,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6830]) ).

cnf(c_0_9768,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6831]) ).

cnf(c_0_9769,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6832]) ).

cnf(c_0_9770,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6833]) ).

cnf(c_0_9771,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6834]) ).

cnf(c_0_9772,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6835]) ).

cnf(c_0_9773,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6836]) ).

cnf(c_0_9774,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6837]) ).

cnf(c_0_9775,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6838]) ).

cnf(c_0_9776,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6839]) ).

cnf(c_0_9777,plain,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6840]) ).

cnf(c_0_9778,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6841]) ).

cnf(c_0_9779,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6842]) ).

cnf(c_0_9780,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6843]) ).

cnf(c_0_9781,plain,
    c_Transitive__Closure_Otrancl(c_union(X1,c_Relation_OId,tc_prod(X2,X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_6844]) ).

cnf(c_0_9782,plain,
    c_Transitive__Closure_Ortrancl(c_union(X1,c_Relation_OId,tc_prod(X2,X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_6845]) ).

cnf(c_0_9783,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6846]) ).

cnf(c_0_9784,plain,
    ( c_less(X1,c_0,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6847]) ).

cnf(c_0_9785,plain,
    ( c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6848]) ).

cnf(c_0_9786,plain,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6849]) ).

cnf(c_0_9787,plain,
    ( c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6850]) ).

cnf(c_0_9788,plain,
    ( X1 = c_emptyset
    | c_in(c_Finite__Set_OMin(X1,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6851]) ).

cnf(c_0_9789,plain,
    ( X1 = c_emptyset
    | c_in(c_Finite__Set_OMax(X1,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6852]) ).

cnf(c_0_9790,plain,
    ( c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6853]) ).

cnf(c_0_9791,plain,
    ( c_uminus(c_minus(X1,X2,X3),X3) = c_minus(X2,X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6854]) ).

cnf(c_0_9792,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X2,X1,X4) != c_times(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6855]) ).

cnf(c_0_9793,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X1,X2,X4) != c_times(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6856]) ).

cnf(c_0_9794,plain,
    c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oused(X3),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6857]) ).

cnf(c_0_9795,plain,
    c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_OinitState(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6858]) ).

cnf(c_0_9796,plain,
    c_List_Orotate(c_Suc(X1),X2,X3) = c_List_Orotate1(c_List_Orotate(X1,X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6859]) ).

cnf(c_0_9797,plain,
    c_lessequals(c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)),c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6860]) ).

cnf(c_0_9798,plain,
    ( X1 = X2
    | c_plus(X1,X3,X4) != c_plus(X2,X3,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6861]) ).

cnf(c_0_9799,plain,
    ( X1 = X2
    | c_plus(X3,X1,X4) != c_plus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6862]) ).

cnf(c_0_9800,plain,
    c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3),
    inference(split_conjunct,[status(thm)],[c_0_6863]) ).

cnf(c_0_9801,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6864]) ).

cnf(c_0_9802,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_List_Oconcat(X2,X3)
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6865]) ).

cnf(c_0_9803,plain,
    ( c_times(X1,c_divide(X2,X1,X3),X3) = X2
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6866]) ).

cnf(c_0_9804,plain,
    ( c_times(c_divide(X1,X2,X3),X2,X3) = X1
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6867]) ).

cnf(c_0_9805,plain,
    ( c_divide(c_times(X1,X2,X3),X2,X3) = X1
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6868]) ).

cnf(c_0_9806,plain,
    ( c_divide(c_times(X1,X2,X3),X1,X3) = X2
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6869]) ).

cnf(c_0_9807,plain,
    ( c_minus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6870]) ).

cnf(c_0_9808,plain,
    ( c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),X3,tc_nat)
    | c_List_Odrop(X3,X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_6871]) ).

cnf(c_0_9809,plain,
    ( c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6872]) ).

cnf(c_0_9810,plain,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6873]) ).

cnf(c_0_9811,plain,
    ( c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6874]) ).

cnf(c_0_9812,plain,
    ( c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6875]) ).

cnf(c_0_9813,plain,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(c_Message_Oagent_OSpy,X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    inference(split_conjunct,[status(thm)],[c_0_6876]) ).

cnf(c_0_9814,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6877]) ).

cnf(c_0_9815,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat) = c_minus(c_Suc(X2),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6878]) ).

cnf(c_0_9816,plain,
    ( c_List_Oset(c_List_Oreplicate(X1,X2,X3),X3) = c_insert(X2,c_emptyset,X3)
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6879]) ).

cnf(c_0_9817,plain,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6880]) ).

cnf(c_0_9818,plain,
    ( c_divide(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_divide(X1,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6881]) ).

cnf(c_0_9819,plain,
    ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6882]) ).

cnf(c_0_9820,plain,
    ( c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    inference(split_conjunct,[status(thm)],[c_0_6883]) ).

cnf(c_0_9821,plain,
    ( c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    inference(split_conjunct,[status(thm)],[c_0_6884]) ).

cnf(c_0_9822,plain,
    ( c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    inference(split_conjunct,[status(thm)],[c_0_6885]) ).

cnf(c_0_9823,plain,
    ( c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6886]) ).

cnf(c_0_9824,plain,
    ( c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6887]) ).

cnf(c_0_9825,plain,
    ( c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6888]) ).

cnf(c_0_9826,plain,
    ( c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6889]) ).

cnf(c_0_9827,plain,
    c_inter(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_6890]) ).

cnf(c_0_9828,plain,
    ( c_List_Olast(c_List_Oupt(X1,X2),tc_nat) = c_minus(X2,c_1,tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6891]) ).

cnf(c_0_9829,plain,
    ( X1 = X2
    | c_Event_Oevent_OSays(X3,X4,X1) != c_Event_Oevent_OSays(X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6892]) ).

cnf(c_0_9830,plain,
    ( X1 = X2
    | c_Event_Oevent_OSays(X3,X1,X4) != c_Event_Oevent_OSays(X5,X2,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_6893]) ).

cnf(c_0_9831,plain,
    ( X1 = X2
    | c_Event_Oevent_OSays(X1,X3,X4) != c_Event_Oevent_OSays(X2,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_6894]) ).

cnf(c_0_9832,plain,
    ( X1 = X2
    | c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6895]) ).

cnf(c_0_9833,plain,
    ( X1 = X2
    | c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6896]) ).

cnf(c_0_9834,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6897]) ).

cnf(c_0_9835,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6898]) ).

cnf(c_0_9836,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6899]) ).

cnf(c_0_9837,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6900]) ).

cnf(c_0_9838,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6901]) ).

cnf(c_0_9839,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6902]) ).

cnf(c_0_9840,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6903]) ).

cnf(c_0_9841,plain,
    ( X1 = X2
    | c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6904]) ).

cnf(c_0_9842,plain,
    ( X1 = X2
    | c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6905]) ).

cnf(c_0_9843,plain,
    ( X1 = X2
    | c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6906]) ).

cnf(c_0_9844,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6907]) ).

cnf(c_0_9845,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6908]) ).

cnf(c_0_9846,plain,
    c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6909]) ).

cnf(c_0_9847,plain,
    c_Message_OkeysFor(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6910]) ).

cnf(c_0_9848,plain,
    c_Orderings_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omin(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6911]) ).

cnf(c_0_9849,plain,
    c_Orderings_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omax(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6912]) ).

cnf(c_0_9850,plain,
    ( c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6913]) ).

cnf(c_0_9851,plain,
    c_IntDef_Oint(c_plus(X1,X2,tc_nat)) = c_plus(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_6914]) ).

cnf(c_0_9852,plain,
    ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X1,X2)),c_Message_OsymKeys,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6915]) ).

cnf(c_0_9853,plain,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Osynth(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6916]) ).

cnf(c_0_9854,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_Message_Oparts(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6917]) ).

cnf(c_0_9855,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oanalz(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6918]) ).

cnf(c_0_9856,plain,
    ( c_times(c_0,c_divide(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6919]) ).

cnf(c_0_9857,plain,
    ( c_times(c_divide(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6920]) ).

cnf(c_0_9858,plain,
    ( c_divide(c_times(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6921]) ).

cnf(c_0_9859,plain,
    ( c_divide(c_0,c_times(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6922]) ).

cnf(c_0_9860,plain,
    ( c_divide(c_times(c_0,X1,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6923]) ).

cnf(c_0_9861,plain,
    ( c_divide(c_0,c_times(c_0,X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6924]) ).

cnf(c_0_9862,plain,
    c_Sum__Type_OInr(X1,X2,X3) != c_Sum__Type_OInl(X4,X3,X2),
    inference(split_conjunct,[status(thm)],[c_0_6925]) ).

cnf(c_0_9863,plain,
    c_Sum__Type_OInl(X1,X2,X3) != c_Sum__Type_OInr(X4,X3,X2),
    inference(split_conjunct,[status(thm)],[c_0_6926]) ).

cnf(c_0_9864,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6927]) ).

cnf(c_0_9865,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6928]) ).

cnf(c_0_9866,plain,
    c_Datatype__Universe_OIn1(X1,X2,X3) != c_Datatype__Universe_OIn0(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6929]) ).

cnf(c_0_9867,plain,
    c_Datatype__Universe_OIn0(X1,X2,X3) != c_Datatype__Universe_OIn1(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_6930]) ).

cnf(c_0_9868,plain,
    ( c_in(c_Message_OinvKey(X1),c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6931]) ).

cnf(c_0_9869,plain,
    ( X1 = X2
    | c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6932]) ).

cnf(c_0_9870,plain,
    ( X1 = X2
    | c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6933]) ).

cnf(c_0_9871,plain,
    ( c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    inference(split_conjunct,[status(thm)],[c_0_6934]) ).

cnf(c_0_9872,plain,
    ( c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    inference(split_conjunct,[status(thm)],[c_0_6935]) ).

cnf(c_0_9873,plain,
    ( c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    inference(split_conjunct,[status(thm)],[c_0_6936]) ).

cnf(c_0_9874,plain,
    c_List_Olist_OCons(X1,c_List_Olist_ONil,X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_6937]) ).

cnf(c_0_9875,plain,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),
    inference(split_conjunct,[status(thm)],[c_0_6938]) ).

cnf(c_0_9876,plain,
    ( c_less(c_uminus(X1,X2),c_0,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6939]) ).

cnf(c_0_9877,plain,
    ( c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6940]) ).

cnf(c_0_9878,plain,
    ( c_less(c_0,c_uminus(X1,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6941]) ).

cnf(c_0_9879,plain,
    ( c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6942]) ).

cnf(c_0_9880,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X2,X1,tc_nat) != c_times(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6943]) ).

cnf(c_0_9881,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X1,X2,tc_nat) != c_times(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6944]) ).

cnf(c_0_9882,plain,
    ( c_in(c_uminus(X1,X2),c_IntDef_OInts,X2)
    | ~ c_in(X1,c_IntDef_OInts,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6945]) ).

cnf(c_0_9883,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),X3),X3)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6946]) ).

cnf(c_0_9884,plain,
    ( c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_Nat_Opower(X1,X3,X2)
    | ~ c_Parity_Oeven(X3,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6947]) ).

cnf(c_0_9885,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6948]) ).

cnf(c_0_9886,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_6949]) ).

cnf(c_0_9887,plain,
    ( X1 = X2
    | c_plus(X1,X3,tc_nat) != c_plus(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6950]) ).

cnf(c_0_9888,plain,
    ( X1 = X2
    | c_plus(X3,X1,tc_nat) != c_plus(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6951]) ).

cnf(c_0_9889,plain,
    ( X1 = X2
    | c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6952]) ).

cnf(c_0_9890,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | c_Numeral_Onumber__of(X1,X3) != c_Numeral_Onumber__of(X2,X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6953]) ).

cnf(c_0_9891,plain,
    ( c_times(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_times(X1,X3,X2)
    | ~ class_Ring__and__Field_Oring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6954]) ).

cnf(c_0_9892,plain,
    ( c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6955]) ).

cnf(c_0_9893,plain,
    ( c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6956]) ).

cnf(c_0_9894,plain,
    ( c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6957]) ).

cnf(c_0_9895,plain,
    ( c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ c_less(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6958]) ).

cnf(c_0_9896,plain,
    ( c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6959]) ).

cnf(c_0_9897,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6960]) ).

cnf(c_0_9898,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6961]) ).

cnf(c_0_9899,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6962]) ).

cnf(c_0_9900,plain,
    ( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_6963]) ).

cnf(c_0_9901,plain,
    c_plus(c_Suc(X1),X2,tc_nat) = c_Suc(c_plus(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6964]) ).

cnf(c_0_9902,plain,
    c_plus(X1,c_Suc(X2),tc_nat) = c_Suc(c_plus(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6965]) ).

cnf(c_0_9903,plain,
    ( c_minus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6966]) ).

cnf(c_0_9904,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6967]) ).

cnf(c_0_9905,plain,
    ( c_plus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6968]) ).

cnf(c_0_9906,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6969]) ).

cnf(c_0_9907,plain,
    ( c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | ~ c_in(X1,c_Message_OkeysFor(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_6970]) ).

cnf(c_0_9908,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6971]) ).

cnf(c_0_9909,plain,
    c_Message_OkeysFor(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)) = c_Message_OkeysFor(X3),
    inference(split_conjunct,[status(thm)],[c_0_6972]) ).

cnf(c_0_9910,plain,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oused(X3),
    inference(split_conjunct,[status(thm)],[c_0_6973]) ).

cnf(c_0_9911,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)) = c_Message_OkeysFor(X3),
    inference(split_conjunct,[status(thm)],[c_0_6974]) ).

cnf(c_0_9912,plain,
    ( X1 = c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6975]) ).

cnf(c_0_9913,plain,
    ( X1 = c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat)
    | c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6976]) ).

cnf(c_0_9914,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X3)),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_6977]) ).

cnf(c_0_9915,plain,
    ( c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6978]) ).

cnf(c_0_9916,plain,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_6979]) ).

cnf(c_0_9917,plain,
    c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6980]) ).

cnf(c_0_9918,plain,
    c_List_Oremove1(X1,c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_6981]) ).

cnf(c_0_9919,plain,
    c_in(X1,c_insert(X1,X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6982]) ).

cnf(c_0_9920,plain,
    c_List_Oop_Amem(X1,c_List_Olist_OCons(X1,X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_6983]) ).

cnf(c_0_9921,plain,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_0,X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6984]) ).

cnf(c_0_9922,plain,
    ( c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6985]) ).

cnf(c_0_9923,plain,
    ( c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_6986]) ).

cnf(c_0_9924,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6987]) ).

cnf(c_0_9925,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6988]) ).

cnf(c_0_9926,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6989]) ).

cnf(c_0_9927,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6990]) ).

cnf(c_0_9928,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6991]) ).

cnf(c_0_9929,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6992]) ).

cnf(c_0_9930,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_6993]) ).

cnf(c_0_9931,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_6994]) ).

cnf(c_0_9932,plain,
    ( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) != c_List_Orev(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6995]) ).

cnf(c_0_9933,plain,
    ( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6996]) ).

cnf(c_0_9934,plain,
    ( c_div(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6997]) ).

cnf(c_0_9935,plain,
    ( c_div(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = X1
    | X2 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6998]) ).

cnf(c_0_9936,plain,
    ( X1 = X2
    | c_less(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6999]) ).

cnf(c_0_9937,plain,
    ( c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7000]) ).

cnf(c_0_9938,plain,
    ( c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7001]) ).

cnf(c_0_9939,plain,
    ( c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7002]) ).

cnf(c_0_9940,plain,
    c_in(X1,c_insert(X1,c_emptyset,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_7003]) ).

cnf(c_0_9941,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7004]) ).

cnf(c_0_9942,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7005]) ).

cnf(c_0_9943,plain,
    ( c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7006]) ).

cnf(c_0_9944,plain,
    c_lessequals(X1,c_plus(X2,X1,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7007]) ).

cnf(c_0_9945,plain,
    c_lessequals(X1,c_plus(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7008]) ).

cnf(c_0_9946,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7009]) ).

cnf(c_0_9947,plain,
    c_lessequals(c_minus(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7010]) ).

cnf(c_0_9948,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7011]) ).

cnf(c_0_9949,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7012]) ).

cnf(c_0_9950,plain,
    c_div(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7013]) ).

cnf(c_0_9951,plain,
    c_div(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7014]) ).

cnf(c_0_9952,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_nat),X2,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7015]) ).

cnf(c_0_9953,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_nat),X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7016]) ).

cnf(c_0_9954,plain,
    c_lessequals(c_div(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7017]) ).

cnf(c_0_9955,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7018]) ).

cnf(c_0_9956,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7019]) ).

cnf(c_0_9957,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7020]) ).

cnf(c_0_9958,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7021]) ).

cnf(c_0_9959,plain,
    ( c_minus(X1,X2,tc_set(X3)) = c_emptyset
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7022]) ).

cnf(c_0_9960,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_minus(X1,X2,tc_set(X3)) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7023]) ).

cnf(c_0_9961,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7024]) ).

cnf(c_0_9962,plain,
    ( c_List_Orotate1(X1,X2) = X1
    | ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7025]) ).

cnf(c_0_9963,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7026]) ).

cnf(c_0_9964,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7027]) ).

cnf(c_0_9965,plain,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7028]) ).

cnf(c_0_9966,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7029]) ).

cnf(c_0_9967,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7030]) ).

cnf(c_0_9968,plain,
    ( c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7031]) ).

cnf(c_0_9969,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7032]) ).

cnf(c_0_9970,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7033]) ).

cnf(c_0_9971,plain,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Onat(X2),c_IntDef_Onat(X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7034]) ).

cnf(c_0_9972,plain,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7035]) ).

cnf(c_0_9973,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7036]) ).

cnf(c_0_9974,plain,
    c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_inter(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7037]) ).

cnf(c_0_9975,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7038]) ).

cnf(c_0_9976,plain,
    ( c_less(c_0,X1,tc_nat)
    | c_Nat_Opower(X2,X1,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7039]) ).

cnf(c_0_9977,plain,
    c_less(c_0,c_Nat_Opower(X1,c_0,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7040]) ).

cnf(c_0_9978,plain,
    c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7041]) ).

cnf(c_0_9979,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7042]) ).

cnf(c_0_9980,plain,
    ( c_less(c_1,X1,tc_IntDef_Oint)
    | ~ c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7043]) ).

cnf(c_0_9981,plain,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7044]) ).

cnf(c_0_9982,plain,
    ( c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7045]) ).

cnf(c_0_9983,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7046]) ).

cnf(c_0_9984,plain,
    ( c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7047]) ).

cnf(c_0_9985,plain,
    ( c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7048]) ).

cnf(c_0_9986,plain,
    ( c_Nat_Opower(c_0,X1,X2) = c_0
    | ~ c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7049]) ).

cnf(c_0_9987,plain,
    ~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7050]) ).

cnf(c_0_9988,plain,
    ( c_SetInterval_OgreaterThanAtMost(X1,X2,X3) = c_emptyset
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7051]) ).

cnf(c_0_9989,plain,
    ( c_SetInterval_OatLeastLessThan(X1,X2,X3) = c_emptyset
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7052]) ).

cnf(c_0_9990,plain,
    ( c_SetInterval_OatLeastAtMost(X1,X2,X3) = c_emptyset
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7053]) ).

cnf(c_0_9991,plain,
    ( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7054]) ).

cnf(c_0_9992,plain,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7055]) ).

cnf(c_0_9993,plain,
    c_Nat_Osize(c_List_Orotate(X1,X2,X3),tc_List_Olist(X3)) = c_Nat_Osize(X2,tc_List_Olist(X3)),
    inference(split_conjunct,[status(thm)],[c_0_7056]) ).

cnf(c_0_9994,plain,
    c_Nat_Osize(c_Sum__Type_OInr(X1,X2,X3),tc_sum(X3,X2)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7057]) ).

cnf(c_0_9995,plain,
    c_Nat_Osize(c_Sum__Type_OInl(X1,X2,X3),tc_sum(X2,X3)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7058]) ).

cnf(c_0_9996,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_less(X1,c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7059]) ).

cnf(c_0_9997,plain,
    ( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7060]) ).

cnf(c_0_9998,plain,
    ( c_List_Odistinct(c_List_Otake(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7061]) ).

cnf(c_0_9999,plain,
    ( c_List_Odistinct(c_List_Osublist(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7062]) ).

cnf(c_0_10000,plain,
    ( c_List_Odistinct(c_List_Orotate(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7063]) ).

cnf(c_0_10001,plain,
    ( c_List_Odistinct(c_List_Oremove1(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7064]) ).

cnf(c_0_10002,plain,
    ( c_List_Odistinct(c_List_Odrop(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7065]) ).

cnf(c_0_10003,plain,
    ( c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat)
    | ~ c_less(c_1,X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7066]) ).

cnf(c_0_10004,plain,
    ( c_less(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7067]) ).

cnf(c_0_10005,plain,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7068]) ).

cnf(c_0_10006,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7069]) ).

cnf(c_0_10007,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    inference(split_conjunct,[status(thm)],[c_0_7070]) ).

cnf(c_0_10008,plain,
    c_Binomial_Obinomial(c_Suc(X1),c_Suc(X2)) = c_plus(c_Binomial_Obinomial(X1,X2),c_Binomial_Obinomial(X1,c_Suc(X2)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7071]) ).

cnf(c_0_10009,plain,
    ( c_in(X1,c_Message_OsymKeys,tc_nat)
    | ~ c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7072]) ).

cnf(c_0_10010,plain,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_0,c_IntDef_Onat(X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7073]) ).

cnf(c_0_10011,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7074]) ).

cnf(c_0_10012,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7075]) ).

cnf(c_0_10013,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7076]) ).

cnf(c_0_10014,plain,
    ( c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7077]) ).

cnf(c_0_10015,plain,
    ( X1 = c_Datatype_Ooption_OSome(X2,X3)
    | ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7078]) ).

cnf(c_0_10016,plain,
    ( c_minus(X1,c_uminus(X2,X3),X3) = c_plus(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7079]) ).

cnf(c_0_10017,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_0 != c_Numeral_Onumber__of(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7080]) ).

cnf(c_0_10018,plain,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_in(c_Main_Oconcat__eq__Nil__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7081]) ).

cnf(c_0_10019,plain,
    ( c_List_Olist_ONil = c_List_Oconcat(X1,X2)
    | c_in(c_Main_ONil__eq__concat__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7082]) ).

cnf(c_0_10020,plain,
    ( c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat)
    | ~ c_in(X1,c_Message_OsymKeys,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7083]) ).

cnf(c_0_10021,plain,
    ( c_less(c_0,c_IntDef_Onat(X1),tc_nat)
    | ~ c_less(c_0,X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7084]) ).

cnf(c_0_10022,plain,
    ( c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7085]) ).

cnf(c_0_10023,plain,
    ( X1 = c_0
    | c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7086]) ).

cnf(c_0_10024,plain,
    ( c_Divides_Oop_Amod(X1,X2,tc_nat) = X1
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7087]) ).

cnf(c_0_10025,plain,
    ( c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) = c_Suc(c_0)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7088]) ).

cnf(c_0_10026,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7089]) ).

cnf(c_0_10027,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7090]) ).

cnf(c_0_10028,plain,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7091]) ).

cnf(c_0_10029,plain,
    ( c_minus(X1,X2,tc_nat) = c_0
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7092]) ).

cnf(c_0_10030,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_minus(X1,X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7093]) ).

cnf(c_0_10031,plain,
    ( c_div(X1,X2,tc_nat) = c_0
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7094]) ).

cnf(c_0_10032,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7095]) ).

cnf(c_0_10033,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7096]) ).

cnf(c_0_10034,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7097]) ).

cnf(c_0_10035,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7098]) ).

cnf(c_0_10036,plain,
    ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7099]) ).

cnf(c_0_10037,plain,
    ( c_List_Olast(c_append(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7100]) ).

cnf(c_0_10038,plain,
    ( c_List_Olast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7101]) ).

cnf(c_0_10039,plain,
    ( c_List_Ohd(c_append(X1,X2,X3),X3) = c_List_Ohd(X1,X3)
    | X1 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7102]) ).

cnf(c_0_10040,plain,
    ( X1 = c_0
    | c_LOrder_Omeet(X1,c_uminus(X1,X2),X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7103]) ).

cnf(c_0_10041,plain,
    ( X1 = c_0
    | c_LOrder_Ojoin(X1,c_uminus(X1,X2),X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7104]) ).

cnf(c_0_10042,plain,
    c_Nat_Osize(c_List_Otl(X1,X2),tc_List_Olist(X2)) = c_minus(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7105]) ).

cnf(c_0_10043,plain,
    c_Nat_Osize(c_List_Obutlast(X1,X2),tc_List_Olist(X2)) = c_minus(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7106]) ).

cnf(c_0_10044,plain,
    ( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7107]) ).

cnf(c_0_10045,plain,
    c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
    inference(split_conjunct,[status(thm)],[c_0_7108]) ).

cnf(c_0_10046,plain,
    c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
    inference(split_conjunct,[status(thm)],[c_0_7109]) ).

cnf(c_0_10047,plain,
    c_List_Oset(c_List_Orotate(X1,X2,X3),X3) = c_List_Oset(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7110]) ).

cnf(c_0_10048,plain,
    c_List_Oitrev(X1,X2,X3) = c_append(c_List_Orev(X1,X3),X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7111]) ).

cnf(c_0_10049,plain,
    ( c_div(X1,X1,tc_nat) = c_1
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7112]) ).

cnf(c_0_10050,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7113]) ).

cnf(c_0_10051,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7114]) ).

cnf(c_0_10052,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_HOL_Oabs(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7115]) ).

cnf(c_0_10053,plain,
    ( c_HOL_Oinverse(c_Numeral_Onumber__of(X1,X2),X2) = c_divide(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7116]) ).

cnf(c_0_10054,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7117]) ).

cnf(c_0_10055,plain,
    c_in(X1,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_7118]) ).

cnf(c_0_10056,plain,
    c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X3) = c_List_Otake(X2,X1,X3),
    inference(split_conjunct,[status(thm)],[c_0_7119]) ).

cnf(c_0_10057,plain,
    c_List_Olast(c_append(X1,c_List_Olist_ONil,X2),X2) = c_List_Olast(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7120]) ).

cnf(c_0_10058,plain,
    ( ~ c_less(c_HOL_Oabs(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7121]) ).

cnf(c_0_10059,plain,
    ( ~ c_less(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7122]) ).

cnf(c_0_10060,plain,
    ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7123]) ).

cnf(c_0_10061,plain,
    c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7124]) ).

cnf(c_0_10062,plain,
    c_Nat_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7125]) ).

cnf(c_0_10063,plain,
    ( ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7126]) ).

cnf(c_0_10064,plain,
    ( c_Finite__Set_OMin(c_insert(X1,c_emptyset,X2),X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7127]) ).

cnf(c_0_10065,plain,
    ( c_Finite__Set_OMax(c_insert(X1,c_emptyset,X2),X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7128]) ).

cnf(c_0_10066,plain,
    c_Numeral_Obin__mult(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X1,X2),c_Numeral_Obit_OB0),X2),
    inference(split_conjunct,[status(thm)],[c_0_7129]) ).

cnf(c_0_10067,plain,
    ( c_0 = c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7130]) ).

cnf(c_0_10068,plain,
    ( c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7131]) ).

cnf(c_0_10069,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(split_conjunct,[status(thm)],[c_0_7132]) ).

cnf(c_0_10070,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(split_conjunct,[status(thm)],[c_0_7133]) ).

cnf(c_0_10071,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(split_conjunct,[status(thm)],[c_0_7134]) ).

cnf(c_0_10072,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(split_conjunct,[status(thm)],[c_0_7135]) ).

cnf(c_0_10073,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(split_conjunct,[status(thm)],[c_0_7136]) ).

cnf(c_0_10074,plain,
    ( c_List_Olast(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7137]) ).

cnf(c_0_10075,plain,
    ( c_List_Ohd(c_List_Oupt(X1,X2),tc_nat) = X1
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7138]) ).

cnf(c_0_10076,plain,
    ( c_List_Ohd(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7139]) ).

cnf(c_0_10077,plain,
    ~ c_in(c_Public_OpublicKey(X1,X2),c_Message_OsymKeys,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7140]) ).

cnf(c_0_10078,plain,
    ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Oparts(c_Event_OinitState(X2)),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7141]) ).

cnf(c_0_10079,plain,
    c_List_Otl(c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    inference(split_conjunct,[status(thm)],[c_0_7142]) ).

cnf(c_0_10080,plain,
    c_List_Ohd(c_List_Olist_OCons(X1,X2,X3),X3) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7143]) ).

cnf(c_0_10081,plain,
    ( c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7144]) ).

cnf(c_0_10082,plain,
    ( c_divide(X1,c_0,X2) = c_divide(X3,c_0,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7145]) ).

cnf(c_0_10083,plain,
    ( c_divide(c_0,X1,X2) = c_divide(c_0,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7146]) ).

cnf(c_0_10084,plain,
    ( c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7147]) ).

cnf(c_0_10085,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7148]) ).

cnf(c_0_10086,plain,
    ( X1 = c_emptyset
    | c_emptyset != c_Union(X2,X3)
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7149]) ).

cnf(c_0_10087,plain,
    ( X1 = c_emptyset
    | c_Union(X2,X3) != c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7150]) ).

cnf(c_0_10088,plain,
    ( X1 = c_UNIV
    | c_UNIV != c_Inter(X2,X3)
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7151]) ).

cnf(c_0_10089,plain,
    ( X1 = c_UNIV
    | c_Inter(X2,X3) != c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7152]) ).

cnf(c_0_10090,plain,
    c_Nat_Osize(c_Event_Oevent_OSays(X1,X2,X3),tc_Event_Oevent) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7153]) ).

cnf(c_0_10091,plain,
    ( c_List_Oremdups(X1,X2) = X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7154]) ).

cnf(c_0_10092,plain,
    ( c_HOL_Oabs(X1,X2) = c_uminus(X1,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7155]) ).

cnf(c_0_10093,plain,
    c_union(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId,tc_prod(X2,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7156]) ).

cnf(c_0_10094,plain,
    c_Set_Ocontents(c_insert(X1,c_emptyset,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7157]) ).

cnf(c_0_10095,plain,
    c_List_Olast(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7158]) ).

cnf(c_0_10096,plain,
    ( X1 = c_0
    | ~ c_less(c_HOL_Oabs(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7159]) ).

cnf(c_0_10097,plain,
    c_less(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7160]) ).

cnf(c_0_10098,plain,
    c_minus(c_Suc(X1),c_Suc(X2),tc_nat) = c_minus(X1,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7161]) ).

cnf(c_0_10099,plain,
    c_List_Obutlast(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7162]) ).

cnf(c_0_10100,plain,
    ( X1 = c_emptyset
    | c_Finite__Set_Ocard(X1,X2) != c_0
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7163]) ).

cnf(c_0_10101,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_Oused(X3),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7164]) ).

cnf(c_0_10102,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_OinitState(X3),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7165]) ).

cnf(c_0_10103,plain,
    c_Nat_Osize(c_Message_Omsg_OCrypt(X1,X2),tc_Message_Omsg) = c_plus(c_Nat_Osize(X2,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7166]) ).

cnf(c_0_10104,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7167]) ).

cnf(c_0_10105,plain,
    ( c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_uminus(c_1,X1)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7168]) ).

cnf(c_0_10106,plain,
    ( c_SetInterval_OatLeastAtMost(X1,X1,X2) = c_insert(X1,c_emptyset,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7169]) ).

cnf(c_0_10107,plain,
    ( c_times(X1,c_0,X2) = c_times(X3,c_0,X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7170]) ).

cnf(c_0_10108,plain,
    ( c_times(c_0,X1,X2) = c_times(c_0,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7171]) ).

cnf(c_0_10109,plain,
    ( c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7172]) ).

cnf(c_0_10110,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_1
    | ~ c_Parity_Oeven(X2,tc_nat)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7173]) ).

cnf(c_0_10111,plain,
    ( c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_1
    | ~ c_Parity_Oeven(X2,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7174]) ).

cnf(c_0_10112,plain,
    c_Nat_Opower(X1,c_1,tc_set(tc_prod(X2,X2))) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7175]) ).

cnf(c_0_10113,plain,
    c_Nat_Opower(X1,c_0,tc_set(tc_prod(X2,X2))) = c_Relation_OId,
    inference(split_conjunct,[status(thm)],[c_0_7176]) ).

cnf(c_0_10114,plain,
    c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7177]) ).

cnf(c_0_10115,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),c_Numeral_OBit(X2,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,c_Numeral_Obin__succ(X2)),c_Numeral_Obit_OB0),
    inference(split_conjunct,[status(thm)],[c_0_7178]) ).

cnf(c_0_10116,plain,
    ( c_List_Olist_OCons(c_List_Ohd(X1,X2),c_List_Otl(X1,X2),X2) = X1
    | X1 = c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7179]) ).

cnf(c_0_10117,plain,
    ( X1 = c_List_Olist_ONil
    | c_in(c_List_Olast(X1,X2),c_List_Oset(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7180]) ).

cnf(c_0_10118,plain,
    ( X1 = c_List_Olist_ONil
    | c_in(c_List_Ohd(X1,X2),c_List_Oset(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7181]) ).

cnf(c_0_10119,plain,
    c_Event_Oevent_ONotes(X1,X2) != c_Event_Oevent_OSays(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_7182]) ).

cnf(c_0_10120,plain,
    c_Event_Oevent_OSays(X1,X2,X3) != c_Event_Oevent_ONotes(X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_7183]) ).

cnf(c_0_10121,plain,
    c_Event_Oevent_OGets(X1,X2) != c_Event_Oevent_OSays(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_7184]) ).

cnf(c_0_10122,plain,
    c_Event_Oevent_OSays(X1,X2,X3) != c_Event_Oevent_OGets(X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_7185]) ).

cnf(c_0_10123,plain,
    ( c_OrderedGroup_Opprt(X1,X2) = X1
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7186]) ).

cnf(c_0_10124,plain,
    ( c_OrderedGroup_Onprt(X1,X2) = X1
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7187]) ).

cnf(c_0_10125,plain,
    ( c_HOL_Oabs(X1,X2) = X1
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7188]) ).

cnf(c_0_10126,plain,
    ( c_NatArith_Oof__nat(c_Suc(X1),X2) = c_plus(c_NatArith_Oof__nat(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7189]) ).

cnf(c_0_10127,plain,
    ( c_OrderedGroup_Opprt(X1,X2) = c_0
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7190]) ).

cnf(c_0_10128,plain,
    ( c_OrderedGroup_Onprt(X1,X2) = c_0
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7191]) ).

cnf(c_0_10129,plain,
    ( c_Finite__Set_Ocard(c_emptyset,X1) = c_0
    | ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_7192]) ).

cnf(c_0_10130,plain,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_1
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7193]) ).

cnf(c_0_10131,plain,
    ( X1 = c_0
    | X2 = c_0
    | c_divide(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7194]) ).

cnf(c_0_10132,plain,
    ( X1 = X2
    | c_1 != c_divide(X1,X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7195]) ).

cnf(c_0_10133,plain,
    ( X1 = X2
    | c_1 != c_divide(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7196]) ).

cnf(c_0_10134,plain,
    ( X1 = X2
    | c_divide(X2,X1,X3) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7197]) ).

cnf(c_0_10135,plain,
    ( X1 = X2
    | c_divide(X1,X2,X3) != c_1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7198]) ).

cnf(c_0_10136,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),c_Numeral_OBit(X2,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_7199]) ).

cnf(c_0_10137,plain,
    c_times(X1,c_0,tc_nat) = c_times(X2,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7200]) ).

cnf(c_0_10138,plain,
    c_times(c_0,X1,tc_nat) = c_times(c_0,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7201]) ).

cnf(c_0_10139,plain,
    ( X1 = c_0
    | c_Nat_Opower(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7202]) ).

cnf(c_0_10140,plain,
    ( c_emptyset = c_Union(X1,X2)
    | c_in(c_Main_Oempty__Union__conv__1(X1,X2),X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7203]) ).

cnf(c_0_10141,plain,
    ( c_Union(X1,X2) = c_emptyset
    | c_in(c_Main_OUnion__empty__conv__1(X1,X2),X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7204]) ).

cnf(c_0_10142,plain,
    ( c_UNIV = c_Inter(X1,X2)
    | c_in(c_Main_OInter__UNIV__conv__2__1(X1,X2),X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7205]) ).

cnf(c_0_10143,plain,
    ( c_Inter(X1,X2) = c_UNIV
    | c_in(c_Main_OInter__UNIV__conv__1__1(X1,X2),X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7206]) ).

cnf(c_0_10144,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oint(X2) != c_Numeral_Onumber__of(X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7207]) ).

cnf(c_0_10145,plain,
    ( c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7208]) ).

cnf(c_0_10146,plain,
    ( c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_uminus(X3,X2) != c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7209]) ).

cnf(c_0_10147,plain,
    ( X1 = c_uminus(c_Numeral_Onumber__of(X2,X3),X3)
    | c_Numeral_Onumber__of(X2,X3) != c_uminus(X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7210]) ).

cnf(c_0_10148,plain,
    ( X1 = c_0
    | c_0 != c_divide(c_1,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7211]) ).

cnf(c_0_10149,plain,
    ( X1 = c_0
    | c_divide(c_1,X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7212]) ).

cnf(c_0_10150,plain,
    ( c_times(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7213]) ).

cnf(c_0_10151,plain,
    ( c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7214]) ).

cnf(c_0_10152,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),c_Numeral_OBit(X2,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,X2),c_Numeral_Obit_OB1),
    inference(split_conjunct,[status(thm)],[c_0_7215]) ).

cnf(c_0_10153,plain,
    ( c_List_Oupt(X1,X2) = c_List_Olist_ONil
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7216]) ).

cnf(c_0_10154,plain,
    ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7217]) ).

cnf(c_0_10155,plain,
    ( c_1 != c_divide(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7218]) ).

cnf(c_0_10156,plain,
    ( c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7219]) ).

cnf(c_0_10157,plain,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7220]) ).

cnf(c_0_10158,plain,
    ( X1 = c_1
    | X2 = c_0
    | X2 != c_times(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7221]) ).

cnf(c_0_10159,plain,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7222]) ).

cnf(c_0_10160,plain,
    ( X1 = c_1
    | X2 = c_0
    | X2 != c_times(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7223]) ).

cnf(c_0_10161,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(X1,X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7224]) ).

cnf(c_0_10162,plain,
    c_Nat_Osize(c_Message_Omsg_OHash(X1),tc_Message_Omsg) = c_plus(c_Nat_Osize(X1,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7225]) ).

cnf(c_0_10163,plain,
    ( X1 = c_0
    | X2 = c_0
    | c_times(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7226]) ).

cnf(c_0_10164,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7227]) ).

cnf(c_0_10165,plain,
    c_Nat_Osize(c_List_Oupt(X1,X2),tc_List_Olist(tc_nat)) = c_minus(X2,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7228]) ).

cnf(c_0_10166,plain,
    ( X1 = X2
    | c_minus(X1,X2,X3) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7229]) ).

cnf(c_0_10167,plain,
    ( X1 = c_emptyset
    | ~ c_lessequals(X1,c_emptyset,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7230]) ).

cnf(c_0_10168,plain,
    c_Relation_Oconverse(c_Relation_Odiag(X1,X2),X2,X2) = c_Relation_Odiag(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7231]) ).

cnf(c_0_10169,plain,
    c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7232]) ).

cnf(c_0_10170,plain,
    ( c_HOL_Oinverse(c_uminus(X1,X2),X2) = c_uminus(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7233]) ).

cnf(c_0_10171,plain,
    ( c_HOL_Oabs(c_HOL_Oinverse(X1,X2),X2) = c_HOL_Oinverse(c_HOL_Oabs(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7234]) ).

cnf(c_0_10172,plain,
    ( c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_Numeral_Onumber__of(X1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7235]) ).

cnf(c_0_10173,plain,
    ~ c_less(X1,c_emptyset,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7236]) ).

cnf(c_0_10174,plain,
    ( ~ c_less(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7237]) ).

cnf(c_0_10175,plain,
    c_inter(X1,c_uminus(X1,tc_set(X2)),X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7238]) ).

cnf(c_0_10176,plain,
    c_inter(c_uminus(X1,tc_set(X2)),X1,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7239]) ).

cnf(c_0_10177,plain,
    c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2) = c_insert(X1,c_emptyset,X2),
    inference(split_conjunct,[status(thm)],[c_0_7240]) ).

cnf(c_0_10178,plain,
    ( c_IntDef_Oint(c_IntDef_Onat(X1)) = X1
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7241]) ).

cnf(c_0_10179,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7242]) ).

cnf(c_0_10180,plain,
    ( X1 = c_Suc(c_0)
    | ~ c_Divides_Oop_Advd(X1,c_Suc(c_0),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7243]) ).

cnf(c_0_10181,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7244]) ).

cnf(c_0_10182,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_0 != c_Numeral_Onumber__of(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7245]) ).

cnf(c_0_10183,plain,
    ( X1 = c_List_Olist_ONil
    | c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7246]) ).

cnf(c_0_10184,plain,
    ~ c_less(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7247]) ).

cnf(c_0_10185,plain,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_7248]) ).

cnf(c_0_10186,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_Suc(c_0),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7249]) ).

cnf(c_0_10187,plain,
    ( c_times(X1,c_HOL_Oinverse(X1,X2),X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7250]) ).

cnf(c_0_10188,plain,
    ( c_times(c_HOL_Oinverse(X1,X2),X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7251]) ).

cnf(c_0_10189,plain,
    ( X1 = c_List_Olist_ONil
    | X2 = c_0
    | c_List_Otake(X2,X1,X3) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7252]) ).

cnf(c_0_10190,plain,
    ( X1 = c_1
    | c_Suc(c_0) != c_times(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7253]) ).

cnf(c_0_10191,plain,
    ( X1 = c_1
    | c_Suc(c_0) != c_times(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7254]) ).

cnf(c_0_10192,plain,
    ( X1 = c_1
    | c_times(X2,X1,tc_nat) != c_Suc(c_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7255]) ).

cnf(c_0_10193,plain,
    ( X1 = c_1
    | c_times(X1,X2,tc_nat) != c_Suc(c_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7256]) ).

cnf(c_0_10194,plain,
    ( X1 = c_List_Olist_ONil
    | X2 != c_append(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7257]) ).

cnf(c_0_10195,plain,
    ( X1 = c_List_Olist_ONil
    | X2 != c_append(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7258]) ).

cnf(c_0_10196,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7259]) ).

cnf(c_0_10197,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7260]) ).

cnf(c_0_10198,plain,
    ~ c_in(X1,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7261]) ).

cnf(c_0_10199,plain,
    ( ~ c_less(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7262]) ).

cnf(c_0_10200,plain,
    ( ~ c_lessequals(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7263]) ).

cnf(c_0_10201,plain,
    ( X1 = c_0
    | c_less(c_0,c_HOL_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7264]) ).

cnf(c_0_10202,plain,
    ( c_plus(X1,c_uminus(X1,X2),X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7265]) ).

cnf(c_0_10203,plain,
    ( c_plus(c_uminus(X1,X2),X1,X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7266]) ).

cnf(c_0_10204,plain,
    ( X1 = c_emptyset
    | c_union(X2,X1,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7267]) ).

cnf(c_0_10205,plain,
    ( X1 = c_emptyset
    | c_union(X1,X2,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7268]) ).

cnf(c_0_10206,plain,
    ( X1 = c_UNIV
    | c_inter(X2,X1,X3) != c_UNIV ),
    inference(split_conjunct,[status(thm)],[c_0_7269]) ).

cnf(c_0_10207,plain,
    ( X1 = c_UNIV
    | c_inter(X1,X2,X3) != c_UNIV ),
    inference(split_conjunct,[status(thm)],[c_0_7270]) ).

cnf(c_0_10208,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orotate(X2,X1,X3) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7271]) ).

cnf(c_0_10209,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7272]) ).

cnf(c_0_10210,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7273]) ).

cnf(c_0_10211,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_append(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7274]) ).

cnf(c_0_10212,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_append(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7275]) ).

cnf(c_0_10213,plain,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7276]) ).

cnf(c_0_10214,plain,
    ( X1 = c_emptyset
    | c_emptyset != c_Equiv__Relations_Oquotient(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7277]) ).

cnf(c_0_10215,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(split_conjunct,[status(thm)],[c_0_7278]) ).

cnf(c_0_10216,plain,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    inference(split_conjunct,[status(thm)],[c_0_7279]) ).

cnf(c_0_10217,plain,
    ( X1 = c_0
    | X2 = c_0
    | c_times(X1,X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7280]) ).

cnf(c_0_10218,plain,
    ( c_Message_OinvKey(X1) = X1
    | ~ c_in(X1,c_Message_OsymKeys,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7281]) ).

cnf(c_0_10219,plain,
    ( c_lessequals(c_0,c_OrderedGroup_Opprt(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7282]) ).

cnf(c_0_10220,plain,
    ( c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7283]) ).

cnf(c_0_10221,plain,
    ( c_lessequals(c_0,c_HOL_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7284]) ).

cnf(c_0_10222,plain,
    ( c_lessequals(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7285]) ).

cnf(c_0_10223,plain,
    ( c_in(c_NatArith_Oof__nat(X1,X2),c_IntDef_ONats,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7286]) ).

cnf(c_0_10224,plain,
    c_insert(X1,X2,X3) != c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7287]) ).

cnf(c_0_10225,plain,
    c_emptyset != c_insert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7288]) ).

cnf(c_0_10226,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7289]) ).

cnf(c_0_10227,plain,
    c_List_Olist_ONil != c_List_Olist_OCons(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7290]) ).

cnf(c_0_10228,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_7291]) ).

cnf(c_0_10229,plain,
    c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),X2) = c_Message_OHPair(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7292]) ).

cnf(c_0_10230,plain,
    c_Message_OHPair(X1,X2) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[c_0_7293]) ).

cnf(c_0_10231,plain,
    ( c_IntDef_Onat(X1) = c_0
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7294]) ).

cnf(c_0_10232,plain,
    ( X1 = c_0
    | c_plus(X2,X1,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7295]) ).

cnf(c_0_10233,plain,
    ( X1 = c_0
    | c_plus(X1,X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7296]) ).

cnf(c_0_10234,plain,
    c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7297]) ).

cnf(c_0_10235,plain,
    c_in(c_List_Olist_ONil,c_List_Olists(X1,X2),tc_List_Olist(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7298]) ).

cnf(c_0_10236,plain,
    c_in(c_List_Oset(X1,X2),c_Finite__Set_OFinites,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7299]) ).

cnf(c_0_10237,plain,
    ( c_IntDef_Oof__int(c_uminus(X1,tc_IntDef_Oint),X2) = c_uminus(c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7300]) ).

cnf(c_0_10238,plain,
    ~ c_in(X1,c_emptyset,X2),
    inference(split_conjunct,[status(thm)],[c_0_7301]) ).

cnf(c_0_10239,plain,
    ~ c_List_Oop_Amem(X1,c_List_Olist_ONil,X2),
    inference(split_conjunct,[status(thm)],[c_0_7302]) ).

cnf(c_0_10240,plain,
    ~ c_less(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7303]) ).

cnf(c_0_10241,plain,
    ( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7304]) ).

cnf(c_0_10242,plain,
    ( c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_1
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7305]) ).

cnf(c_0_10243,plain,
    ( c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7306]) ).

cnf(c_0_10244,plain,
    ( c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7307]) ).

cnf(c_0_10245,plain,
    ( c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7308]) ).

cnf(c_0_10246,plain,
    ( c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7309]) ).

cnf(c_0_10247,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7310]) ).

cnf(c_0_10248,plain,
    ( X1 = c_0
    | ~ c_lessequals(X1,c_0,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7311]) ).

cnf(c_0_10249,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7312]) ).

cnf(c_0_10250,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7313]) ).

cnf(c_0_10251,plain,
    ( X1 = c_emptyset
    | c_in(c_Main_Oall__not__in__conv__1(X1,X2),X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7314]) ).

cnf(c_0_10252,plain,
    c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7315]) ).

cnf(c_0_10253,plain,
    c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7316]) ).

cnf(c_0_10254,plain,
    ( c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X1),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7317]) ).

cnf(c_0_10255,plain,
    ~ c_less(X1,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7318]) ).

cnf(c_0_10256,plain,
    c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7319]) ).

cnf(c_0_10257,plain,
    c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7320]) ).

cnf(c_0_10258,plain,
    c_in(c_SetInterval_OlessThan(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_7321]) ).

cnf(c_0_10259,plain,
    c_in(c_SetInterval_OatMost(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_7322]) ).

cnf(c_0_10260,plain,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    inference(split_conjunct,[status(thm)],[c_0_7323]) ).

cnf(c_0_10261,plain,
    ~ c_less(c_0,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7324]) ).

cnf(c_0_10262,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orev(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7325]) ).

cnf(c_0_10263,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate1(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7326]) ).

cnf(c_0_10264,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oused(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7327]) ).

cnf(c_0_10265,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_OinitState(X1),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7328]) ).

cnf(c_0_10266,plain,
    ( X1 = c_0
    | c_lessequals(X1,X2,tc_nat)
    | c_List_Oupt(X2,X1) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7329]) ).

cnf(c_0_10267,plain,
    ( X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3))
    | c_Message_Omsg_OMPair(X1,X4) != c_Message_OHPair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7330]) ).

cnf(c_0_10268,plain,
    ( X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3))
    | c_Message_OHPair(X2,X3) != c_Message_Omsg_OMPair(X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7331]) ).

cnf(c_0_10269,plain,
    c_Message_Oparts(c_Message_Osynth(X1)) = c_union(c_Message_Oparts(X1),c_Message_Osynth(X1),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7332]) ).

cnf(c_0_10270,plain,
    c_Message_Oanalz(c_Message_Osynth(X1)) = c_union(c_Message_Oanalz(X1),c_Message_Osynth(X1),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7333]) ).

cnf(c_0_10271,plain,
    c_Numeral_Obin__mult(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2) = c_Numeral_OBit(c_Numeral_Obin__mult(X1,X2),c_Numeral_Obit_OB0),
    inference(split_conjunct,[status(thm)],[c_0_7334]) ).

cnf(c_0_10272,plain,
    ( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7335]) ).

cnf(c_0_10273,plain,
    ( c_minus(c_0,X1,X2) = c_uminus(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7336]) ).

cnf(c_0_10274,plain,
    ( c_List_Oupt(X1,c_Suc(X2)) = c_List_Olist_ONil
    | c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7337]) ).

cnf(c_0_10275,plain,
    ( c_Finite__Set_Ocard(X1,X2) = c_0
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7338]) ).

cnf(c_0_10276,plain,
    c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7339]) ).

cnf(c_0_10277,plain,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7340]) ).

cnf(c_0_10278,plain,
    c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7341]) ).

cnf(c_0_10279,plain,
    c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7342]) ).

cnf(c_0_10280,plain,
    ( c_1 = c_divide(X1,X1,X2)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7343]) ).

cnf(c_0_10281,plain,
    ( c_divide(X1,X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7344]) ).

cnf(c_0_10282,plain,
    c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7345]) ).

cnf(c_0_10283,plain,
    c_List_Olistset(c_List_Olist_ONil,X1) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7346]) ).

cnf(c_0_10284,plain,
    c_Public_OpublicKey(X1,X2) != c_Message_OinvKey(c_Public_OpublicKey(X3,X4)),
    inference(split_conjunct,[status(thm)],[c_0_7347]) ).

cnf(c_0_10285,plain,
    c_Message_OinvKey(c_Public_OpublicKey(X1,X2)) != c_Public_OpublicKey(X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_7348]) ).

cnf(c_0_10286,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7349]) ).

cnf(c_0_10287,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7350]) ).

cnf(c_0_10288,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7351]) ).

cnf(c_0_10289,plain,
    ( c_0 = c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7352]) ).

cnf(c_0_10290,plain,
    ( c_0 = c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7353]) ).

cnf(c_0_10291,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7354]) ).

cnf(c_0_10292,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7355]) ).

cnf(c_0_10293,plain,
    c_IntDef_Oint(c_Suc(X1)) = c_plus(c_1,c_IntDef_Oint(X1),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7356]) ).

cnf(c_0_10294,plain,
    ( c_divide(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7357]) ).

cnf(c_0_10295,plain,
    ( c_divide(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7358]) ).

cnf(c_0_10296,plain,
    ( c_uminus(c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_SetInterval_OatLeast(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7359]) ).

cnf(c_0_10297,plain,
    ( c_uminus(c_SetInterval_OgreaterThan(X1,X2),tc_set(X2)) = c_SetInterval_OatMost(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7360]) ).

cnf(c_0_10298,plain,
    ( c_uminus(c_SetInterval_OatMost(X1,X2),tc_set(X2)) = c_SetInterval_OgreaterThan(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7361]) ).

cnf(c_0_10299,plain,
    ( c_uminus(c_SetInterval_OatLeast(X1,X2),tc_set(X2)) = c_SetInterval_OlessThan(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7362]) ).

cnf(c_0_10300,plain,
    ( c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7363]) ).

cnf(c_0_10301,plain,
    ( c_Nat_Opower(c_0,c_Suc(X1),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7364]) ).

cnf(c_0_10302,plain,
    c_Nat_Osize(c_List_Orotate1(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7365]) ).

cnf(c_0_10303,plain,
    c_Nat_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7366]) ).

cnf(c_0_10304,plain,
    ( c_0 = c_divide(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7367]) ).

cnf(c_0_10305,plain,
    ( c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7368]) ).

cnf(c_0_10306,plain,
    ( c_divide(c_0,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7369]) ).

cnf(c_0_10307,plain,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7370]) ).

cnf(c_0_10308,plain,
    ( X1 = X2
    | c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7371]) ).

cnf(c_0_10309,plain,
    c_in(c_Message_Omsg_ONumber(X1),c_Message_Osynth(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7372]) ).

cnf(c_0_10310,plain,
    c_in(c_Message_Omsg_OAgent(X1),c_Message_Osynth(X2),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_7373]) ).

cnf(c_0_10311,plain,
    ( c_List_Odistinct(c_List_Orev(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7374]) ).

cnf(c_0_10312,plain,
    ( c_List_Odistinct(c_List_Orotate1(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7375]) ).

cnf(c_0_10313,plain,
    ( c_Orderings_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7376]) ).

cnf(c_0_10314,plain,
    ( c_Orderings_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7377]) ).

cnf(c_0_10315,plain,
    ( c_LOrder_Omeet(X1,X1,X2) = X1
    | ~ class_LOrder_Omeet__semilorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7378]) ).

cnf(c_0_10316,plain,
    ( c_LOrder_Ojoin(X1,X1,X2) = X1
    | ~ class_LOrder_Ojoin__semilorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7379]) ).

cnf(c_0_10317,plain,
    ( c_IntDef_Oint(c_IntDef_Onat(X1)) = c_0
    | c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7380]) ).

cnf(c_0_10318,plain,
    ( c_minus(X1,X1,X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7381]) ).

cnf(c_0_10319,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7382]) ).

cnf(c_0_10320,plain,
    ( X1 = c_times(c_1,X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7383]) ).

cnf(c_0_10321,plain,
    ( X1 = c_times(X1,c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7384]) ).

cnf(c_0_10322,plain,
    ( c_divide(X1,c_1,X2) = X1
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7385]) ).

cnf(c_0_10323,plain,
    ( c_Nat_Opower(X1,c_1,X2) = X1
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7386]) ).

cnf(c_0_10324,plain,
    ( c_times(X1,c_1,X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7387]) ).

cnf(c_0_10325,plain,
    ( c_times(c_1,X1,X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7388]) ).

cnf(c_0_10326,plain,
    ( c_minus(X1,c_0,X2) = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7389]) ).

cnf(c_0_10327,plain,
    ( c_plus(c_0,X1,X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7390]) ).

cnf(c_0_10328,plain,
    ( c_plus(X1,c_0,X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7391]) ).

cnf(c_0_10329,plain,
    ( c_HOL_Oabs(c_uminus(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7392]) ).

cnf(c_0_10330,plain,
    ( c_HOL_Oabs(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7393]) ).

cnf(c_0_10331,plain,
    c_minus(X1,X1,tc_set(X2)) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7394]) ).

cnf(c_0_10332,plain,
    c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7395]) ).

cnf(c_0_10333,plain,
    ( X1 = X2
    | c_HOL_Oinverse(X1,X3) != c_HOL_Oinverse(X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7396]) ).

cnf(c_0_10334,plain,
    c_lessequals(X1,X1,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7397]) ).

cnf(c_0_10335,plain,
    ( c_times(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7398]) ).

cnf(c_0_10336,plain,
    ( c_times(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7399]) ).

cnf(c_0_10337,plain,
    ( c_0 = c_times(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7400]) ).

cnf(c_0_10338,plain,
    ( c_0 = c_times(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7401]) ).

cnf(c_0_10339,plain,
    ( c_Nat_Opower(X1,c_0,X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7402]) ).

cnf(c_0_10340,plain,
    ( c_Nat_Opower(c_1,X1,X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7403]) ).

cnf(c_0_10341,plain,
    c_minus(X1,c_emptyset,tc_set(X2)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7404]) ).

cnf(c_0_10342,plain,
    c_lessequals(X1,c_UNIV,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7405]) ).

cnf(c_0_10343,plain,
    c_minus(c_emptyset,X1,tc_set(X2)) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7406]) ).

cnf(c_0_10344,plain,
    c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7407]) ).

cnf(c_0_10345,plain,
    c_minus(X1,c_UNIV,tc_set(X2)) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7408]) ).

cnf(c_0_10346,plain,
    c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7409]) ).

cnf(c_0_10347,plain,
    c_lessequals(c_emptyset,X1,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_7410]) ).

cnf(c_0_10348,plain,
    c_less(X1,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7411]) ).

cnf(c_0_10349,plain,
    ( c_lessequals(c_0,c_1,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7412]) ).

cnf(c_0_10350,plain,
    ( c_less(c_0,c_1,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7413]) ).

cnf(c_0_10351,plain,
    ( c_in(c_1,c_IntDef_ONats,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7414]) ).

cnf(c_0_10352,plain,
    ( c_in(c_0,c_IntDef_ONats,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7415]) ).

cnf(c_0_10353,plain,
    ( c_in(c_1,c_IntDef_OInts,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7416]) ).

cnf(c_0_10354,plain,
    ( c_in(c_0,c_IntDef_OInts,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7417]) ).

cnf(c_0_10355,plain,
    ( c_IntDef_Oof__int(c_NatArith_Oof__nat(X1,tc_IntDef_Oint),X2) = c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7418]) ).

cnf(c_0_10356,plain,
    c_in(c_Public_OshrK(X1),c_Message_OsymKeys,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7419]) ).

cnf(c_0_10357,plain,
    c_lessequals(c_emptyset,c_emptyset,tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7420]) ).

cnf(c_0_10358,plain,
    c_Numeral_Obin__minus(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X1)),c_Numeral_Obit_OB1),
    inference(split_conjunct,[status(thm)],[c_0_7421]) ).

cnf(c_0_10359,plain,
    c_lessequals(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7422]) ).

cnf(c_0_10360,plain,
    c_less(c_0,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7423]) ).

cnf(c_0_10361,plain,
    c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7424]) ).

cnf(c_0_10362,plain,
    c_div(X1,c_Suc(c_0),tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7425]) ).

cnf(c_0_10363,plain,
    c_Divides_Oop_Amod(X1,c_Suc(c_0),tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7426]) ).

cnf(c_0_10364,plain,
    c_Divides_Oop_Advd(c_Suc(c_0),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7427]) ).

cnf(c_0_10365,plain,
    ( c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7428]) ).

cnf(c_0_10366,plain,
    c_union(X1,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7429]) ).

cnf(c_0_10367,plain,
    c_inter(X1,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7430]) ).

cnf(c_0_10368,plain,
    ( c_HOL_Oinverse(c_HOL_Oinverse(X1,X2),X2) = X1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7431]) ).

cnf(c_0_10369,plain,
    c_less(c_0,c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7432]) ).

cnf(c_0_10370,plain,
    ( c_div(X1,X1,tc_IntDef_Oint) = c_1
    | X1 = c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7433]) ).

cnf(c_0_10371,plain,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7434]) ).

cnf(c_0_10372,plain,
    ( X1 = c_IntDef_Onat(c_Numeral_Onumber__of(X2,tc_IntDef_Oint))
    | c_IntDef_Oint(X1) != c_Numeral_Onumber__of(X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_7435]) ).

cnf(c_0_10373,plain,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7436]) ).

cnf(c_0_10374,plain,
    c_union(X1,c_emptyset,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7437]) ).

cnf(c_0_10375,plain,
    c_union(c_emptyset,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7438]) ).

cnf(c_0_10376,plain,
    c_inter(X1,c_UNIV,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7439]) ).

cnf(c_0_10377,plain,
    c_inter(c_UNIV,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7440]) ).

cnf(c_0_10378,plain,
    c_List_Oset(c_List_Orotate1(X1,X2),X2) = c_List_Oset(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7441]) ).

cnf(c_0_10379,plain,
    c_List_Oset(c_List_Orev(X1,X2),X2) = c_List_Oset(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7442]) ).

cnf(c_0_10380,plain,
    c_List_Oset(c_List_Oremdups(X1,X2),X2) = c_List_Oset(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7443]) ).

cnf(c_0_10381,plain,
    X1 = c_append(X1,c_List_Olist_ONil,X2),
    inference(split_conjunct,[status(thm)],[c_0_7444]) ).

cnf(c_0_10382,plain,
    X1 = c_append(c_List_Olist_ONil,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7445]) ).

cnf(c_0_10383,plain,
    c_List_Oitrev(c_List_Olist_ONil,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7446]) ).

cnf(c_0_10384,plain,
    c_List_Odrop(c_0,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7447]) ).

cnf(c_0_10385,plain,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7448]) ).

cnf(c_0_10386,plain,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7449]) ).

cnf(c_0_10387,plain,
    c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7450]) ).

cnf(c_0_10388,plain,
    c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7451]) ).

cnf(c_0_10389,plain,
    c_Message_OinvKey(c_Public_OpublicKey(X1,X2)) != c_Public_OshrK(X3),
    inference(split_conjunct,[status(thm)],[c_0_7452]) ).

cnf(c_0_10390,plain,
    c_Public_OshrK(X1) != c_Message_OinvKey(c_Public_OpublicKey(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_7453]) ).

cnf(c_0_10391,plain,
    ( X1 = X2
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7454]) ).

cnf(c_0_10392,plain,
    ( X1 = X2
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7455]) ).

cnf(c_0_10393,plain,
    ( X1 = X2
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7456]) ).

cnf(c_0_10394,plain,
    ( X1 = X2
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7457]) ).

cnf(c_0_10395,plain,
    ( X1 = X2
    | c_uminus(X1,X3) != c_uminus(X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7458]) ).

cnf(c_0_10396,plain,
    ( X1 = X2
    | c_NatArith_Oof__nat(X1,X3) != c_NatArith_Oof__nat(X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7459]) ).

cnf(c_0_10397,plain,
    ( X1 = X2
    | c_IntDef_Oof__int(X1,X3) != c_IntDef_Oof__int(X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7460]) ).

cnf(c_0_10398,plain,
    ( c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7461]) ).

cnf(c_0_10399,plain,
    c_union(X1,c_UNIV,X2) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7462]) ).

cnf(c_0_10400,plain,
    c_union(c_UNIV,X1,X2) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7463]) ).

cnf(c_0_10401,plain,
    c_inter(X1,c_emptyset,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7464]) ).

cnf(c_0_10402,plain,
    c_inter(c_emptyset,X1,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7465]) ).

cnf(c_0_10403,plain,
    c_Relation_Oconverse(c_Relation_OId,X1,X1) = c_Relation_OId,
    inference(split_conjunct,[status(thm)],[c_0_7466]) ).

cnf(c_0_10404,plain,
    c_Relation_ORange(c_emptyset,X1,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7467]) ).

cnf(c_0_10405,plain,
    c_Relation_ORange(c_Relation_OId,X1,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7468]) ).

cnf(c_0_10406,plain,
    c_Relation_ODomain(c_emptyset,X1,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7469]) ).

cnf(c_0_10407,plain,
    c_Relation_ODomain(c_Relation_OId,X1,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7470]) ).

cnf(c_0_10408,plain,
    ( X1 = c_0
    | c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7471]) ).

cnf(c_0_10409,plain,
    c_minus(X1,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7472]) ).

cnf(c_0_10410,plain,
    c_List_Otake(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7473]) ).

cnf(c_0_10411,plain,
    c_List_Otake(c_0,X1,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7474]) ).

cnf(c_0_10412,plain,
    c_List_Osublist(c_List_Olist_ONil,X1,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7475]) ).

cnf(c_0_10413,plain,
    c_List_Osublist(X1,c_emptyset,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7476]) ).

cnf(c_0_10414,plain,
    c_List_Orotate(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7477]) ).

cnf(c_0_10415,plain,
    c_List_Oreplicate(c_0,X1,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7478]) ).

cnf(c_0_10416,plain,
    c_List_Oremove1(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7479]) ).

cnf(c_0_10417,plain,
    c_List_Olist__inter(c_List_Olist_ONil,X1,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7480]) ).

cnf(c_0_10418,plain,
    c_List_Olexn(X1,c_0,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7481]) ).

cnf(c_0_10419,plain,
    c_List_Odrop(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7482]) ).

cnf(c_0_10420,plain,
    c_Divides_Oop_Amod(X1,X1,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7483]) ).

cnf(c_0_10421,plain,
    c_Divides_Oop_Advd(X1,X1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7484]) ).

cnf(c_0_10422,plain,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7485]) ).

cnf(c_0_10423,plain,
    c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7486]) ).

cnf(c_0_10424,plain,
    c_Divides_Oop_Amod(X1,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7487]) ).

cnf(c_0_10425,plain,
    c_Divides_Oop_Advd(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7488]) ).

cnf(c_0_10426,plain,
    c_in(X1,c_UNIV,X2),
    inference(split_conjunct,[status(thm)],[c_0_7489]) ).

cnf(c_0_10427,plain,
    c_minus(X1,c_0,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7490]) ).

cnf(c_0_10428,plain,
    c_plus(c_0,X1,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7491]) ).

cnf(c_0_10429,plain,
    c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7492]) ).

cnf(c_0_10430,plain,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    inference(split_conjunct,[status(thm)],[c_0_7493]) ).

cnf(c_0_10431,plain,
    c_Orderings_Omax(X1,c_0,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7494]) ).

cnf(c_0_10432,plain,
    c_Orderings_Omax(c_0,X1,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7495]) ).

cnf(c_0_10433,plain,
    c_plus(X1,c_0,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7496]) ).

cnf(c_0_10434,plain,
    c_div(X1,c_1,tc_IntDef_Oint) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7497]) ).

cnf(c_0_10435,plain,
    c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7498]) ).

cnf(c_0_10436,plain,
    c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7499]) ).

cnf(c_0_10437,plain,
    c_union(c_emptyset,c_emptyset,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7500]) ).

cnf(c_0_10438,plain,
    c_inter(c_UNIV,c_UNIV,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7501]) ).

cnf(c_0_10439,plain,
    c_Nat_Opower(X1,c_0,tc_nat) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_7502]) ).

cnf(c_0_10440,plain,
    c_times(c_0,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7503]) ).

cnf(c_0_10441,plain,
    c_times(X1,c_0,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7504]) ).

cnf(c_0_10442,plain,
    c_Orderings_Omin(X1,c_0,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7505]) ).

cnf(c_0_10443,plain,
    c_Orderings_Omin(c_0,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7506]) ).

cnf(c_0_10444,plain,
    c_minus(c_0,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7507]) ).

cnf(c_0_10445,plain,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7508]) ).

cnf(c_0_10446,plain,
    c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_7509]) ).

cnf(c_0_10447,plain,
    c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7510]) ).

cnf(c_0_10448,plain,
    c_Divides_Oop_Amod(X1,c_1,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7511]) ).

cnf(c_0_10449,plain,
    c_div(c_0,X1,tc_IntDef_Oint) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7512]) ).

cnf(c_0_10450,plain,
    c_Nat_Opower(X1,c_0,tc_IntDef_Oint) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_7513]) ).

cnf(c_0_10451,plain,
    c_Divides_Oop_Amod(c_0,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7514]) ).

cnf(c_0_10452,plain,
    c_div(c_0,X1,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7515]) ).

cnf(c_0_10453,plain,
    c_div(X1,c_0,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7516]) ).

cnf(c_0_10454,plain,
    c_lessequals(c_0,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7517]) ).

cnf(c_0_10455,plain,
    c_Divides_Oop_Advd(c_1,X1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7518]) ).

cnf(c_0_10456,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7519]) ).

cnf(c_0_10457,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7520]) ).

cnf(c_0_10458,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7521]) ).

cnf(c_0_10459,plain,
    ( c_uminus(c_uminus(c_1,X1),X1) = c_1
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7522]) ).

cnf(c_0_10460,plain,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7523]) ).

cnf(c_0_10461,plain,
    ( X1 = c_uminus(c_1,X2)
    | c_uminus(X1,X2) != c_1
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7524]) ).

cnf(c_0_10462,plain,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    inference(split_conjunct,[status(thm)],[c_0_7525]) ).

cnf(c_0_10463,plain,
    ( ~ c_Parity_Oeven(c_Suc(X1),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7526]) ).

cnf(c_0_10464,plain,
    c_less(c_0,c_1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7527]) ).

cnf(c_0_10465,plain,
    c_lessequals(c_0,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7528]) ).

cnf(c_0_10466,plain,
    c_plus(c_0,c_0,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7529]) ).

cnf(c_0_10467,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7530]) ).

cnf(c_0_10468,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7531]) ).

cnf(c_0_10469,plain,
    c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,X1)) != c_Public_OshrK(X2),
    inference(split_conjunct,[status(thm)],[c_0_7532]) ).

cnf(c_0_10470,plain,
    ( c_uminus(c_uminus(X1,X2),X2) = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7533]) ).

cnf(c_0_10471,plain,
    ( X1 = X2
    | c_Public_OpublicKey(X3,X1) != c_Public_OpublicKey(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7534]) ).

cnf(c_0_10472,plain,
    ( X1 = X2
    | c_Public_OpublicKey(X1,X3) != c_Public_OpublicKey(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7535]) ).

cnf(c_0_10473,plain,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X3,X1) != c_Message_OHPair(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7536]) ).

cnf(c_0_10474,plain,
    ( X1 = X2
    | c_Message_OHPair(X3,X2) != c_Message_Omsg_OMPair(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7537]) ).

cnf(c_0_10475,plain,
    ( X1 = X2
    | c_Message_OHPair(X3,X1) != c_Message_OHPair(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7538]) ).

cnf(c_0_10476,plain,
    ( X1 = X2
    | c_Message_OHPair(X1,X3) != c_Message_OHPair(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7539]) ).

cnf(c_0_10477,plain,
    ( X1 = X2
    | c_Event_Oevent_ONotes(X3,X1) != c_Event_Oevent_ONotes(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7540]) ).

cnf(c_0_10478,plain,
    ( X1 = X2
    | c_Event_Oevent_ONotes(X1,X3) != c_Event_Oevent_ONotes(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7541]) ).

cnf(c_0_10479,plain,
    ( X1 = X2
    | c_Event_Oevent_OGets(X3,X1) != c_Event_Oevent_OGets(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7542]) ).

cnf(c_0_10480,plain,
    ( X1 = X2
    | c_Event_Oevent_OGets(X1,X3) != c_Event_Oevent_OGets(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7543]) ).

cnf(c_0_10481,plain,
    ( X1 = X2
    | c_Message_Omsg_OCrypt(X3,X1) != c_Message_Omsg_OCrypt(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7544]) ).

cnf(c_0_10482,plain,
    ( X1 = X2
    | c_Message_Omsg_OCrypt(X1,X3) != c_Message_Omsg_OCrypt(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7545]) ).

cnf(c_0_10483,plain,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X3,X1) != c_Message_Omsg_OMPair(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7546]) ).

cnf(c_0_10484,plain,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X1,X3) != c_Message_Omsg_OMPair(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7547]) ).

cnf(c_0_10485,plain,
    ( X1 = X2
    | c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7548]) ).

cnf(c_0_10486,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7549]) ).

cnf(c_0_10487,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7550]) ).

cnf(c_0_10488,plain,
    ( X1 = X2
    | c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7551]) ).

cnf(c_0_10489,plain,
    c_Nat_Osize(c_Datatype_Ooption_OSome(X1,X2),tc_Datatype_Ooption(X2)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7552]) ).

cnf(c_0_10490,plain,
    c_Numeral_Obin__succ(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X1),c_Numeral_Obit_OB0),
    inference(split_conjunct,[status(thm)],[c_0_7553]) ).

cnf(c_0_10491,plain,
    c_Numeral_Obin__pred(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X1),c_Numeral_Obit_OB1),
    inference(split_conjunct,[status(thm)],[c_0_7554]) ).

cnf(c_0_10492,plain,
    c_Numeral_Obin__minus(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X1),c_Numeral_Obit_OB0),
    inference(split_conjunct,[status(thm)],[c_0_7555]) ).

cnf(c_0_10493,plain,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7556]) ).

cnf(c_0_10494,plain,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7557]) ).

cnf(c_0_10495,plain,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7558]) ).

cnf(c_0_10496,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7559]) ).

cnf(c_0_10497,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OCrypt(X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_7560]) ).

cnf(c_0_10498,plain,
    c_Message_Omsg_OCrypt(X1,X2) != c_Message_OHPair(X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_7561]) ).

cnf(c_0_10499,plain,
    c_Event_Oevent_ONotes(X1,X2) != c_Event_Oevent_OGets(X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_7562]) ).

cnf(c_0_10500,plain,
    c_Event_Oevent_OGets(X1,X2) != c_Event_Oevent_ONotes(X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_7563]) ).

cnf(c_0_10501,plain,
    ( X1 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X1,X2),X2)
    | X1 = c_Datatype_Ooption_ONone ),
    inference(split_conjunct,[status(thm)],[c_0_7564]) ).

cnf(c_0_10502,plain,
    ( X1 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X1,X2),X2)
    | X1 = c_Datatype_Ooption_ONone ),
    inference(split_conjunct,[status(thm)],[c_0_7565]) ).

cnf(c_0_10503,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) = c_1
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7566]) ).

cnf(c_0_10504,plain,
    ( c_IntDef_Oof__int(c_IntDef_Oint(X1),X2) = c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7567]) ).

cnf(c_0_10505,plain,
    c_Union(c_Pow(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7568]) ).

cnf(c_0_10506,plain,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7569]) ).

cnf(c_0_10507,plain,
    c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7570]) ).

cnf(c_0_10508,plain,
    c_List_Odistinct(c_List_Oremdups(X1,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_7571]) ).

cnf(c_0_10509,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat) = c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_7572]) ).

cnf(c_0_10510,plain,
    c_Numeral_Obin__succ(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(X1,c_Numeral_Obit_OB1),
    inference(split_conjunct,[status(thm)],[c_0_7573]) ).

cnf(c_0_10511,plain,
    c_Numeral_Obin__pred(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(X1,c_Numeral_Obit_OB0),
    inference(split_conjunct,[status(thm)],[c_0_7574]) ).

cnf(c_0_10512,plain,
    c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7575]) ).

cnf(c_0_10513,plain,
    c_IntDef_Onat(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7576]) ).

cnf(c_0_10514,plain,
    c_Nat_Osize(c_Event_Oevent_ONotes(X1,X2),tc_Event_Oevent) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7577]) ).

cnf(c_0_10515,plain,
    c_Nat_Osize(c_Event_Oevent_OGets(X1,X2),tc_Event_Oevent) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7578]) ).

cnf(c_0_10516,plain,
    c_List_Odistinct(c_List_Oupt(X1,X2),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_7579]) ).

cnf(c_0_10517,plain,
    c_Nat_Osize(c_List_Ochar_OChar(X1,X2),tc_List_Ochar) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7580]) ).

cnf(c_0_10518,plain,
    ( X1 = c_0
    | c_HOL_Oinverse(X1,X2) != c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7581]) ).

cnf(c_0_10519,plain,
    ( X1 = c_1
    | c_HOL_Oinverse(X1,X2) != c_1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7582]) ).

cnf(c_0_10520,plain,
    ( X1 = c_0
    | c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) != c_IntDef_Oint(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7583]) ).

cnf(c_0_10521,plain,
    ( X1 = c_0
    | c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint) != c_IntDef_Oint(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7584]) ).

cnf(c_0_10522,plain,
    ( c_emptyset = c_Union(X1,X2)
    | c_Main_Oempty__Union__conv__1(X1,X2) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7585]) ).

cnf(c_0_10523,plain,
    ( c_Union(X1,X2) = c_emptyset
    | c_Main_OUnion__empty__conv__1(X1,X2) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7586]) ).

cnf(c_0_10524,plain,
    ( c_UNIV = c_Inter(X1,X2)
    | c_Main_OInter__UNIV__conv__2__1(X1,X2) != c_UNIV ),
    inference(split_conjunct,[status(thm)],[c_0_7587]) ).

cnf(c_0_10525,plain,
    ( c_Inter(X1,X2) = c_UNIV
    | c_Main_OInter__UNIV__conv__1__1(X1,X2) != c_UNIV ),
    inference(split_conjunct,[status(thm)],[c_0_7588]) ).

cnf(c_0_10526,plain,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_Main_Oconcat__eq__Nil__conv__1(X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7589]) ).

cnf(c_0_10527,plain,
    ( c_List_Olist_ONil = c_List_Oconcat(X1,X2)
    | c_Main_ONil__eq__concat__conv__1(X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7590]) ).

cnf(c_0_10528,plain,
    c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7591]) ).

cnf(c_0_10529,plain,
    ( X1 = c_List_Olist_ONil
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7592]) ).

cnf(c_0_10530,plain,
    c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_7593]) ).

cnf(c_0_10531,plain,
    ( c_uminus(c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7594]) ).

cnf(c_0_10532,plain,
    ( c_Parity_Oeven(c_Suc(X1),tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_7595]) ).

cnf(c_0_10533,plain,
    ( X1 = c_0
    | c_uminus(X1,X2) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7596]) ).

cnf(c_0_10534,plain,
    ( c_0 = X1
    | c_0 != c_uminus(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7597]) ).

cnf(c_0_10535,plain,
    ( X1 = c_0
    | c_HOL_Oabs(X1,X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7598]) ).

cnf(c_0_10536,plain,
    ( X1 = c_0
    | c_0 != c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7599]) ).

cnf(c_0_10537,plain,
    ( X1 = c_0
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7600]) ).

cnf(c_0_10538,plain,
    ( c_0 = X1
    | c_0 != c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7601]) ).

cnf(c_0_10539,plain,
    ( X1 = c_0
    | c_IntDef_Oof__int(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7602]) ).

cnf(c_0_10540,plain,
    ( c_0 = X1
    | c_0 != c_IntDef_Oof__int(X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7603]) ).

cnf(c_0_10541,plain,
    class_Nat_Opower(tc_fun(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_7604]) ).

cnf(c_0_10542,plain,
    ~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7605]) ).

cnf(c_0_10543,plain,
    c_Public_OpublicKey(X1,X2) != c_Public_OshrK(X3),
    inference(split_conjunct,[status(thm)],[c_0_7606]) ).

cnf(c_0_10544,plain,
    c_Public_OshrK(X1) != c_Public_OpublicKey(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7607]) ).

cnf(c_0_10545,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_ONumber(X3),
    inference(split_conjunct,[status(thm)],[c_0_7608]) ).

cnf(c_0_10546,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_ONonce(X3),
    inference(split_conjunct,[status(thm)],[c_0_7609]) ).

cnf(c_0_10547,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OKey(X3),
    inference(split_conjunct,[status(thm)],[c_0_7610]) ).

cnf(c_0_10548,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OHash(X3),
    inference(split_conjunct,[status(thm)],[c_0_7611]) ).

cnf(c_0_10549,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OAgent(X3),
    inference(split_conjunct,[status(thm)],[c_0_7612]) ).

cnf(c_0_10550,plain,
    c_Message_Omsg_OHash(X1) != c_Message_OHPair(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7613]) ).

cnf(c_0_10551,plain,
    c_Message_Omsg_OKey(X1) != c_Message_OHPair(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7614]) ).

cnf(c_0_10552,plain,
    c_Message_Omsg_ONumber(X1) != c_Message_OHPair(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7615]) ).

cnf(c_0_10553,plain,
    c_Message_Omsg_ONonce(X1) != c_Message_OHPair(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7616]) ).

cnf(c_0_10554,plain,
    c_Message_Omsg_OAgent(X1) != c_Message_OHPair(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_7617]) ).

cnf(c_0_10555,plain,
    ( ~ c_IntDef_Oneg(c_1,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7618]) ).

cnf(c_0_10556,plain,
    ( ~ c_IntDef_Oneg(c_0,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7619]) ).

cnf(c_0_10557,plain,
    ( ~ c_IntDef_Oiszero(c_1,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7620]) ).

cnf(c_0_10558,plain,
    ( c_HOL_Oinverse(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7621]) ).

cnf(c_0_10559,plain,
    ( c_HOL_Oinverse(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7622]) ).

cnf(c_0_10560,plain,
    c_Binomial_Obinomial(c_Suc(X1),X1) = c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_7623]) ).

cnf(c_0_10561,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7624]) ).

cnf(c_0_10562,plain,
    ( X1 = c_List_Olist_ONil
    | c_emptyset != c_List_Oset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7625]) ).

cnf(c_0_10563,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orotate1(X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7626]) ).

cnf(c_0_10564,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7627]) ).

cnf(c_0_10565,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_List_Oremdups(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7628]) ).

cnf(c_0_10566,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_7629]) ).

cnf(c_0_10567,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_List_Orev(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7630]) ).

cnf(c_0_10568,plain,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Oo2s(X1,X2) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_7631]) ).

cnf(c_0_10569,plain,
    c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X1))) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7632]) ).

cnf(c_0_10570,plain,
    c_HOL_Oabs(c_IntDef_Oint(X1),tc_IntDef_Oint) = c_IntDef_Oint(X1),
    inference(split_conjunct,[status(thm)],[c_0_7633]) ).

cnf(c_0_10571,plain,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    inference(split_conjunct,[status(thm)],[c_0_7634]) ).

cnf(c_0_10572,plain,
    c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_7635]) ).

cnf(c_0_10573,plain,
    ( c_HOL_Oabs(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7636]) ).

cnf(c_0_10574,plain,
    ( c_OrderedGroup_Opprt(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7637]) ).

cnf(c_0_10575,plain,
    ( c_OrderedGroup_Onprt(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7638]) ).

cnf(c_0_10576,plain,
    ( c_uminus(c_0,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7639]) ).

cnf(c_0_10577,plain,
    ( c_0 = c_uminus(c_0,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7640]) ).

cnf(c_0_10578,plain,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7641]) ).

cnf(c_0_10579,plain,
    ( c_0 = c_HOL_Oabs(c_0,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7642]) ).

cnf(c_0_10580,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OPls,X1) = c_0
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7643]) ).

cnf(c_0_10581,plain,
    ( c_NatArith_Oof__nat(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7644]) ).

cnf(c_0_10582,plain,
    ( c_NatArith_Oof__nat(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7645]) ).

cnf(c_0_10583,plain,
    ( c_0 = c_NatArith_Oof__nat(c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7646]) ).

cnf(c_0_10584,plain,
    ( c_IntDef_Oof__int(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7647]) ).

cnf(c_0_10585,plain,
    ( c_IntDef_Oof__int(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7648]) ).

cnf(c_0_10586,plain,
    ( c_0 = c_IntDef_Oof__int(c_0,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7649]) ).

cnf(c_0_10587,plain,
    c_Nat_Osize(c_Message_Omsg_OKey(X1),tc_Message_Omsg) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7650]) ).

cnf(c_0_10588,plain,
    c_Nat_Osize(c_Message_Omsg_ONonce(X1),tc_Message_Omsg) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7651]) ).

cnf(c_0_10589,plain,
    c_Nat_Osize(c_Message_Omsg_ONumber(X1),tc_Message_Omsg) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7652]) ).

cnf(c_0_10590,plain,
    c_Nat_Osize(c_Message_Omsg_OAgent(X1),tc_Message_Omsg) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7653]) ).

cnf(c_0_10591,plain,
    c_Nat_Osize(c_Message_Oagent_OFriend(X1),tc_Message_Oagent) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7654]) ).

cnf(c_0_10592,plain,
    c_uminus(c_emptyset,tc_set(X1)) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7655]) ).

cnf(c_0_10593,plain,
    c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7656]) ).

cnf(c_0_10594,plain,
    c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7657]) ).

cnf(c_0_10595,plain,
    c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7658]) ).

cnf(c_0_10596,plain,
    c_Binomial_Obinomial(c_0,c_Suc(X1)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7659]) ).

cnf(c_0_10597,plain,
    c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
    inference(split_conjunct,[status(thm)],[c_0_7660]) ).

cnf(c_0_10598,plain,
    c_Binomial_Obinomial(X1,c_Suc(c_0)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7661]) ).

cnf(c_0_10599,plain,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_7662]) ).

cnf(c_0_10600,plain,
    ( class_Finite__Set_Ofinite(tc_set(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7663]) ).

cnf(c_0_10601,plain,
    ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7664]) ).

cnf(c_0_10602,plain,
    c_Event_Oknows(X1,c_List_Olist_ONil) = c_Event_OinitState(X1),
    inference(split_conjunct,[status(thm)],[c_0_7665]) ).

cnf(c_0_10603,plain,
    c_Numeral_Obin__mult(c_Numeral_OMin,X1) = c_Numeral_Obin__minus(X1),
    inference(split_conjunct,[status(thm)],[c_0_7666]) ).

cnf(c_0_10604,plain,
    c_Numeral_Obin__add(X1,c_Numeral_OMin) = c_Numeral_Obin__pred(X1),
    inference(split_conjunct,[status(thm)],[c_0_7667]) ).

cnf(c_0_10605,plain,
    c_Numeral_Obin__add(c_Numeral_OMin,X1) = c_Numeral_Obin__pred(X1),
    inference(split_conjunct,[status(thm)],[c_0_7668]) ).

cnf(c_0_10606,plain,
    ( X1 = X2
    | c_Public_OshrK(X1) != c_Public_OshrK(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7669]) ).

cnf(c_0_10607,plain,
    ( X1 = X2
    | c_Message_Omsg_OHash(X1) != c_Message_Omsg_OHash(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7670]) ).

cnf(c_0_10608,plain,
    ( X1 = X2
    | c_Message_Omsg_OKey(X1) != c_Message_Omsg_OKey(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7671]) ).

cnf(c_0_10609,plain,
    ( X1 = X2
    | c_Message_Omsg_ONonce(X1) != c_Message_Omsg_ONonce(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7672]) ).

cnf(c_0_10610,plain,
    ( X1 = X2
    | c_Message_Omsg_ONumber(X1) != c_Message_Omsg_ONumber(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7673]) ).

cnf(c_0_10611,plain,
    ( X1 = X2
    | c_Message_Omsg_OAgent(X1) != c_Message_Omsg_OAgent(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7674]) ).

cnf(c_0_10612,plain,
    ( X1 = X2
    | c_Message_OinvKey(X1) != c_Message_OinvKey(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7675]) ).

cnf(c_0_10613,plain,
    ( X1 = X2
    | c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OFriend(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7676]) ).

cnf(c_0_10614,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7677]) ).

cnf(c_0_10615,plain,
    ( X1 = X2
    | c_IntDef_Oint(X1) != c_IntDef_Oint(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7678]) ).

cnf(c_0_10616,plain,
    c_Fun_Oid(X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7679]) ).

cnf(c_0_10617,plain,
    c_Message_OinvKey(c_Public_OshrK(X1)) = c_Public_OshrK(X1),
    inference(split_conjunct,[status(thm)],[c_0_7680]) ).

cnf(c_0_10618,plain,
    c_Message_Oparts(c_Message_Oparts(X1)) = c_Message_Oparts(X1),
    inference(split_conjunct,[status(thm)],[c_0_7681]) ).

cnf(c_0_10619,plain,
    c_Message_Oparts(c_Message_Oanalz(X1)) = c_Message_Oparts(X1),
    inference(split_conjunct,[status(thm)],[c_0_7682]) ).

cnf(c_0_10620,plain,
    c_Message_Oanalz(c_Message_Oparts(X1)) = c_Message_Oparts(X1),
    inference(split_conjunct,[status(thm)],[c_0_7683]) ).

cnf(c_0_10621,plain,
    c_Message_Oanalz(c_Message_Oanalz(X1)) = c_Message_Oanalz(X1),
    inference(split_conjunct,[status(thm)],[c_0_7684]) ).

cnf(c_0_10622,plain,
    c_Binomial_Obinomial(X1,X1) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_7685]) ).

cnf(c_0_10623,plain,
    c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    inference(split_conjunct,[status(thm)],[c_0_7686]) ).

cnf(c_0_10624,plain,
    c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
    inference(split_conjunct,[status(thm)],[c_0_7687]) ).

cnf(c_0_10625,plain,
    c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),
    inference(split_conjunct,[status(thm)],[c_0_7688]) ).

cnf(c_0_10626,plain,
    c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7689]) ).

cnf(c_0_10627,plain,
    c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7690]) ).

cnf(c_0_10628,plain,
    c_NatArith_Oof__nat(X1,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7691]) ).

cnf(c_0_10629,plain,
    c_Transitive__Closure_Otrancl(c_emptyset,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7692]) ).

cnf(c_0_10630,plain,
    c_Transitive__Closure_Ortrancl(c_emptyset,X1) = c_Relation_OId,
    inference(split_conjunct,[status(thm)],[c_0_7693]) ).

cnf(c_0_10631,plain,
    c_Union(c_emptyset,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7694]) ).

cnf(c_0_10632,plain,
    c_Union(c_UNIV,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7695]) ).

cnf(c_0_10633,plain,
    c_Pow(c_UNIV,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7696]) ).

cnf(c_0_10634,plain,
    c_Inter(c_emptyset,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7697]) ).

cnf(c_0_10635,plain,
    c_Inter(c_UNIV,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7698]) ).

cnf(c_0_10636,plain,
    c_Relation_Odiag(c_emptyset,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7699]) ).

cnf(c_0_10637,plain,
    c_Numeral_Obin__mult(c_Numeral_OPls,X1) = c_Numeral_OPls,
    inference(split_conjunct,[status(thm)],[c_0_7700]) ).

cnf(c_0_10638,plain,
    c_List_Oupt(X1,c_0) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7701]) ).

cnf(c_0_10639,plain,
    c_List_Otl(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7702]) ).

cnf(c_0_10640,plain,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7703]) ).

cnf(c_0_10641,plain,
    c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_7704]) ).

cnf(c_0_10642,plain,
    c_List_Orotate1(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7705]) ).

cnf(c_0_10643,plain,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7706]) ).

cnf(c_0_10644,plain,
    c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_7707]) ).

cnf(c_0_10645,plain,
    c_List_Oremdups(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7708]) ).

cnf(c_0_10646,plain,
    c_List_Onull(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_7709]) ).

cnf(c_0_10647,plain,
    c_List_Olists(c_UNIV,X1) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_7710]) ).

cnf(c_0_10648,plain,
    c_List_Odistinct(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_7711]) ).

cnf(c_0_10649,plain,
    c_List_Oconcat(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7712]) ).

cnf(c_0_10650,plain,
    c_List_Obutlast(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_7713]) ).

cnf(c_0_10651,plain,
    c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_7714]) ).

cnf(c_0_10652,plain,
    c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_7715]) ).

cnf(c_0_10653,plain,
    c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_7716]) ).

cnf(c_0_10654,plain,
    c_Binomial_Obinomial(X1,c_0) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_7717]) ).

cnf(c_0_10655,plain,
    c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    inference(split_conjunct,[status(thm)],[c_0_7718]) ).

cnf(c_0_10656,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7719]) ).

cnf(c_0_10657,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7720]) ).

cnf(c_0_10658,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7721]) ).

cnf(c_0_10659,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7722]) ).

cnf(c_0_10660,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7723]) ).

cnf(c_0_10661,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7724]) ).

cnf(c_0_10662,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7725]) ).

cnf(c_0_10663,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7726]) ).

cnf(c_0_10664,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7727]) ).

cnf(c_0_10665,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7728]) ).

cnf(c_0_10666,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7729]) ).

cnf(c_0_10667,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7730]) ).

cnf(c_0_10668,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7731]) ).

cnf(c_0_10669,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7732]) ).

cnf(c_0_10670,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7733]) ).

cnf(c_0_10671,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7734]) ).

cnf(c_0_10672,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7735]) ).

cnf(c_0_10673,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7736]) ).

cnf(c_0_10674,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7737]) ).

cnf(c_0_10675,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7738]) ).

cnf(c_0_10676,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7739]) ).

cnf(c_0_10677,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7740]) ).

cnf(c_0_10678,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7741]) ).

cnf(c_0_10679,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7742]) ).

cnf(c_0_10680,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7743]) ).

cnf(c_0_10681,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7744]) ).

cnf(c_0_10682,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7745]) ).

cnf(c_0_10683,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7746]) ).

cnf(c_0_10684,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7747]) ).

cnf(c_0_10685,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7748]) ).

cnf(c_0_10686,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7749]) ).

cnf(c_0_10687,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7750]) ).

cnf(c_0_10688,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7751]) ).

cnf(c_0_10689,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7752]) ).

cnf(c_0_10690,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7753]) ).

cnf(c_0_10691,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7754]) ).

cnf(c_0_10692,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7755]) ).

cnf(c_0_10693,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7756]) ).

cnf(c_0_10694,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7757]) ).

cnf(c_0_10695,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7758]) ).

cnf(c_0_10696,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7759]) ).

cnf(c_0_10697,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7760]) ).

cnf(c_0_10698,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7761]) ).

cnf(c_0_10699,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7762]) ).

cnf(c_0_10700,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7763]) ).

cnf(c_0_10701,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7764]) ).

cnf(c_0_10702,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7765]) ).

cnf(c_0_10703,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7766]) ).

cnf(c_0_10704,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7767]) ).

cnf(c_0_10705,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7768]) ).

cnf(c_0_10706,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7769]) ).

cnf(c_0_10707,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7770]) ).

cnf(c_0_10708,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7771]) ).

cnf(c_0_10709,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7772]) ).

cnf(c_0_10710,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7773]) ).

cnf(c_0_10711,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7774]) ).

cnf(c_0_10712,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7775]) ).

cnf(c_0_10713,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7776]) ).

cnf(c_0_10714,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7777]) ).

cnf(c_0_10715,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7778]) ).

cnf(c_0_10716,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7779]) ).

cnf(c_0_10717,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7780]) ).

cnf(c_0_10718,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7781]) ).

cnf(c_0_10719,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7782]) ).

cnf(c_0_10720,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7783]) ).

cnf(c_0_10721,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7784]) ).

cnf(c_0_10722,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7785]) ).

cnf(c_0_10723,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7786]) ).

cnf(c_0_10724,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7787]) ).

cnf(c_0_10725,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7788]) ).

cnf(c_0_10726,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7789]) ).

cnf(c_0_10727,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7790]) ).

cnf(c_0_10728,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7791]) ).

cnf(c_0_10729,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7792]) ).

cnf(c_0_10730,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7793]) ).

cnf(c_0_10731,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7794]) ).

cnf(c_0_10732,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7795]) ).

cnf(c_0_10733,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7796]) ).

cnf(c_0_10734,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7797]) ).

cnf(c_0_10735,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7798]) ).

cnf(c_0_10736,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7799]) ).

cnf(c_0_10737,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7800]) ).

cnf(c_0_10738,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7801]) ).

cnf(c_0_10739,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7802]) ).

cnf(c_0_10740,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7803]) ).

cnf(c_0_10741,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7804]) ).

cnf(c_0_10742,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7805]) ).

cnf(c_0_10743,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7806]) ).

cnf(c_0_10744,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7807]) ).

cnf(c_0_10745,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7808]) ).

cnf(c_0_10746,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7809]) ).

cnf(c_0_10747,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7810]) ).

cnf(c_0_10748,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7811]) ).

cnf(c_0_10749,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7812]) ).

cnf(c_0_10750,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7813]) ).

cnf(c_0_10751,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7814]) ).

cnf(c_0_10752,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7815]) ).

cnf(c_0_10753,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7816]) ).

cnf(c_0_10754,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7817]) ).

cnf(c_0_10755,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7818]) ).

cnf(c_0_10756,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7819]) ).

cnf(c_0_10757,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7820]) ).

cnf(c_0_10758,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7821]) ).

cnf(c_0_10759,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7822]) ).

cnf(c_0_10760,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7823]) ).

cnf(c_0_10761,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7824]) ).

cnf(c_0_10762,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7825]) ).

cnf(c_0_10763,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7826]) ).

cnf(c_0_10764,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7827]) ).

cnf(c_0_10765,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7828]) ).

cnf(c_0_10766,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7829]) ).

cnf(c_0_10767,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7830]) ).

cnf(c_0_10768,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7831]) ).

cnf(c_0_10769,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7832]) ).

cnf(c_0_10770,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7833]) ).

cnf(c_0_10771,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7834]) ).

cnf(c_0_10772,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7835]) ).

cnf(c_0_10773,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7836]) ).

cnf(c_0_10774,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7837]) ).

cnf(c_0_10775,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7838]) ).

cnf(c_0_10776,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7839]) ).

cnf(c_0_10777,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7840]) ).

cnf(c_0_10778,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7841]) ).

cnf(c_0_10779,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7842]) ).

cnf(c_0_10780,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7843]) ).

cnf(c_0_10781,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7844]) ).

cnf(c_0_10782,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7845]) ).

cnf(c_0_10783,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7846]) ).

cnf(c_0_10784,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7847]) ).

cnf(c_0_10785,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7848]) ).

cnf(c_0_10786,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7849]) ).

cnf(c_0_10787,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7850]) ).

cnf(c_0_10788,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7851]) ).

cnf(c_0_10789,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7852]) ).

cnf(c_0_10790,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7853]) ).

cnf(c_0_10791,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7854]) ).

cnf(c_0_10792,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7855]) ).

cnf(c_0_10793,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7856]) ).

cnf(c_0_10794,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7857]) ).

cnf(c_0_10795,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7858]) ).

cnf(c_0_10796,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7859]) ).

cnf(c_0_10797,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7860]) ).

cnf(c_0_10798,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7861]) ).

cnf(c_0_10799,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7862]) ).

cnf(c_0_10800,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7863]) ).

cnf(c_0_10801,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7864]) ).

cnf(c_0_10802,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7865]) ).

cnf(c_0_10803,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7866]) ).

cnf(c_0_10804,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7867]) ).

cnf(c_0_10805,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7868]) ).

cnf(c_0_10806,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7869]) ).

cnf(c_0_10807,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7870]) ).

cnf(c_0_10808,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7871]) ).

cnf(c_0_10809,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7872]) ).

cnf(c_0_10810,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7873]) ).

cnf(c_0_10811,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7874]) ).

cnf(c_0_10812,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7875]) ).

cnf(c_0_10813,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7876]) ).

cnf(c_0_10814,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7877]) ).

cnf(c_0_10815,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7878]) ).

cnf(c_0_10816,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7879]) ).

cnf(c_0_10817,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7880]) ).

cnf(c_0_10818,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7881]) ).

cnf(c_0_10819,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7882]) ).

cnf(c_0_10820,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7883]) ).

cnf(c_0_10821,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7884]) ).

cnf(c_0_10822,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7885]) ).

cnf(c_0_10823,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7886]) ).

cnf(c_0_10824,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7887]) ).

cnf(c_0_10825,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7888]) ).

cnf(c_0_10826,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7889]) ).

cnf(c_0_10827,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7890]) ).

cnf(c_0_10828,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7891]) ).

cnf(c_0_10829,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7892]) ).

cnf(c_0_10830,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7893]) ).

cnf(c_0_10831,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7894]) ).

cnf(c_0_10832,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7895]) ).

cnf(c_0_10833,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7896]) ).

cnf(c_0_10834,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7897]) ).

cnf(c_0_10835,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7898]) ).

cnf(c_0_10836,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7899]) ).

cnf(c_0_10837,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7900]) ).

cnf(c_0_10838,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7901]) ).

cnf(c_0_10839,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7902]) ).

cnf(c_0_10840,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7903]) ).

cnf(c_0_10841,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7904]) ).

cnf(c_0_10842,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7905]) ).

cnf(c_0_10843,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7906]) ).

cnf(c_0_10844,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7907]) ).

cnf(c_0_10845,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7908]) ).

cnf(c_0_10846,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7909]) ).

cnf(c_0_10847,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7910]) ).

cnf(c_0_10848,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7911]) ).

cnf(c_0_10849,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7912]) ).

cnf(c_0_10850,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7913]) ).

cnf(c_0_10851,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7914]) ).

cnf(c_0_10852,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7915]) ).

cnf(c_0_10853,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7916]) ).

cnf(c_0_10854,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7917]) ).

cnf(c_0_10855,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7918]) ).

cnf(c_0_10856,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7919]) ).

cnf(c_0_10857,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7920]) ).

cnf(c_0_10858,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7921]) ).

cnf(c_0_10859,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7922]) ).

cnf(c_0_10860,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7923]) ).

cnf(c_0_10861,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7924]) ).

cnf(c_0_10862,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7925]) ).

cnf(c_0_10863,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7926]) ).

cnf(c_0_10864,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7927]) ).

cnf(c_0_10865,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7928]) ).

cnf(c_0_10866,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7929]) ).

cnf(c_0_10867,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7930]) ).

cnf(c_0_10868,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7931]) ).

cnf(c_0_10869,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7932]) ).

cnf(c_0_10870,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7933]) ).

cnf(c_0_10871,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7934]) ).

cnf(c_0_10872,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7935]) ).

cnf(c_0_10873,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7936]) ).

cnf(c_0_10874,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7937]) ).

cnf(c_0_10875,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7938]) ).

cnf(c_0_10876,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7939]) ).

cnf(c_0_10877,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7940]) ).

cnf(c_0_10878,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7941]) ).

cnf(c_0_10879,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7942]) ).

cnf(c_0_10880,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7943]) ).

cnf(c_0_10881,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7944]) ).

cnf(c_0_10882,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7945]) ).

cnf(c_0_10883,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7946]) ).

cnf(c_0_10884,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7947]) ).

cnf(c_0_10885,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7948]) ).

cnf(c_0_10886,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7949]) ).

cnf(c_0_10887,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7950]) ).

cnf(c_0_10888,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7951]) ).

cnf(c_0_10889,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7952]) ).

cnf(c_0_10890,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7953]) ).

cnf(c_0_10891,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7954]) ).

cnf(c_0_10892,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7955]) ).

cnf(c_0_10893,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7956]) ).

cnf(c_0_10894,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7957]) ).

cnf(c_0_10895,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7958]) ).

cnf(c_0_10896,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7959]) ).

cnf(c_0_10897,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7960]) ).

cnf(c_0_10898,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7961]) ).

cnf(c_0_10899,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7962]) ).

cnf(c_0_10900,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7963]) ).

cnf(c_0_10901,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7964]) ).

cnf(c_0_10902,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7965]) ).

cnf(c_0_10903,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7966]) ).

cnf(c_0_10904,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7967]) ).

cnf(c_0_10905,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7968]) ).

cnf(c_0_10906,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7969]) ).

cnf(c_0_10907,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7970]) ).

cnf(c_0_10908,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7971]) ).

cnf(c_0_10909,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7972]) ).

cnf(c_0_10910,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7973]) ).

cnf(c_0_10911,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7974]) ).

cnf(c_0_10912,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7975]) ).

cnf(c_0_10913,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7976]) ).

cnf(c_0_10914,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7977]) ).

cnf(c_0_10915,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7978]) ).

cnf(c_0_10916,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7979]) ).

cnf(c_0_10917,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7980]) ).

cnf(c_0_10918,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7981]) ).

cnf(c_0_10919,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7982]) ).

cnf(c_0_10920,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7983]) ).

cnf(c_0_10921,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7984]) ).

cnf(c_0_10922,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7985]) ).

cnf(c_0_10923,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7986]) ).

cnf(c_0_10924,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7987]) ).

cnf(c_0_10925,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7988]) ).

cnf(c_0_10926,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7989]) ).

cnf(c_0_10927,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7990]) ).

cnf(c_0_10928,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7991]) ).

cnf(c_0_10929,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7992]) ).

cnf(c_0_10930,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7993]) ).

cnf(c_0_10931,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7994]) ).

cnf(c_0_10932,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7995]) ).

cnf(c_0_10933,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7996]) ).

cnf(c_0_10934,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7997]) ).

cnf(c_0_10935,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7998]) ).

cnf(c_0_10936,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7999]) ).

cnf(c_0_10937,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8000]) ).

cnf(c_0_10938,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8001]) ).

cnf(c_0_10939,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8002]) ).

cnf(c_0_10940,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8003]) ).

cnf(c_0_10941,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8004]) ).

cnf(c_0_10942,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8005]) ).

cnf(c_0_10943,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8006]) ).

cnf(c_0_10944,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8007]) ).

cnf(c_0_10945,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8008]) ).

cnf(c_0_10946,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8009]) ).

cnf(c_0_10947,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8010]) ).

cnf(c_0_10948,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8011]) ).

cnf(c_0_10949,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8012]) ).

cnf(c_0_10950,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8013]) ).

cnf(c_0_10951,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8014]) ).

cnf(c_0_10952,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8015]) ).

cnf(c_0_10953,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8016]) ).

cnf(c_0_10954,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8017]) ).

cnf(c_0_10955,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8018]) ).

cnf(c_0_10956,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8019]) ).

cnf(c_0_10957,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8020]) ).

cnf(c_0_10958,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8021]) ).

cnf(c_0_10959,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8022]) ).

cnf(c_0_10960,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8023]) ).

cnf(c_0_10961,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8024]) ).

cnf(c_0_10962,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8025]) ).

cnf(c_0_10963,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8026]) ).

cnf(c_0_10964,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8027]) ).

cnf(c_0_10965,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8028]) ).

cnf(c_0_10966,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8029]) ).

cnf(c_0_10967,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8030]) ).

cnf(c_0_10968,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8031]) ).

cnf(c_0_10969,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8032]) ).

cnf(c_0_10970,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8033]) ).

cnf(c_0_10971,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8034]) ).

cnf(c_0_10972,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8035]) ).

cnf(c_0_10973,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8036]) ).

cnf(c_0_10974,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8037]) ).

cnf(c_0_10975,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8038]) ).

cnf(c_0_10976,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8039]) ).

cnf(c_0_10977,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8040]) ).

cnf(c_0_10978,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8041]) ).

cnf(c_0_10979,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8042]) ).

cnf(c_0_10980,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8043]) ).

cnf(c_0_10981,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8044]) ).

cnf(c_0_10982,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8045]) ).

cnf(c_0_10983,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8046]) ).

cnf(c_0_10984,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8047]) ).

cnf(c_0_10985,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8048]) ).

cnf(c_0_10986,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8049]) ).

cnf(c_0_10987,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8050]) ).

cnf(c_0_10988,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8051]) ).

cnf(c_0_10989,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8052]) ).

cnf(c_0_10990,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8053]) ).

cnf(c_0_10991,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8054]) ).

cnf(c_0_10992,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8055]) ).

cnf(c_0_10993,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8056]) ).

cnf(c_0_10994,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8057]) ).

cnf(c_0_10995,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8058]) ).

cnf(c_0_10996,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8059]) ).

cnf(c_0_10997,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8060]) ).

cnf(c_0_10998,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8061]) ).

cnf(c_0_10999,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8062]) ).

cnf(c_0_11000,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8063]) ).

cnf(c_0_11001,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8064]) ).

cnf(c_0_11002,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8065]) ).

cnf(c_0_11003,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8066]) ).

cnf(c_0_11004,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8067]) ).

cnf(c_0_11005,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8068]) ).

cnf(c_0_11006,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8069]) ).

cnf(c_0_11007,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8070]) ).

cnf(c_0_11008,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8071]) ).

cnf(c_0_11009,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8072]) ).

cnf(c_0_11010,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8073]) ).

cnf(c_0_11011,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8074]) ).

cnf(c_0_11012,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8075]) ).

cnf(c_0_11013,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8076]) ).

cnf(c_0_11014,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8077]) ).

cnf(c_0_11015,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8078]) ).

cnf(c_0_11016,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8079]) ).

cnf(c_0_11017,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8080]) ).

cnf(c_0_11018,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8081]) ).

cnf(c_0_11019,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8082]) ).

cnf(c_0_11020,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8083]) ).

cnf(c_0_11021,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8084]) ).

cnf(c_0_11022,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8085]) ).

cnf(c_0_11023,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8086]) ).

cnf(c_0_11024,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8087]) ).

cnf(c_0_11025,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8088]) ).

cnf(c_0_11026,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8089]) ).

cnf(c_0_11027,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8090]) ).

cnf(c_0_11028,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8091]) ).

cnf(c_0_11029,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8092]) ).

cnf(c_0_11030,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8093]) ).

cnf(c_0_11031,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8094]) ).

cnf(c_0_11032,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8095]) ).

cnf(c_0_11033,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8096]) ).

cnf(c_0_11034,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8097]) ).

cnf(c_0_11035,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8098]) ).

cnf(c_0_11036,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8099]) ).

cnf(c_0_11037,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8100]) ).

cnf(c_0_11038,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8101]) ).

cnf(c_0_11039,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8102]) ).

cnf(c_0_11040,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8103]) ).

cnf(c_0_11041,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8104]) ).

cnf(c_0_11042,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8105]) ).

cnf(c_0_11043,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8106]) ).

cnf(c_0_11044,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8107]) ).

cnf(c_0_11045,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8108]) ).

cnf(c_0_11046,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8109]) ).

cnf(c_0_11047,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8110]) ).

cnf(c_0_11048,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8111]) ).

cnf(c_0_11049,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8112]) ).

cnf(c_0_11050,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8113]) ).

cnf(c_0_11051,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8114]) ).

cnf(c_0_11052,plain,
    ( class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8115]) ).

cnf(c_0_11053,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8116]) ).

cnf(c_0_11054,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8117]) ).

cnf(c_0_11055,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8118]) ).

cnf(c_0_11056,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8119]) ).

cnf(c_0_11057,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8120]) ).

cnf(c_0_11058,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8121]) ).

cnf(c_0_11059,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8122]) ).

cnf(c_0_11060,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8123]) ).

cnf(c_0_11061,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8124]) ).

cnf(c_0_11062,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8125]) ).

cnf(c_0_11063,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8126]) ).

cnf(c_0_11064,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8127]) ).

cnf(c_0_11065,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8128]) ).

cnf(c_0_11066,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8129]) ).

cnf(c_0_11067,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8130]) ).

cnf(c_0_11068,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8131]) ).

cnf(c_0_11069,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8132]) ).

cnf(c_0_11070,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8133]) ).

cnf(c_0_11071,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8134]) ).

cnf(c_0_11072,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8135]) ).

cnf(c_0_11073,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8136]) ).

cnf(c_0_11074,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8137]) ).

cnf(c_0_11075,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8138]) ).

cnf(c_0_11076,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8139]) ).

cnf(c_0_11077,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8140]) ).

cnf(c_0_11078,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8141]) ).

cnf(c_0_11079,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8142]) ).

cnf(c_0_11080,plain,
    ( class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8143]) ).

cnf(c_0_11081,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8144]) ).

cnf(c_0_11082,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8145]) ).

cnf(c_0_11083,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8146]) ).

cnf(c_0_11084,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8147]) ).

cnf(c_0_11085,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8148]) ).

cnf(c_0_11086,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8149]) ).

cnf(c_0_11087,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8150]) ).

cnf(c_0_11088,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8151]) ).

cnf(c_0_11089,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8152]) ).

cnf(c_0_11090,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8153]) ).

cnf(c_0_11091,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8154]) ).

cnf(c_0_11092,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8155]) ).

cnf(c_0_11093,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8156]) ).

cnf(c_0_11094,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8157]) ).

cnf(c_0_11095,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8158]) ).

cnf(c_0_11096,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8159]) ).

cnf(c_0_11097,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8160]) ).

cnf(c_0_11098,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8161]) ).

cnf(c_0_11099,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8162]) ).

cnf(c_0_11100,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8163]) ).

cnf(c_0_11101,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8164]) ).

cnf(c_0_11102,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8165]) ).

cnf(c_0_11103,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8166]) ).

cnf(c_0_11104,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8167]) ).

cnf(c_0_11105,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8168]) ).

cnf(c_0_11106,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8169]) ).

cnf(c_0_11107,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8170]) ).

cnf(c_0_11108,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8171]) ).

cnf(c_0_11109,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8172]) ).

cnf(c_0_11110,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8173]) ).

cnf(c_0_11111,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8174]) ).

cnf(c_0_11112,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8175]) ).

cnf(c_0_11113,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8176]) ).

cnf(c_0_11114,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8177]) ).

cnf(c_0_11115,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8178]) ).

cnf(c_0_11116,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8179]) ).

cnf(c_0_11117,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8180]) ).

cnf(c_0_11118,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8181]) ).

cnf(c_0_11119,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8182]) ).

cnf(c_0_11120,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8183]) ).

cnf(c_0_11121,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8184]) ).

cnf(c_0_11122,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8185]) ).

cnf(c_0_11123,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8186]) ).

cnf(c_0_11124,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8187]) ).

cnf(c_0_11125,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8188]) ).

cnf(c_0_11126,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8189]) ).

cnf(c_0_11127,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8190]) ).

cnf(c_0_11128,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8191]) ).

cnf(c_0_11129,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8192]) ).

cnf(c_0_11130,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8193]) ).

cnf(c_0_11131,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8194]) ).

cnf(c_0_11132,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8195]) ).

cnf(c_0_11133,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8196]) ).

cnf(c_0_11134,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8197]) ).

cnf(c_0_11135,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8198]) ).

cnf(c_0_11136,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8199]) ).

cnf(c_0_11137,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8200]) ).

cnf(c_0_11138,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8201]) ).

cnf(c_0_11139,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8202]) ).

cnf(c_0_11140,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8203]) ).

cnf(c_0_11141,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8204]) ).

cnf(c_0_11142,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8205]) ).

cnf(c_0_11143,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8206]) ).

cnf(c_0_11144,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8207]) ).

cnf(c_0_11145,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8208]) ).

cnf(c_0_11146,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8209]) ).

cnf(c_0_11147,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8210]) ).

cnf(c_0_11148,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8211]) ).

cnf(c_0_11149,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8212]) ).

cnf(c_0_11150,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8213]) ).

cnf(c_0_11151,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8214]) ).

cnf(c_0_11152,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8215]) ).

cnf(c_0_11153,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8216]) ).

cnf(c_0_11154,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8217]) ).

cnf(c_0_11155,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8218]) ).

cnf(c_0_11156,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8219]) ).

cnf(c_0_11157,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8220]) ).

cnf(c_0_11158,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8221]) ).

cnf(c_0_11159,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8222]) ).

cnf(c_0_11160,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8223]) ).

cnf(c_0_11161,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8224]) ).

cnf(c_0_11162,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8225]) ).

cnf(c_0_11163,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8226]) ).

cnf(c_0_11164,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8227]) ).

cnf(c_0_11165,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8228]) ).

cnf(c_0_11166,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8229]) ).

cnf(c_0_11167,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8230]) ).

cnf(c_0_11168,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8231]) ).

cnf(c_0_11169,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8232]) ).

cnf(c_0_11170,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8233]) ).

cnf(c_0_11171,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8234]) ).

cnf(c_0_11172,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8235]) ).

cnf(c_0_11173,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8236]) ).

cnf(c_0_11174,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8237]) ).

cnf(c_0_11175,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8238]) ).

cnf(c_0_11176,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8239]) ).

cnf(c_0_11177,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8240]) ).

cnf(c_0_11178,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8241]) ).

cnf(c_0_11179,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8242]) ).

cnf(c_0_11180,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8243]) ).

cnf(c_0_11181,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8244]) ).

cnf(c_0_11182,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8245]) ).

cnf(c_0_11183,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8246]) ).

cnf(c_0_11184,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8247]) ).

cnf(c_0_11185,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8248]) ).

cnf(c_0_11186,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8249]) ).

cnf(c_0_11187,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8250]) ).

cnf(c_0_11188,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8251]) ).

cnf(c_0_11189,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8252]) ).

cnf(c_0_11190,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8253]) ).

cnf(c_0_11191,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8254]) ).

cnf(c_0_11192,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8255]) ).

cnf(c_0_11193,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8256]) ).

cnf(c_0_11194,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8257]) ).

cnf(c_0_11195,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8258]) ).

cnf(c_0_11196,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8259]) ).

cnf(c_0_11197,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8260]) ).

cnf(c_0_11198,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8261]) ).

cnf(c_0_11199,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8262]) ).

cnf(c_0_11200,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8263]) ).

cnf(c_0_11201,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8264]) ).

cnf(c_0_11202,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8265]) ).

cnf(c_0_11203,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8266]) ).

cnf(c_0_11204,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8267]) ).

cnf(c_0_11205,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8268]) ).

cnf(c_0_11206,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8269]) ).

cnf(c_0_11207,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8270]) ).

cnf(c_0_11208,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8271]) ).

cnf(c_0_11209,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8272]) ).

cnf(c_0_11210,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8273]) ).

cnf(c_0_11211,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8274]) ).

cnf(c_0_11212,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8275]) ).

cnf(c_0_11213,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8276]) ).

cnf(c_0_11214,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8277]) ).

cnf(c_0_11215,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8278]) ).

cnf(c_0_11216,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8279]) ).

cnf(c_0_11217,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8280]) ).

cnf(c_0_11218,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8281]) ).

cnf(c_0_11219,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8282]) ).

cnf(c_0_11220,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8283]) ).

cnf(c_0_11221,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8284]) ).

cnf(c_0_11222,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8285]) ).

cnf(c_0_11223,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8286]) ).

cnf(c_0_11224,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8287]) ).

cnf(c_0_11225,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8288]) ).

cnf(c_0_11226,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8289]) ).

cnf(c_0_11227,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8290]) ).

cnf(c_0_11228,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8291]) ).

cnf(c_0_11229,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8292]) ).

cnf(c_0_11230,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8293]) ).

cnf(c_0_11231,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8294]) ).

cnf(c_0_11232,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8295]) ).

cnf(c_0_11233,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8296]) ).

cnf(c_0_11234,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8297]) ).

cnf(c_0_11235,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8298]) ).

cnf(c_0_11236,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8299]) ).

cnf(c_0_11237,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8300]) ).

cnf(c_0_11238,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8301]) ).

cnf(c_0_11239,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8302]) ).

cnf(c_0_11240,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8303]) ).

cnf(c_0_11241,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8304]) ).

cnf(c_0_11242,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8305]) ).

cnf(c_0_11243,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8306]) ).

cnf(c_0_11244,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8307]) ).

cnf(c_0_11245,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8308]) ).

cnf(c_0_11246,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8309]) ).

cnf(c_0_11247,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8310]) ).

cnf(c_0_11248,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8311]) ).

cnf(c_0_11249,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8312]) ).

cnf(c_0_11250,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8313]) ).

cnf(c_0_11251,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8314]) ).

cnf(c_0_11252,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8315]) ).

cnf(c_0_11253,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8316]) ).

cnf(c_0_11254,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8317]) ).

cnf(c_0_11255,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8318]) ).

cnf(c_0_11256,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8319]) ).

cnf(c_0_11257,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8320]) ).

cnf(c_0_11258,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8321]) ).

cnf(c_0_11259,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8322]) ).

cnf(c_0_11260,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8323]) ).

cnf(c_0_11261,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8324]) ).

cnf(c_0_11262,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8325]) ).

cnf(c_0_11263,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8326]) ).

cnf(c_0_11264,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8327]) ).

cnf(c_0_11265,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8328]) ).

cnf(c_0_11266,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8329]) ).

cnf(c_0_11267,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8330]) ).

cnf(c_0_11268,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8331]) ).

cnf(c_0_11269,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8332]) ).

cnf(c_0_11270,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8333]) ).

cnf(c_0_11271,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8334]) ).

cnf(c_0_11272,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8335]) ).

cnf(c_0_11273,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8336]) ).

cnf(c_0_11274,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8337]) ).

cnf(c_0_11275,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8338]) ).

cnf(c_0_11276,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8339]) ).

cnf(c_0_11277,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8340]) ).

cnf(c_0_11278,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8341]) ).

cnf(c_0_11279,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8342]) ).

cnf(c_0_11280,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8343]) ).

cnf(c_0_11281,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8344]) ).

cnf(c_0_11282,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8345]) ).

cnf(c_0_11283,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8346]) ).

cnf(c_0_11284,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8347]) ).

cnf(c_0_11285,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8348]) ).

cnf(c_0_11286,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8349]) ).

cnf(c_0_11287,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8350]) ).

cnf(c_0_11288,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8351]) ).

cnf(c_0_11289,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8352]) ).

cnf(c_0_11290,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8353]) ).

cnf(c_0_11291,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8354]) ).

cnf(c_0_11292,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8355]) ).

cnf(c_0_11293,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8356]) ).

cnf(c_0_11294,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8357]) ).

cnf(c_0_11295,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8358]) ).

cnf(c_0_11296,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8359]) ).

cnf(c_0_11297,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8360]) ).

cnf(c_0_11298,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8361]) ).

cnf(c_0_11299,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8362]) ).

cnf(c_0_11300,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8363]) ).

cnf(c_0_11301,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8364]) ).

cnf(c_0_11302,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8365]) ).

cnf(c_0_11303,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8366]) ).

cnf(c_0_11304,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8367]) ).

cnf(c_0_11305,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8368]) ).

cnf(c_0_11306,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8369]) ).

cnf(c_0_11307,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8370]) ).

cnf(c_0_11308,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8371]) ).

cnf(c_0_11309,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8372]) ).

cnf(c_0_11310,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8373]) ).

cnf(c_0_11311,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8374]) ).

cnf(c_0_11312,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8375]) ).

cnf(c_0_11313,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8376]) ).

cnf(c_0_11314,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8377]) ).

cnf(c_0_11315,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8378]) ).

cnf(c_0_11316,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8379]) ).

cnf(c_0_11317,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8380]) ).

cnf(c_0_11318,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8381]) ).

cnf(c_0_11319,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8382]) ).

cnf(c_0_11320,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8383]) ).

cnf(c_0_11321,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8384]) ).

cnf(c_0_11322,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8385]) ).

cnf(c_0_11323,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8386]) ).

cnf(c_0_11324,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8387]) ).

cnf(c_0_11325,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8388]) ).

cnf(c_0_11326,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8389]) ).

cnf(c_0_11327,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8390]) ).

cnf(c_0_11328,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8391]) ).

cnf(c_0_11329,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8392]) ).

cnf(c_0_11330,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8393]) ).

cnf(c_0_11331,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8394]) ).

cnf(c_0_11332,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8395]) ).

cnf(c_0_11333,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8396]) ).

cnf(c_0_11334,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8397]) ).

cnf(c_0_11335,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8398]) ).

cnf(c_0_11336,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8399]) ).

cnf(c_0_11337,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8400]) ).

cnf(c_0_11338,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8401]) ).

cnf(c_0_11339,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8402]) ).

cnf(c_0_11340,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8403]) ).

cnf(c_0_11341,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8404]) ).

cnf(c_0_11342,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8405]) ).

cnf(c_0_11343,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8406]) ).

cnf(c_0_11344,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8407]) ).

cnf(c_0_11345,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8408]) ).

cnf(c_0_11346,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8409]) ).

cnf(c_0_11347,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8410]) ).

cnf(c_0_11348,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8411]) ).

cnf(c_0_11349,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8412]) ).

cnf(c_0_11350,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8413]) ).

cnf(c_0_11351,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8414]) ).

cnf(c_0_11352,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8415]) ).

cnf(c_0_11353,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8416]) ).

cnf(c_0_11354,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8417]) ).

cnf(c_0_11355,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8418]) ).

cnf(c_0_11356,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8419]) ).

cnf(c_0_11357,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8420]) ).

cnf(c_0_11358,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8421]) ).

cnf(c_0_11359,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8422]) ).

cnf(c_0_11360,plain,
    ( class_Nat_Opower(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8423]) ).

cnf(c_0_11361,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8424]) ).

cnf(c_0_11362,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8425]) ).

cnf(c_0_11363,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8426]) ).

cnf(c_0_11364,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8427]) ).

cnf(c_0_11365,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8428]) ).

cnf(c_0_11366,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8429]) ).

cnf(c_0_11367,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8430]) ).

cnf(c_0_11368,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8431]) ).

cnf(c_0_11369,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8432]) ).

cnf(c_0_11370,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8433]) ).

cnf(c_0_11371,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8434]) ).

cnf(c_0_11372,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8435]) ).

cnf(c_0_11373,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8436]) ).

cnf(c_0_11374,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8437]) ).

cnf(c_0_11375,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8438]) ).

cnf(c_0_11376,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8439]) ).

cnf(c_0_11377,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8440]) ).

cnf(c_0_11378,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8441]) ).

cnf(c_0_11379,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8442]) ).

cnf(c_0_11380,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8443]) ).

cnf(c_0_11381,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8444]) ).

cnf(c_0_11382,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8445]) ).

cnf(c_0_11383,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8446]) ).

cnf(c_0_11384,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8447]) ).

cnf(c_0_11385,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8448]) ).

cnf(c_0_11386,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8449]) ).

cnf(c_0_11387,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8450]) ).

cnf(c_0_11388,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8451]) ).

cnf(c_0_11389,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8452]) ).

cnf(c_0_11390,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8453]) ).

cnf(c_0_11391,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8454]) ).

cnf(c_0_11392,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8455]) ).

cnf(c_0_11393,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8456]) ).

cnf(c_0_11394,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8457]) ).

cnf(c_0_11395,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8458]) ).

cnf(c_0_11396,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8459]) ).

cnf(c_0_11397,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8460]) ).

cnf(c_0_11398,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8461]) ).

cnf(c_0_11399,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8462]) ).

cnf(c_0_11400,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8463]) ).

cnf(c_0_11401,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8464]) ).

cnf(c_0_11402,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8465]) ).

cnf(c_0_11403,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8466]) ).

cnf(c_0_11404,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8467]) ).

cnf(c_0_11405,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8468]) ).

cnf(c_0_11406,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8469]) ).

cnf(c_0_11407,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8470]) ).

cnf(c_0_11408,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8471]) ).

cnf(c_0_11409,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8472]) ).

cnf(c_0_11410,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8473]) ).

cnf(c_0_11411,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8474]) ).

cnf(c_0_11412,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8475]) ).

cnf(c_0_11413,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8476]) ).

cnf(c_0_11414,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8477]) ).

cnf(c_0_11415,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8478]) ).

cnf(c_0_11416,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8479]) ).

cnf(c_0_11417,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8480]) ).

cnf(c_0_11418,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8481]) ).

cnf(c_0_11419,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8482]) ).

cnf(c_0_11420,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8483]) ).

cnf(c_0_11421,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8484]) ).

cnf(c_0_11422,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8485]) ).

cnf(c_0_11423,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8486]) ).

cnf(c_0_11424,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8487]) ).

cnf(c_0_11425,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8488]) ).

cnf(c_0_11426,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8489]) ).

cnf(c_0_11427,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8490]) ).

cnf(c_0_11428,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8491]) ).

cnf(c_0_11429,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8492]) ).

cnf(c_0_11430,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8493]) ).

cnf(c_0_11431,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8494]) ).

cnf(c_0_11432,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8495]) ).

cnf(c_0_11433,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8496]) ).

cnf(c_0_11434,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8497]) ).

cnf(c_0_11435,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8498]) ).

cnf(c_0_11436,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8499]) ).

cnf(c_0_11437,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8500]) ).

cnf(c_0_11438,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8501]) ).

cnf(c_0_11439,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8502]) ).

cnf(c_0_11440,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8503]) ).

cnf(c_0_11441,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8504]) ).

cnf(c_0_11442,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8505]) ).

cnf(c_0_11443,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8506]) ).

cnf(c_0_11444,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8507]) ).

cnf(c_0_11445,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8508]) ).

cnf(c_0_11446,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8509]) ).

cnf(c_0_11447,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8510]) ).

cnf(c_0_11448,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8511]) ).

cnf(c_0_11449,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8512]) ).

cnf(c_0_11450,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8513]) ).

cnf(c_0_11451,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8514]) ).

cnf(c_0_11452,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8515]) ).

cnf(c_0_11453,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8516]) ).

cnf(c_0_11454,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8517]) ).

cnf(c_0_11455,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8518]) ).

cnf(c_0_11456,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8519]) ).

cnf(c_0_11457,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8520]) ).

cnf(c_0_11458,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8521]) ).

cnf(c_0_11459,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8522]) ).

cnf(c_0_11460,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8523]) ).

cnf(c_0_11461,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8524]) ).

cnf(c_0_11462,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8525]) ).

cnf(c_0_11463,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8526]) ).

cnf(c_0_11464,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8527]) ).

cnf(c_0_11465,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8528]) ).

cnf(c_0_11466,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8529]) ).

cnf(c_0_11467,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8530]) ).

cnf(c_0_11468,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8531]) ).

cnf(c_0_11469,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8532]) ).

cnf(c_0_11470,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8533]) ).

cnf(c_0_11471,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8534]) ).

cnf(c_0_11472,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8535]) ).

cnf(c_0_11473,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8536]) ).

cnf(c_0_11474,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8537]) ).

cnf(c_0_11475,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8538]) ).

cnf(c_0_11476,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8539]) ).

cnf(c_0_11477,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8540]) ).

cnf(c_0_11478,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8541]) ).

cnf(c_0_11479,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8542]) ).

cnf(c_0_11480,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8543]) ).

cnf(c_0_11481,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8544]) ).

cnf(c_0_11482,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8545]) ).

cnf(c_0_11483,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8546]) ).

cnf(c_0_11484,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8547]) ).

cnf(c_0_11485,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8548]) ).

cnf(c_0_11486,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8549]) ).

cnf(c_0_11487,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8550]) ).

cnf(c_0_11488,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8551]) ).

cnf(c_0_11489,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8552]) ).

cnf(c_0_11490,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8553]) ).

cnf(c_0_11491,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8554]) ).

cnf(c_0_11492,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8555]) ).

cnf(c_0_11493,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8556]) ).

cnf(c_0_11494,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8557]) ).

cnf(c_0_11495,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8558]) ).

cnf(c_0_11496,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8559]) ).

cnf(c_0_11497,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8560]) ).

cnf(c_0_11498,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8561]) ).

cnf(c_0_11499,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8562]) ).

cnf(c_0_11500,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8563]) ).

cnf(c_0_11501,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8564]) ).

cnf(c_0_11502,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8565]) ).

cnf(c_0_11503,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8566]) ).

cnf(c_0_11504,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8567]) ).

cnf(c_0_11505,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8568]) ).

cnf(c_0_11506,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8569]) ).

cnf(c_0_11507,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8570]) ).

cnf(c_0_11508,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8571]) ).

cnf(c_0_11509,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8572]) ).

cnf(c_0_11510,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8573]) ).

cnf(c_0_11511,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8574]) ).

cnf(c_0_11512,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8575]) ).

cnf(c_0_11513,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8576]) ).

cnf(c_0_11514,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8577]) ).

cnf(c_0_11515,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8578]) ).

cnf(c_0_11516,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8579]) ).

cnf(c_0_11517,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8580]) ).

cnf(c_0_11518,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8581]) ).

cnf(c_0_11519,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8582]) ).

cnf(c_0_11520,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8583]) ).

cnf(c_0_11521,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8584]) ).

cnf(c_0_11522,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8585]) ).

cnf(c_0_11523,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8586]) ).

cnf(c_0_11524,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8587]) ).

cnf(c_0_11525,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8588]) ).

cnf(c_0_11526,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8589]) ).

cnf(c_0_11527,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8590]) ).

cnf(c_0_11528,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8591]) ).

cnf(c_0_11529,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8592]) ).

cnf(c_0_11530,plain,
    ( class_Numeral_Onumber(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8593]) ).

cnf(c_0_11531,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8594]) ).

cnf(c_0_11532,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8595]) ).

cnf(c_0_11533,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8596]) ).

cnf(c_0_11534,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8597]) ).

cnf(c_0_11535,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8598]) ).

cnf(c_0_11536,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8599]) ).

cnf(c_0_11537,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8600]) ).

cnf(c_0_11538,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8601]) ).

cnf(c_0_11539,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8602]) ).

cnf(c_0_11540,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8603]) ).

cnf(c_0_11541,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8604]) ).

cnf(c_0_11542,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8605]) ).

cnf(c_0_11543,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8606]) ).

cnf(c_0_11544,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8607]) ).

cnf(c_0_11545,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8608]) ).

cnf(c_0_11546,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8609]) ).

cnf(c_0_11547,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8610]) ).

cnf(c_0_11548,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8611]) ).

cnf(c_0_11549,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8612]) ).

cnf(c_0_11550,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8613]) ).

cnf(c_0_11551,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8614]) ).

cnf(c_0_11552,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8615]) ).

cnf(c_0_11553,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8616]) ).

cnf(c_0_11554,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8617]) ).

cnf(c_0_11555,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8618]) ).

cnf(c_0_11556,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8619]) ).

cnf(c_0_11557,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8620]) ).

cnf(c_0_11558,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8621]) ).

cnf(c_0_11559,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8622]) ).

cnf(c_0_11560,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8623]) ).

cnf(c_0_11561,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8624]) ).

cnf(c_0_11562,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8625]) ).

cnf(c_0_11563,plain,
    c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8626]) ).

cnf(c_0_11564,plain,
    c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8627]) ).

cnf(c_0_11565,plain,
    c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8628]) ).

cnf(c_0_11566,plain,
    c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8629]) ).

cnf(c_0_11567,plain,
    c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8630]) ).

cnf(c_0_11568,plain,
    c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_8631]) ).

cnf(c_0_11569,plain,
    c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
    inference(split_conjunct,[status(thm)],[c_0_8632]) ).

cnf(c_0_11570,plain,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8633]) ).

cnf(c_0_11571,plain,
    c_Parity_Oeven(c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8634]) ).

cnf(c_0_11572,plain,
    c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8635]) ).

cnf(c_0_11573,plain,
    c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8636]) ).

cnf(c_0_11574,plain,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
    inference(split_conjunct,[status(thm)],[c_0_8637]) ).

cnf(c_0_11575,plain,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
    inference(split_conjunct,[status(thm)],[c_0_8638]) ).

cnf(c_0_11576,plain,
    c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8639]) ).

cnf(c_0_11577,plain,
    c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8640]) ).

cnf(c_0_11578,plain,
    c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8641]) ).

cnf(c_0_11579,plain,
    c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8642]) ).

cnf(c_0_11580,plain,
    c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8643]) ).

cnf(c_0_11581,plain,
    c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8644]) ).

cnf(c_0_11582,plain,
    c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8645]) ).

cnf(c_0_11583,plain,
    c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8646]) ).

cnf(c_0_11584,plain,
    c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8647]) ).

cnf(c_0_11585,plain,
    c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8648]) ).

cnf(c_0_11586,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8649]) ).

cnf(c_0_11587,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8650]) ).

cnf(c_0_11588,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8651]) ).

cnf(c_0_11589,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8652]) ).

cnf(c_0_11590,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8653]) ).

cnf(c_0_11591,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8654]) ).

cnf(c_0_11592,plain,
    c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8655]) ).

cnf(c_0_11593,plain,
    c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8656]) ).

cnf(c_0_11594,plain,
    c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8657]) ).

cnf(c_0_11595,plain,
    c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8658]) ).

cnf(c_0_11596,plain,
    c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8659]) ).

cnf(c_0_11597,plain,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8660]) ).

cnf(c_0_11598,plain,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8661]) ).

cnf(c_0_11599,plain,
    class_Nat_Opower(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_8662]) ).

cnf(c_0_11600,plain,
    class_Orderings_Oorder(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_8663]) ).

cnf(c_0_11601,plain,
    class_Orderings_Oord(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_8664]) ).

cnf(c_0_11602,plain,
    class_HOL_Ominus(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_8665]) ).

cnf(c_0_11603,plain,
    ( X1 = c_0
    | c_IntDef_Oint(X1) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_8666]) ).

cnf(c_0_11604,plain,
    ( c_1 != c_0
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8667]) ).

cnf(c_0_11605,plain,
    ( c_0 != c_1
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8668]) ).

cnf(c_0_11606,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X1),
    inference(split_conjunct,[status(thm)],[c_0_8669]) ).

cnf(c_0_11607,plain,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OSpy,
    inference(split_conjunct,[status(thm)],[c_0_8670]) ).

cnf(c_0_11608,plain,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OServer,
    inference(split_conjunct,[status(thm)],[c_0_8671]) ).

cnf(c_0_11609,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X1),
    inference(split_conjunct,[status(thm)],[c_0_8672]) ).

cnf(c_0_11610,plain,
    c_0 != c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_8673]) ).

cnf(c_0_11611,plain,
    c_Suc(X1) != c_0,
    inference(split_conjunct,[status(thm)],[c_0_8674]) ).

cnf(c_0_11612,plain,
    c_IntDef_Onat(c_1) = c_Suc(c_0),
    inference(split_conjunct,[status(thm)],[c_0_8675]) ).

cnf(c_0_11613,plain,
    c_Message_Oanalz(c_emptyset) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_8676]) ).

cnf(c_0_11614,plain,
    c_Message_Oparts(c_emptyset) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_8677]) ).

cnf(c_0_11615,plain,
    c_Message_OkeysFor(c_emptyset) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_8678]) ).

cnf(c_0_11616,plain,
    c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
    inference(split_conjunct,[status(thm)],[c_0_8679]) ).

cnf(c_0_11617,plain,
    c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
    inference(split_conjunct,[status(thm)],[c_0_8680]) ).

cnf(c_0_11618,plain,
    c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
    inference(split_conjunct,[status(thm)],[c_0_8681]) ).

cnf(c_0_11619,plain,
    c_1 = c_Suc(c_0),
    inference(split_conjunct,[status(thm)],[c_0_8682]) ).

cnf(c_0_11620,plain,
    c_IntDef_Onat(c_0) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8683]) ).

cnf(c_0_11621,plain,
    c_IntDef_Oint(c_0) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_8684]) ).

cnf(c_0_11622,plain,
    c_IntDef_Oint(c_1) = c_1,
    inference(split_conjunct,[status(thm)],[c_0_8685]) ).

cnf(c_0_11623,plain,
    class_HOL_Ominus(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8686]) ).

cnf(c_0_11624,plain,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8687]) ).

cnf(c_0_11625,plain,
    class_Orderings_Olinorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8688]) ).

cnf(c_0_11626,plain,
    class_LOrder_Olorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8689]) ).

cnf(c_0_11627,plain,
    class_LOrder_Ojoin__semilorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8690]) ).

cnf(c_0_11628,plain,
    class_Parity_Oeven__odd(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8691]) ).

cnf(c_0_11629,plain,
    class_Numeral_Onumber(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8692]) ).

cnf(c_0_11630,plain,
    class_Power_Orecpower(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8693]) ).

cnf(c_0_11631,plain,
    class_Divides_Odiv(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8694]) ).

cnf(c_0_11632,plain,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8695]) ).

cnf(c_0_11633,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8696]) ).

cnf(c_0_11634,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8697]) ).

cnf(c_0_11635,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8698]) ).

cnf(c_0_11636,plain,
    class_LOrder_Omeet__semilorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8699]) ).

cnf(c_0_11637,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8700]) ).

cnf(c_0_11638,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8701]) ).

cnf(c_0_11639,plain,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8702]) ).

cnf(c_0_11640,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8703]) ).

cnf(c_0_11641,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8704]) ).

cnf(c_0_11642,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8705]) ).

cnf(c_0_11643,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8706]) ).

cnf(c_0_11644,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8707]) ).

cnf(c_0_11645,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8708]) ).

cnf(c_0_11646,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8709]) ).

cnf(c_0_11647,plain,
    class_Orderings_Oorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8710]) ).

cnf(c_0_11648,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8711]) ).

cnf(c_0_11649,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8712]) ).

cnf(c_0_11650,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8713]) ).

cnf(c_0_11651,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8714]) ).

cnf(c_0_11652,plain,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8715]) ).

cnf(c_0_11653,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8716]) ).

cnf(c_0_11654,plain,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8717]) ).

cnf(c_0_11655,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8718]) ).

cnf(c_0_11656,plain,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8719]) ).

cnf(c_0_11657,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8720]) ).

cnf(c_0_11658,plain,
    class_Orderings_Oord(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8721]) ).

cnf(c_0_11659,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8722]) ).

cnf(c_0_11660,plain,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8723]) ).

cnf(c_0_11661,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8724]) ).

cnf(c_0_11662,plain,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8725]) ).

cnf(c_0_11663,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8726]) ).

cnf(c_0_11664,plain,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8727]) ).

cnf(c_0_11665,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8728]) ).

cnf(c_0_11666,plain,
    class_Nat_Opower(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8729]) ).

cnf(c_0_11667,plain,
    class_HOL_Otimes(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8730]) ).

cnf(c_0_11668,plain,
    class_HOL_Oplus(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8731]) ).

cnf(c_0_11669,plain,
    class_HOL_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8732]) ).

cnf(c_0_11670,plain,
    class_HOL_Oone(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_8733]) ).

cnf(c_0_11671,plain,
    class_Finite__Set_Ofinite(tc_bool),
    inference(split_conjunct,[status(thm)],[c_0_8734]) ).

cnf(c_0_11672,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[c_0_8735]) ).

cnf(c_0_11673,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8736]) ).

cnf(c_0_11674,plain,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8737]) ).

cnf(c_0_11675,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8738]) ).

cnf(c_0_11676,plain,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8739]) ).

cnf(c_0_11677,plain,
    class_Power_Orecpower(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8740]) ).

cnf(c_0_11678,plain,
    class_Nat_Opower(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8741]) ).

cnf(c_0_11679,plain,
    class_Divides_Odiv(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8742]) ).

cnf(c_0_11680,plain,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8743]) ).

cnf(c_0_11681,plain,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8744]) ).

cnf(c_0_11682,plain,
    class_Numeral_Onumber(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8745]) ).

cnf(c_0_11683,plain,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8746]) ).

cnf(c_0_11684,plain,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8747]) ).

cnf(c_0_11685,plain,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8748]) ).

cnf(c_0_11686,plain,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8749]) ).

cnf(c_0_11687,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8750]) ).

cnf(c_0_11688,plain,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8751]) ).

cnf(c_0_11689,plain,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8752]) ).

cnf(c_0_11690,plain,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8753]) ).

cnf(c_0_11691,plain,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8754]) ).

cnf(c_0_11692,plain,
    class_Orderings_Oord(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8755]) ).

cnf(c_0_11693,plain,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8756]) ).

cnf(c_0_11694,plain,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8757]) ).

cnf(c_0_11695,plain,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8758]) ).

cnf(c_0_11696,plain,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8759]) ).

cnf(c_0_11697,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8760]) ).

cnf(c_0_11698,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8761]) ).

cnf(c_0_11699,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8762]) ).

cnf(c_0_11700,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8763]) ).

cnf(c_0_11701,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8764]) ).

cnf(c_0_11702,plain,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8765]) ).

cnf(c_0_11703,plain,
    class_HOL_Ozero(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8766]) ).

cnf(c_0_11704,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8767]) ).

cnf(c_0_11705,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8768]) ).

cnf(c_0_11706,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8769]) ).

cnf(c_0_11707,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8770]) ).

cnf(c_0_11708,plain,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8771]) ).

cnf(c_0_11709,plain,
    class_LOrder_Olorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8772]) ).

cnf(c_0_11710,plain,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8773]) ).

cnf(c_0_11711,plain,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8774]) ).

cnf(c_0_11712,plain,
    class_Orderings_Oorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8775]) ).

cnf(c_0_11713,plain,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8776]) ).

cnf(c_0_11714,plain,
    class_HOL_Otimes(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8777]) ).

cnf(c_0_11715,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8778]) ).

cnf(c_0_11716,plain,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8779]) ).

cnf(c_0_11717,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8780]) ).

cnf(c_0_11718,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8781]) ).

cnf(c_0_11719,plain,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8782]) ).

cnf(c_0_11720,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8783]) ).

cnf(c_0_11721,plain,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8784]) ).

cnf(c_0_11722,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8785]) ).

cnf(c_0_11723,plain,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8786]) ).

cnf(c_0_11724,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8787]) ).

cnf(c_0_11725,plain,
    class_HOL_Oplus(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8788]) ).

cnf(c_0_11726,plain,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8789]) ).

cnf(c_0_11727,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8790]) ).

cnf(c_0_11728,plain,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8791]) ).

cnf(c_0_11729,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8792]) ).

cnf(c_0_11730,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8793]) ).

cnf(c_0_11731,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8794]) ).

cnf(c_0_11732,plain,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8795]) ).

cnf(c_0_11733,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8796]) ).

cnf(c_0_11734,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8797]) ).

cnf(c_0_11735,plain,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8798]) ).

cnf(c_0_11736,plain,
    class_HOL_Oone(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8799]) ).

cnf(c_0_11737,plain,
    class_HOL_Ominus(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_8800]) ).

cnf(c_0_11738,plain,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    inference(split_conjunct,[status(thm)],[c_0_8801]) ).

cnf(c_0_11739,plain,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    inference(split_conjunct,[status(thm)],[c_0_8802]) ).

cnf(c_0_11740,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(split_conjunct,[status(thm)],[c_0_8803]) ).

cnf(c_0_11741,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(split_conjunct,[status(thm)],[c_0_8804]) ).

cnf(c_0_11742,plain,
    c_UNIV != c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_8805]) ).

cnf(c_0_11743,plain,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    inference(split_conjunct,[status(thm)],[c_0_8806]) ).

cnf(c_0_11744,plain,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    inference(split_conjunct,[status(thm)],[c_0_8807]) ).

cnf(c_0_11745,plain,
    c_0 != c_1,
    inference(split_conjunct,[status(thm)],[c_0_8808]) ).

cnf(c_0_11746,plain,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    inference(split_conjunct,[status(thm)],[c_0_8809]) ).

cnf(c_0_11747,plain,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    inference(split_conjunct,[status(thm)],[c_0_8810]) ).

cnf(c_0_11748,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble8,X17) = X9,
    c_0_8811,
    [final] ).

cnf(c_0_11749,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble7,X17) = X8,
    c_0_8812,
    [final] ).

cnf(c_0_11750,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble6,X17) = X7,
    c_0_8813,
    [final] ).

cnf(c_0_11751,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble5,X17) = X6,
    c_0_8814,
    [final] ).

cnf(c_0_11752,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble4,X17) = X5,
    c_0_8815,
    [final] ).

cnf(c_0_11753,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble3,X17) = X4,
    c_0_8816,
    [final] ).

cnf(c_0_11754,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble2,X17) = X3,
    c_0_8817,
    [final] ).

cnf(c_0_11755,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble1,X17) = X2,
    c_0_8818,
    [final] ).

cnf(c_0_11756,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble0,X17) = X1,
    c_0_8819,
    [final] ).

cnf(c_0_11757,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleF,X17) = X16,
    c_0_8820,
    [final] ).

cnf(c_0_11758,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleE,X17) = X15,
    c_0_8821,
    [final] ).

cnf(c_0_11759,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleD,X17) = X14,
    c_0_8822,
    [final] ).

cnf(c_0_11760,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleC,X17) = X13,
    c_0_8823,
    [final] ).

cnf(c_0_11761,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleB,X17) = X12,
    c_0_8824,
    [final] ).

cnf(c_0_11762,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleA,X17) = X11,
    c_0_8825,
    [final] ).

cnf(c_0_11763,plain,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble9,X17) = X10,
    c_0_8826,
    [final] ).

cnf(c_0_11764,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble8,X17) = X9,
    c_0_8827,
    [final] ).

cnf(c_0_11765,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble7,X17) = X8,
    c_0_8828,
    [final] ).

cnf(c_0_11766,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble6,X17) = X7,
    c_0_8829,
    [final] ).

cnf(c_0_11767,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble5,X17) = X6,
    c_0_8830,
    [final] ).

cnf(c_0_11768,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble4,X17) = X5,
    c_0_8831,
    [final] ).

cnf(c_0_11769,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble3,X17) = X4,
    c_0_8832,
    [final] ).

cnf(c_0_11770,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble2,X17) = X3,
    c_0_8833,
    [final] ).

cnf(c_0_11771,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble1,X17) = X2,
    c_0_8834,
    [final] ).

cnf(c_0_11772,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble0,X17) = X1,
    c_0_8835,
    [final] ).

cnf(c_0_11773,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleF,X17) = X16,
    c_0_8836,
    [final] ).

cnf(c_0_11774,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleE,X17) = X15,
    c_0_8837,
    [final] ).

cnf(c_0_11775,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleD,X17) = X14,
    c_0_8838,
    [final] ).

cnf(c_0_11776,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleC,X17) = X13,
    c_0_8839,
    [final] ).

cnf(c_0_11777,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleB,X17) = X12,
    c_0_8840,
    [final] ).

cnf(c_0_11778,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleA,X17) = X11,
    c_0_8841,
    [final] ).

cnf(c_0_11779,plain,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble9,X17) = X10,
    c_0_8842,
    [final] ).

cnf(c_0_11780,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    c_0_8843,
    [final] ).

cnf(c_0_11781,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    c_0_8844,
    [final] ).

cnf(c_0_11782,plain,
    ( c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5) = X1
    | ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5)) ),
    c_0_8845,
    [final] ).

cnf(c_0_11783,plain,
    ( c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    c_0_8846,
    [final] ).

cnf(c_0_11784,plain,
    ( c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    c_0_8847,
    [final] ).

cnf(c_0_11785,plain,
    ( c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    c_0_8848,
    [final] ).

cnf(c_0_11786,plain,
    ( c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_8849,
    [final] ).

cnf(c_0_11787,plain,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_8850,
    [final] ).

cnf(c_0_11788,plain,
    ( c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_8851,
    [final] ).

cnf(c_0_11789,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_8852,
    [final] ).

cnf(c_0_11790,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_8853,
    [final] ).

cnf(c_0_11791,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_8854,
    [final] ).

cnf(c_0_11792,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_8855,
    [final] ).

cnf(c_0_11793,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_8856,
    [final] ).

cnf(c_0_11794,plain,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_8857,
    [final] ).

cnf(c_0_11795,plain,
    ( c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    c_0_8858,
    [final] ).

cnf(c_0_11796,plain,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_8859,
    [final] ).

cnf(c_0_11797,plain,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_8860,
    [final] ).

cnf(c_0_11798,plain,
    ( c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    c_0_8861,
    [final] ).

cnf(c_0_11799,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    c_0_8862,
    [final] ).

cnf(c_0_11800,plain,
    ( c_plus(X1,X2,tc_nat) = c_plus(X3,X4,tc_nat)
    | ~ c_in(c_Pair(c_Pair(X1,X4,tc_nat,tc_nat),c_Pair(X3,X2,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    c_0_8863,
    [final] ).

cnf(c_0_11801,plain,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8864,
    [final] ).

cnf(c_0_11802,plain,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8865,
    [final] ).

cnf(c_0_11803,plain,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8866,
    [final] ).

cnf(c_0_11804,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    c_0_8867,
    [final] ).

cnf(c_0_11805,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    c_0_8868,
    [final] ).

cnf(c_0_11806,plain,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8869,
    [final] ).

cnf(c_0_11807,plain,
    ( c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    c_0_8870,
    [final] ).

cnf(c_0_11808,plain,
    ( c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    c_0_8871,
    [final] ).

cnf(c_0_11809,plain,
    ( c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8872,
    [final] ).

cnf(c_0_11810,plain,
    ( c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    c_0_8873,
    [final] ).

cnf(c_0_11811,plain,
    ( c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8874,
    [final] ).

cnf(c_0_11812,plain,
    ( c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    c_0_8875,
    [final] ).

cnf(c_0_11813,plain,
    ( c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    c_0_8876,
    [final] ).

cnf(c_0_11814,plain,
    ( c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    c_0_8877,
    [final] ).

cnf(c_0_11815,plain,
    ( c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    c_0_8878,
    [final] ).

cnf(c_0_11816,plain,
    ( c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    c_0_8879,
    [final] ).

cnf(c_0_11817,plain,
    ( c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    c_0_8880,
    [final] ).

cnf(c_0_11818,plain,
    c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X1,X2,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    c_0_8881,
    [final] ).

cnf(c_0_11819,plain,
    ( c_in(c_Pair(c_Pair(X1,X2,tc_nat,tc_nat),c_Pair(X3,X4,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_plus(X1,X4,tc_nat) != c_plus(X3,X2,tc_nat) ),
    c_0_8882,
    [final] ).

cnf(c_0_11820,plain,
    ( c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3)) ),
    c_0_8883,
    [final] ).

cnf(c_0_11821,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    c_0_8884,
    [final] ).

cnf(c_0_11822,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    c_0_8885,
    [final] ).

cnf(c_0_11823,plain,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | c_in(c_Pair(X1,X3,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X2),c_List_Olist_OCons(X6,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_8886,
    [final] ).

cnf(c_0_11824,plain,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    c_0_8887,
    [final] ).

cnf(c_0_11825,plain,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    c_0_8888,
    [final] ).

cnf(c_0_11826,plain,
    ( c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_8889,
    [final] ).

cnf(c_0_11827,plain,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_8890,
    [final] ).

cnf(c_0_11828,plain,
    ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_8891,
    [final] ).

cnf(c_0_11829,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    c_0_8892,
    [final] ).

cnf(c_0_11830,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    c_0_8893,
    [final] ).

cnf(c_0_11831,plain,
    ( c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    c_0_8894,
    [final] ).

cnf(c_0_11832,plain,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_8895,
    [final] ).

cnf(c_0_11833,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X3))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    c_0_8896,
    [final] ).

cnf(c_0_11834,plain,
    ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    c_0_8897,
    [final] ).

cnf(c_0_11835,plain,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    c_0_8898,
    [final] ).

cnf(c_0_11836,plain,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    c_0_8899,
    [final] ).

cnf(c_0_11837,plain,
    ( c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    c_0_8900,
    [final] ).

cnf(c_0_11838,plain,
    ( c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    c_0_8901,
    [final] ).

cnf(c_0_11839,plain,
    c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X1,X2,X4,X5),c_Datatype__Universe_Ontrunc(X1,X3,X4,X5),X4,X5) = c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OScons(X2,X3,X4,X5),X4,X5),
    c_0_8902,
    [final] ).

cnf(c_0_11840,plain,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    c_0_8903,
    [final] ).

cnf(c_0_11841,plain,
    ( c_Wellfounded__Recursion_Owf(X1,X2)
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    c_0_8904,
    [final] ).

cnf(c_0_11842,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    c_0_8905,
    [final] ).

cnf(c_0_11843,plain,
    ( c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
    | ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
    c_0_8906,
    [final] ).

cnf(c_0_11844,plain,
    ( c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
    | ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    c_0_8907,
    [final] ).

cnf(c_0_11845,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    c_0_8908,
    [final] ).

cnf(c_0_11846,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    c_0_8909,
    [final] ).

cnf(c_0_11847,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4) ),
    c_0_8910,
    [final] ).

cnf(c_0_11848,plain,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | X4 = X5
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X2),c_List_Olist_OCons(X5,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X6,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_8911,
    [final] ).

cnf(c_0_11849,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat) ),
    c_0_8912,
    [final] ).

cnf(c_0_11850,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    c_0_8913,
    [final] ).

cnf(c_0_11851,plain,
    ( c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5)
    | ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
    c_0_8914,
    [final] ).

cnf(c_0_11852,plain,
    ( c_append(c_List_Ozip(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_append(X1,X2,X3),c_append(X4,X5,X6),X3,X6)
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X4,tc_List_Olist(X6))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X6)) ),
    c_0_8915,
    [final] ).

cnf(c_0_11853,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
    c_0_8916,
    [final] ).

cnf(c_0_11854,plain,
    c_Datatype__Universe_Ousum(c_Relation_ODomain(X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Relation_ODomain(X2,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X3,X4) = c_Relation_ODomain(c_Datatype__Universe_Odsum(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),
    c_0_8917,
    [final] ).

cnf(c_0_11855,plain,
    c_Datatype__Universe_Ouprod(c_Relation_ODomain(X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Relation_ODomain(X2,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X3,X4) = c_Relation_ODomain(c_Datatype__Universe_Odprod(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),
    c_0_8918,
    [final] ).

cnf(c_0_11856,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
    c_0_8919,
    [final] ).

cnf(c_0_11857,plain,
    ( c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8920,
    [final] ).

cnf(c_0_11858,plain,
    ( c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8921,
    [final] ).

cnf(c_0_11859,plain,
    ( c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8922,
    [final] ).

cnf(c_0_11860,plain,
    ( c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8923,
    [final] ).

cnf(c_0_11861,plain,
    ( c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8924,
    [final] ).

cnf(c_0_11862,plain,
    c_Relation_Orel__comp(X1,c_Nat_Opower(X1,X2,tc_set(tc_prod(X3,X3))),X3,X3,X3) = c_Nat_Opower(X1,c_Suc(X2),tc_set(tc_prod(X3,X3))),
    c_0_8925,
    [final] ).

cnf(c_0_11863,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    c_0_8926,
    [final] ).

cnf(c_0_11864,plain,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    c_0_8927,
    [final] ).

cnf(c_0_11865,plain,
    ( c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3) = X1
    | ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3)) ),
    c_0_8928,
    [final] ).

cnf(c_0_11866,plain,
    c_List_Olist_OCons(c_Pair(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X6),X3,X6),
    c_0_8929,
    [final] ).

cnf(c_0_11867,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
    c_0_8930,
    [final] ).

cnf(c_0_11868,plain,
    ( c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_8931,
    [final] ).

cnf(c_0_11869,plain,
    ( c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8932,
    [final] ).

cnf(c_0_11870,plain,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) != c_Nat_Osize(X3,tc_List_Olist(X4))
    | c_Map_Omap__of(c_List_Ozip(X1,X3,X2,X4),X5,X2,X4) != c_Datatype_Ooption_ONone
    | ~ c_in(X5,c_List_Oset(X1,X2),X2) ),
    c_0_8933,
    [final] ).

cnf(c_0_11871,plain,
    ( c_Pair(c_List_Onth(X1,X5,X3),c_List_Onth(X2,X5,X4),X3,X4) = c_List_Onth(c_List_Ozip(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_less(X5,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_less(X5,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat) ),
    c_0_8934,
    [final] ).

cnf(c_0_11872,plain,
    ( c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8935,
    [final] ).

cnf(c_0_11873,plain,
    ( c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8936,
    [final] ).

cnf(c_0_11874,plain,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    c_0_8937,
    [final] ).

cnf(c_0_11875,plain,
    c_Relation_Orel__comp(X1,c_Relation_OId,X2,X3,X2) = X1,
    c_0_8938,
    [final] ).

cnf(c_0_11876,plain,
    c_Relation_Orel__comp(c_Relation_OId,X1,X2,X2,X3) = X1,
    c_0_8939,
    [final] ).

cnf(c_0_11877,plain,
    ( c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    c_0_8940,
    [final] ).

cnf(c_0_11878,plain,
    c_GCD_Ogcd(c_Pair(X1,c_plus(X2,X1,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    c_0_8941,
    [final] ).

cnf(c_0_11879,plain,
    c_GCD_Ogcd(c_Pair(X1,c_plus(X1,X2,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    c_0_8942,
    [final] ).

cnf(c_0_11880,plain,
    c_GCD_Ogcd(c_Pair(c_plus(X1,X2,tc_nat),X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    c_0_8943,
    [final] ).

cnf(c_0_11881,plain,
    c_List_Oreplicate(c_Orderings_Omin(X1,X4,tc_nat),c_Pair(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X5,X6),X3,X6),
    c_0_8944,
    [final] ).

cnf(c_0_11882,plain,
    ( c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4) = c_List_Olist__update(X1,X2,X5,X4)
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    c_0_8945,
    [final] ).

cnf(c_0_11883,plain,
    ( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X2),c_Main_Olexord__Nil__left__2(X1,X2),X2) = X1
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_8946,
    [final] ).

cnf(c_0_11884,plain,
    ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8947,
    [final] ).

cnf(c_0_11885,plain,
    ( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
    | ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
    c_0_8948,
    [final] ).

cnf(c_0_11886,plain,
    ( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
    c_0_8949,
    [final] ).

cnf(c_0_11887,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X2,tc_nat),
    c_0_8950,
    [final] ).

cnf(c_0_11888,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X1,tc_nat),
    c_0_8951,
    [final] ).

cnf(c_0_11889,plain,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_8952,
    [final] ).

cnf(c_0_11890,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_8953,
    [final] ).

cnf(c_0_11891,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8954,
    [final] ).

cnf(c_0_11892,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8955,
    [final] ).

cnf(c_0_11893,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_8956,
    [final] ).

cnf(c_0_11894,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_8957,
    [final] ).

cnf(c_0_11895,plain,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    c_0_8958,
    [final] ).

cnf(c_0_11896,plain,
    ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    c_0_8959,
    [final] ).

cnf(c_0_11897,plain,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    c_0_8960,
    [final] ).

cnf(c_0_11898,plain,
    ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_8961,
    [final] ).

cnf(c_0_11899,plain,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_8962,
    [final] ).

cnf(c_0_11900,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_8963,
    [final] ).

cnf(c_0_11901,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8964,
    [final] ).

cnf(c_0_11902,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8965,
    [final] ).

cnf(c_0_11903,plain,
    ( c_Nat_Opower(c_uminus(X1,X2),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2) = c_Nat_Opower(X1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_8966,
    [final] ).

cnf(c_0_11904,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    c_0_8967,
    [final] ).

cnf(c_0_11905,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X1)),c_Datatype__Universe_OIn1(X2,X3,X4),X3,X4) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X1),X2,X3,X4),X3,X4),
    c_0_8968,
    [final] ).

cnf(c_0_11906,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X1)),c_Datatype__Universe_OIn0(X2,X3,X4),X3,X4) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X1),X2,X3,X4),X3,X4),
    c_0_8969,
    [final] ).

cnf(c_0_11907,plain,
    ( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
    | ~ c_Wellfounded__Recursion_Owf(X3,X2) ),
    c_0_8970,
    [final] ).

cnf(c_0_11908,plain,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1
    | ~ c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    c_0_8971,
    [final] ).

cnf(c_0_11909,plain,
    ( X1 = X2
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
    c_0_8972,
    [final] ).

cnf(c_0_11910,plain,
    c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)),
    c_0_8973,
    [final] ).

cnf(c_0_11911,plain,
    ( c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    c_0_8974,
    [final] ).

cnf(c_0_11912,plain,
    ( c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    c_0_8975,
    [final] ).

cnf(c_0_11913,plain,
    c_insert(c_Message_OHPair(X1,X2),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oparts(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)),
    c_0_8976,
    [final] ).

cnf(c_0_11914,plain,
    c_insert(c_Message_OHPair(X1,X2),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)),
    c_0_8977,
    [final] ).

cnf(c_0_11915,plain,
    ( c_Map_Omap__of(c_List_Ozip(X1,X2,X3,X4),X5,X3,X4) = c_Datatype_Ooption_ONone
    | c_in(X5,c_List_Oset(X1,X3),X3)
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    c_0_8978,
    [final] ).

cnf(c_0_11916,plain,
    c_insert(c_Message_Omsg_OMPair(X1,X2),c_Message_Oparts(c_insert(X1,c_insert(X2,X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)),
    c_0_8979,
    [final] ).

cnf(c_0_11917,plain,
    c_insert(c_Message_Omsg_OMPair(X1,X2),c_Message_Oanalz(c_insert(X1,c_insert(X2,X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)),
    c_0_8980,
    [final] ).

cnf(c_0_11918,plain,
    c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    c_0_8981,
    [final] ).

cnf(c_0_11919,plain,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_8982,
    [final] ).

cnf(c_0_11920,plain,
    c_append(c_List_Otake(X1,X2,X4),c_List_Otake(c_minus(X1,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4) = c_List_Otake(X1,c_append(X2,X3,X4),X4),
    c_0_8983,
    [final] ).

cnf(c_0_11921,plain,
    c_append(c_List_Odrop(X1,X2,X4),c_List_Odrop(c_minus(X1,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4) = c_List_Odrop(X1,c_append(X2,X3,X4),X4),
    c_0_8984,
    [final] ).

cnf(c_0_11922,plain,
    ( X1 = X2
    | c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
    c_0_8985,
    [final] ).

cnf(c_0_11923,plain,
    ( X1 = X2
    | c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
    c_0_8986,
    [final] ).

cnf(c_0_11924,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5) ),
    c_0_8987,
    [final] ).

cnf(c_0_11925,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5) ),
    c_0_8988,
    [final] ).

cnf(c_0_11926,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8989,
    [final] ).

cnf(c_0_11927,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8990,
    [final] ).

cnf(c_0_11928,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8991,
    [final] ).

cnf(c_0_11929,plain,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8992,
    [final] ).

cnf(c_0_11930,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8993,
    [final] ).

cnf(c_0_11931,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8994,
    [final] ).

cnf(c_0_11932,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8995,
    [final] ).

cnf(c_0_11933,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_8996,
    [final] ).

cnf(c_0_11934,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_8997,
    [final] ).

cnf(c_0_11935,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_8998,
    [final] ).

cnf(c_0_11936,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_8999,
    [final] ).

cnf(c_0_11937,plain,
    ( c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9000,
    [final] ).

cnf(c_0_11938,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9001,
    [final] ).

cnf(c_0_11939,plain,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9002,
    [final] ).

cnf(c_0_11940,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9003,
    [final] ).

cnf(c_0_11941,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9004,
    [final] ).

cnf(c_0_11942,plain,
    ( c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1 ),
    c_0_9005,
    [final] ).

cnf(c_0_11943,plain,
    c_List_Olist__update(c_append(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize(X1,tc_List_Olist(X4)),X5,X4) = c_append(X1,c_List_Olist_OCons(X5,X3,X4),X4),
    c_0_9006,
    [final] ).

cnf(c_0_11944,plain,
    ( c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2))
    | ~ c_in(X1,X5,X2) ),
    c_0_9007,
    [final] ).

cnf(c_0_11945,plain,
    ( c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3))
    | ~ c_in(X1,X4,X2) ),
    c_0_9008,
    [final] ).

cnf(c_0_11946,plain,
    c_Pair(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegateSnd(c_Pair(X1,X2,tc_IntDef_Oint,tc_IntDef_Oint)),
    c_0_9009,
    [final] ).

cnf(c_0_11947,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9010,
    [final] ).

cnf(c_0_11948,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9011,
    [final] ).

cnf(c_0_11949,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9012,
    [final] ).

cnf(c_0_11950,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9013,
    [final] ).

cnf(c_0_11951,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9014,
    [final] ).

cnf(c_0_11952,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9015,
    [final] ).

cnf(c_0_11953,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9016,
    [final] ).

cnf(c_0_11954,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9017,
    [final] ).

cnf(c_0_11955,plain,
    c_IntDiv_OposDivAlg(c_Pair(c_0,X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    c_0_9018,
    [final] ).

cnf(c_0_11956,plain,
    c_GCD_Ogcd(c_Pair(X1,c_times(X1,X2,tc_nat),tc_nat,tc_nat)) = X1,
    c_0_9019,
    [final] ).

cnf(c_0_11957,plain,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9020,
    [final] ).

cnf(c_0_11958,plain,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9021,
    [final] ).

cnf(c_0_11959,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9022,
    [final] ).

cnf(c_0_11960,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9023,
    [final] ).

cnf(c_0_11961,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9024,
    [final] ).

cnf(c_0_11962,plain,
    ( c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9025,
    [final] ).

cnf(c_0_11963,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9026,
    [final] ).

cnf(c_0_11964,plain,
    ( c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9027,
    [final] ).

cnf(c_0_11965,plain,
    c_Nat_Osize(c_List_Ozip(X1,X2,X3,X4),tc_List_Olist(tc_prod(X3,X4))) = c_Orderings_Omin(c_Nat_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),
    c_0_9028,
    [final] ).

cnf(c_0_11966,plain,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X2,X4) = X3
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    c_0_9029,
    [final] ).

cnf(c_0_11967,plain,
    ( c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2))
    | ~ c_in(X1,X3,X2) ),
    c_0_9030,
    [final] ).

cnf(c_0_11968,plain,
    ( c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    c_0_9031,
    [final] ).

cnf(c_0_11969,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Olist_OCons(X2,c_List_Otake(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4),X4) = c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) ),
    c_0_9032,
    [final] ).

cnf(c_0_11970,plain,
    ( c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_9033,
    [final] ).

cnf(c_0_11971,plain,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    c_0_9034,
    [final] ).

cnf(c_0_11972,plain,
    ( c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3) = X1
    | ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3)) ),
    c_0_9035,
    [final] ).

cnf(c_0_11973,plain,
    ( c_List_Onth(c_List_Odrop(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_plus(X1,X4,tc_nat),X3)
    | ~ c_lessequals(c_plus(X1,X4,tc_nat),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    c_0_9036,
    [final] ).

cnf(c_0_11974,plain,
    c_div(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    c_0_9037,
    [final] ).

cnf(c_0_11975,plain,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5 ),
    c_0_9038,
    [final] ).

cnf(c_0_11976,plain,
    ( c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_plus(X3,c_div(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9039,
    [final] ).

cnf(c_0_11977,plain,
    ( c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_plus(X2,c_div(X1,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    c_0_9040,
    [final] ).

cnf(c_0_11978,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
    c_0_9041,
    [final] ).

cnf(c_0_11979,plain,
    c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X1))),c_Numeral_Onumber__of(X2,tc_nat),tc_nat),
    c_0_9042,
    [final] ).

cnf(c_0_11980,plain,
    c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_div(c_Suc(c_Suc(c_Suc(X1))),c_Numeral_Onumber__of(X2,tc_nat),tc_nat),
    c_0_9043,
    [final] ).

cnf(c_0_11981,plain,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X1,X2,X3),X4,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X3,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X4),tc_Message_Omsg),
    c_0_9044,
    [final] ).

cnf(c_0_11982,plain,
    ( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    c_0_9045,
    [final] ).

cnf(c_0_11983,plain,
    ( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X1,X3)
    | ~ c_Relation_Otrans(X2,X4) ),
    c_0_9046,
    [final] ).

cnf(c_0_11984,plain,
    ( c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg))
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    c_0_9047,
    [final] ).

cnf(c_0_11985,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    c_0_9048,
    [final] ).

cnf(c_0_11986,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    c_0_9049,
    [final] ).

cnf(c_0_11987,plain,
    ( c_plus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_plus(X3,X4,X2),X2)
    | ~ class_Ring__and__Field_Osemiring(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9050,
    [final] ).

cnf(c_0_11988,plain,
    ( c_minus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_minus(X3,X4,X2),X2)
    | ~ class_Ring__and__Field_Oring(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9051,
    [final] ).

cnf(c_0_11989,plain,
    ( c_plus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_plus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Osemiring(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9052,
    [final] ).

cnf(c_0_11990,plain,
    ( c_minus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_minus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oring(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9053,
    [final] ).

cnf(c_0_11991,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
    c_0_9054,
    [final] ).

cnf(c_0_11992,plain,
    ( ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9055,
    [final] ).

cnf(c_0_11993,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9056,
    [final] ).

cnf(c_0_11994,plain,
    ( c_lessequals(X1,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9057,
    [final] ).

cnf(c_0_11995,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9058,
    [final] ).

cnf(c_0_11996,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9059,
    [final] ).

cnf(c_0_11997,plain,
    ( c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9060,
    [final] ).

cnf(c_0_11998,plain,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(X1,X4,X3)
    | ~ c_less(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9061,
    [final] ).

cnf(c_0_11999,plain,
    ( c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9062,
    [final] ).

cnf(c_0_12000,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9063,
    [final] ).

cnf(c_0_12001,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9064,
    [final] ).

cnf(c_0_12002,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9065,
    [final] ).

cnf(c_0_12003,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9066,
    [final] ).

cnf(c_0_12004,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9067,
    [final] ).

cnf(c_0_12005,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9068,
    [final] ).

cnf(c_0_12006,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9069,
    [final] ).

cnf(c_0_12007,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9070,
    [final] ).

cnf(c_0_12008,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9071,
    [final] ).

cnf(c_0_12009,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9072,
    [final] ).

cnf(c_0_12010,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X5,X4,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9073,
    [final] ).

cnf(c_0_12011,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9074,
    [final] ).

cnf(c_0_12012,plain,
    c_snd(c_Pair(X1,X2,X3,X4),X3,X4) = X2,
    c_0_9075,
    [final] ).

cnf(c_0_12013,plain,
    c_fst(c_Pair(X1,X2,X3,X4),X3,X4) = X1,
    c_0_9076,
    [final] ).

cnf(c_0_12014,plain,
    c_Divides_Oop_Amod(X1,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat),
    c_0_9077,
    [final] ).

cnf(c_0_12015,plain,
    c_div(X1,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat),
    c_0_9078,
    [final] ).

cnf(c_0_12016,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9079,
    [final] ).

cnf(c_0_12017,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9080,
    [final] ).

cnf(c_0_12018,plain,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9081,
    [final] ).

cnf(c_0_12019,plain,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9082,
    [final] ).

cnf(c_0_12020,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    c_0_9083,
    [final] ).

cnf(c_0_12021,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    c_0_9084,
    [final] ).

cnf(c_0_12022,plain,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(c_List_Osublist(X2,X4,X3),X3),X3) ),
    c_0_9085,
    [final] ).

cnf(c_0_12023,plain,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(c_List_Oremove1(X4,X2,X3),X3),X3) ),
    c_0_9086,
    [final] ).

cnf(c_0_12024,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) ),
    c_0_9087,
    [final] ).

cnf(c_0_12025,plain,
    c_Nat_Osize(c_List_Olist__update(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize(X1,tc_List_Olist(X4)),
    c_0_9088,
    [final] ).

cnf(c_0_12026,plain,
    c_Nat_Osize(c_Pair(X1,X2,X3,X4),tc_prod(X3,X4)) = c_0,
    c_0_9089,
    [final] ).

cnf(c_0_12027,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9090,
    [final] ).

cnf(c_0_12028,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9091,
    [final] ).

cnf(c_0_12029,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9092,
    [final] ).

cnf(c_0_12030,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9093,
    [final] ).

cnf(c_0_12031,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9094,
    [final] ).

cnf(c_0_12032,plain,
    ( c_minus(c_Suc(c_minus(X1,X2,tc_nat)),X3,tc_nat) = c_minus(c_Suc(X1),c_plus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_9095,
    [final] ).

cnf(c_0_12033,plain,
    ( c_minus(c_plus(X1,X3,tc_nat),c_Suc(X2),tc_nat) = c_minus(X1,c_Suc(c_minus(X2,X3,tc_nat)),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    c_0_9096,
    [final] ).

cnf(c_0_12034,plain,
    ( X1 = X2
    | c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) ),
    c_0_9097,
    [final] ).

cnf(c_0_12035,plain,
    ( X1 = X2
    | c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4) ),
    c_0_9098,
    [final] ).

cnf(c_0_12036,plain,
    ( c_List_Olist__update(X1,X2,c_List_Onth(X1,X2,X3),X3) = X1
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    c_0_9099,
    [final] ).

cnf(c_0_12037,plain,
    c_GCD_Ogcd(c_Pair(c_Suc(c_0),X1,tc_nat,tc_nat)) = c_1,
    c_0_9100,
    [final] ).

cnf(c_0_12038,plain,
    c_GCD_Ogcd(c_Pair(X1,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
    c_0_9101,
    [final] ).

cnf(c_0_12039,plain,
    ( c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | X2 = c_Numeral_Obit_OB0
    | c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9102,
    [final] ).

cnf(c_0_12040,plain,
    c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1,
    c_0_9103,
    [final] ).

cnf(c_0_12041,plain,
    c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1,
    c_0_9104,
    [final] ).

cnf(c_0_12042,plain,
    c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1,
    c_0_9105,
    [final] ).

cnf(c_0_12043,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9106,
    [final] ).

cnf(c_0_12044,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9107,
    [final] ).

cnf(c_0_12045,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9108,
    [final] ).

cnf(c_0_12046,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9109,
    [final] ).

cnf(c_0_12047,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9110,
    [final] ).

cnf(c_0_12048,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9111,
    [final] ).

cnf(c_0_12049,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9112,
    [final] ).

cnf(c_0_12050,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9113,
    [final] ).

cnf(c_0_12051,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9114,
    [final] ).

cnf(c_0_12052,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9115,
    [final] ).

cnf(c_0_12053,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9116,
    [final] ).

cnf(c_0_12054,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9117,
    [final] ).

cnf(c_0_12055,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9118,
    [final] ).

cnf(c_0_12056,plain,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    c_0_9119,
    [final] ).

cnf(c_0_12057,plain,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9120,
    [final] ).

cnf(c_0_12058,plain,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9121,
    [final] ).

cnf(c_0_12059,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_ONumb(X5,X3,X4),
    c_0_9122,
    [final] ).

cnf(c_0_12060,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OLeaf(X5,X3,X4),
    c_0_9123,
    [final] ).

cnf(c_0_12061,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OAtom(X5,X3,X4),
    c_0_9124,
    [final] ).

cnf(c_0_12062,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    c_0_9125,
    [final] ).

cnf(c_0_12063,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    c_0_9126,
    [final] ).

cnf(c_0_12064,plain,
    c_Datatype__Universe_OAtom(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    c_0_9127,
    [final] ).

cnf(c_0_12065,plain,
    ( c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    c_0_9128,
    [final] ).

cnf(c_0_12066,plain,
    ( c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    c_0_9129,
    [final] ).

cnf(c_0_12067,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat) ),
    c_0_9130,
    [final] ).

cnf(c_0_12068,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat) ),
    c_0_9131,
    [final] ).

cnf(c_0_12069,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat) ),
    c_0_9132,
    [final] ).

cnf(c_0_12070,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat) ),
    c_0_9133,
    [final] ).

cnf(c_0_12071,plain,
    c_Pair(c_Main_Osurj__pair__1(X1,X2,X3),c_Main_Osurj__pair__2(X1,X2,X3),X2,X3) = X1,
    c_0_9134,
    [final] ).

cnf(c_0_12072,plain,
    c_Pair(c_fst(X1,X2,X3),c_snd(X1,X2,X3),X2,X3) = X1,
    c_0_9135,
    [final] ).

cnf(c_0_12073,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_times(X2,X1,tc_nat),c_times(X3,X1,tc_nat),tc_nat) ),
    c_0_9136,
    [final] ).

cnf(c_0_12074,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) ),
    c_0_9137,
    [final] ).

cnf(c_0_12075,plain,
    ( c_less(c_0,X1,X2)
    | c_less(X1,c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9138,
    [final] ).

cnf(c_0_12076,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9139,
    [final] ).

cnf(c_0_12077,plain,
    ( c_less(c_0,X1,X2)
    | c_less(X1,c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9140,
    [final] ).

cnf(c_0_12078,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9141,
    [final] ).

cnf(c_0_12079,plain,
    c_Relation_OImage(c_List_Olistrel(X1,X2),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X2)),tc_List_Olist(X2),tc_List_Olist(X2)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X2)),
    c_0_9142,
    [final] ).

cnf(c_0_12080,plain,
    ( c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X2,X5,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9143,
    [final] ).

cnf(c_0_12081,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9144,
    [final] ).

cnf(c_0_12082,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    c_0_9145,
    [final] ).

cnf(c_0_12083,plain,
    c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oparts(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)),
    c_0_9146,
    [final] ).

cnf(c_0_12084,plain,
    ( c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_less(c_1,X1,X3)
    | ~ c_less(X2,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9147,
    [final] ).

cnf(c_0_12085,plain,
    ( c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_less(c_1,X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9148,
    [final] ).

cnf(c_0_12086,plain,
    ( c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Olist__inter(X2,X4,X3),X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3) ),
    c_0_9149,
    [final] ).

cnf(c_0_12087,plain,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9150,
    [final] ).

cnf(c_0_12088,plain,
    ( c_List_Otake(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(X2,c_plus(X2,X1,tc_nat))
    | ~ c_lessequals(c_plus(X2,X1,tc_nat),X3,tc_nat) ),
    c_0_9151,
    [final] ).

cnf(c_0_12089,plain,
    ( c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9152,
    [final] ).

cnf(c_0_12090,plain,
    ( c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9153,
    [final] ).

cnf(c_0_12091,plain,
    ( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9154,
    [final] ).

cnf(c_0_12092,plain,
    ( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9155,
    [final] ).

cnf(c_0_12093,plain,
    ( c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9156,
    [final] ).

cnf(c_0_12094,plain,
    ( c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9157,
    [final] ).

cnf(c_0_12095,plain,
    ( c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9158,
    [final] ).

cnf(c_0_12096,plain,
    ( c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9159,
    [final] ).

cnf(c_0_12097,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,X2,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9160,
    [final] ).

cnf(c_0_12098,plain,
    ( X1 = c_emptyset
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9161,
    [final] ).

cnf(c_0_12099,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9162,
    [final] ).

cnf(c_0_12100,plain,
    ( X1 = c_emptyset
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9163,
    [final] ).

cnf(c_0_12101,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9164,
    [final] ).

cnf(c_0_12102,plain,
    c_insert(X1,c_minus(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)),X3) = c_insert(X1,X2,X3),
    c_0_9165,
    [final] ).

cnf(c_0_12103,plain,
    c_List_Orev(c_append(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil,X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    c_0_9166,
    [final] ).

cnf(c_0_12104,plain,
    c_inter(c_insert(X1,X2,X3),c_insert(X1,X4,X3),X3) = c_insert(X1,c_inter(X2,X4,X3),X3),
    c_0_9167,
    [final] ).

cnf(c_0_12105,plain,
    c_IntDef_Onat(c_plus(c_minus(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9168,
    [final] ).

cnf(c_0_12106,plain,
    ( c_lessequals(c_0,X1,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9169,
    [final] ).

cnf(c_0_12107,plain,
    ( c_lessequals(X1,c_0,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9170,
    [final] ).

cnf(c_0_12108,plain,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X2,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X3),tc_Message_Omsg),
    c_0_9171,
    [final] ).

cnf(c_0_12109,plain,
    ( c_less(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(X1,X3,tc_nat) ),
    c_0_9172,
    [final] ).

cnf(c_0_12110,plain,
    ( c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    c_0_9173,
    [final] ).

cnf(c_0_12111,plain,
    c_IntDef_Onat(c_minus(X2,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9174,
    [final] ).

cnf(c_0_12112,plain,
    ( c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2) = X1
    | ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2)) ),
    c_0_9175,
    [final] ).

cnf(c_0_12113,plain,
    ( c_minus(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X1,X4,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X4,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9176,
    [final] ).

cnf(c_0_12114,plain,
    c_Divides_Oop_Amod(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    c_0_9177,
    [final] ).

cnf(c_0_12115,plain,
    c_Divides_Oop_Amod(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    c_0_9178,
    [final] ).

cnf(c_0_12116,plain,
    c_Divides_Oop_Amod(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_Divides_Oop_Amod(X1,X3,tc_nat),
    c_0_9179,
    [final] ).

cnf(c_0_12117,plain,
    ( c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_9180,
    [final] ).

cnf(c_0_12118,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_ONumb(X2,X3,X4),X3,X4) = c_Datatype__Universe_ONumb(X2,X3,X4),
    c_0_9181,
    [final] ).

cnf(c_0_12119,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OLeaf(X2,X3,X4),X3,X4) = c_Datatype__Universe_OLeaf(X2,X3,X4),
    c_0_9182,
    [final] ).

cnf(c_0_12120,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OAtom(X2,X3,X4),X3,X4) = c_Datatype__Universe_OAtom(X2,X3,X4),
    c_0_9183,
    [final] ).

cnf(c_0_12121,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9184,
    [final] ).

cnf(c_0_12122,plain,
    c_List_Onth(c_append(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize(X1,tc_List_Olist(X4)),X4) = X2,
    c_0_9185,
    [final] ).

cnf(c_0_12123,plain,
    ( c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9186,
    [final] ).

cnf(c_0_12124,plain,
    c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X1,X2,X3),X4,tc_Event_Oevent)) = c_insert(X3,c_Event_Oknows(c_Message_Oagent_OSpy,X4),tc_Message_Omsg),
    c_0_9187,
    [final] ).

cnf(c_0_12125,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9188,
    [final] ).

cnf(c_0_12126,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9189,
    [final] ).

cnf(c_0_12127,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9190,
    [final] ).

cnf(c_0_12128,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9191,
    [final] ).

cnf(c_0_12129,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9192,
    [final] ).

cnf(c_0_12130,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9193,
    [final] ).

cnf(c_0_12131,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9194,
    [final] ).

cnf(c_0_12132,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9195,
    [final] ).

cnf(c_0_12133,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_minus(X3,c_Numeral_Onumber__of(X4,X2),X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X4)),X2),X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9196,
    [final] ).

cnf(c_0_12134,plain,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    c_0_9197,
    [final] ).

cnf(c_0_12135,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9198,
    [final] ).

cnf(c_0_12136,plain,
    ( c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9199,
    [final] ).

cnf(c_0_12137,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Onth(c_List_Olist_OCons(X2,X3,X4),c_Numeral_Onumber__of(X1,tc_nat),X4) = c_List_Onth(X3,c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X4) ),
    c_0_9200,
    [final] ).

cnf(c_0_12138,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4) ),
    c_0_9201,
    [final] ).

cnf(c_0_12139,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,c_0,X2)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9202,
    [final] ).

cnf(c_0_12140,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    c_0_9203,
    [final] ).

cnf(c_0_12141,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    c_0_9204,
    [final] ).

cnf(c_0_12142,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    c_0_9205,
    [final] ).

cnf(c_0_12143,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    c_0_9206,
    [final] ).

cnf(c_0_12144,plain,
    ( c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat) = c_minus(X1,c_minus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    c_0_9207,
    [final] ).

cnf(c_0_12145,plain,
    ( c_minus(c_plus(X1,X2,tc_nat),X3,tc_nat) = c_plus(X1,c_minus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    c_0_9208,
    [final] ).

cnf(c_0_12146,plain,
    ( c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat) = c_plus(c_minus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_9209,
    [final] ).

cnf(c_0_12147,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9210,
    [final] ).

cnf(c_0_12148,plain,
    c_List_Onth(c_append(X1,X2,X3),c_plus(c_Nat_Osize(X1,tc_List_Olist(X3)),X4,tc_nat),X3) = c_List_Onth(X2,X4,X3),
    c_0_9211,
    [final] ).

cnf(c_0_12149,plain,
    ( c_div(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) = c_div(X1,X3,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9212,
    [final] ).

cnf(c_0_12150,plain,
    ( c_div(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) = c_div(X2,X3,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9213,
    [final] ).

cnf(c_0_12151,plain,
    ( ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9214,
    [final] ).

cnf(c_0_12152,plain,
    ( c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    c_0_9215,
    [final] ).

cnf(c_0_12153,plain,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    c_0_9216,
    [final] ).

cnf(c_0_12154,plain,
    ( X1 = c_0
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9217,
    [final] ).

cnf(c_0_12155,plain,
    c_union(c_Message_Oanalz(c_union(X1,X2,tc_Message_Omsg)),c_Message_Osynth(X1),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(X1),X2,tc_Message_Omsg)),
    c_0_9218,
    [final] ).

cnf(c_0_12156,plain,
    ( c_List_Olist__update(X1,X2,X3,X4) = X1
    | ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X2,tc_nat) ),
    c_0_9219,
    [final] ).

cnf(c_0_12157,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9220,
    [final] ).

cnf(c_0_12158,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_9221,
    [final] ).

cnf(c_0_12159,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_9222,
    [final] ).

cnf(c_0_12160,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_9223,
    [final] ).

cnf(c_0_12161,plain,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    c_0_9224,
    [final] ).

cnf(c_0_12162,plain,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    c_0_9225,
    [final] ).

cnf(c_0_12163,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),tc_nat),tc_nat) ),
    c_0_9226,
    [final] ).

cnf(c_0_12164,plain,
    ( c_List_Onth(c_List_Oupt(X1,X2),X3,tc_nat) = c_plus(X1,X3,tc_nat)
    | ~ c_less(c_plus(X1,X3,tc_nat),X2,tc_nat) ),
    c_0_9227,
    [final] ).

cnf(c_0_12165,plain,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_times(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2),X4,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9228,
    [final] ).

cnf(c_0_12166,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_plus(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2),X4,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9229,
    [final] ).

cnf(c_0_12167,plain,
    ( X1 = c_emptyset
    | c_less(X2,X3,X4)
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_9230,
    [final] ).

cnf(c_0_12168,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,X3,X4)
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_9231,
    [final] ).

cnf(c_0_12169,plain,
    ( X1 = c_emptyset
    | c_less(X2,X3,X4)
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_9232,
    [final] ).

cnf(c_0_12170,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,X3,X4)
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_9233,
    [final] ).

cnf(c_0_12171,plain,
    ( c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9234,
    [final] ).

cnf(c_0_12172,plain,
    ( c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9235,
    [final] ).

cnf(c_0_12173,plain,
    ( c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9236,
    [final] ).

cnf(c_0_12174,plain,
    ( c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    c_0_9237,
    [final] ).

cnf(c_0_12175,plain,
    ( c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    c_0_9238,
    [final] ).

cnf(c_0_12176,plain,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    c_0_9239,
    [final] ).

cnf(c_0_12177,plain,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    c_0_9240,
    [final] ).

cnf(c_0_12178,plain,
    ( c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3)
    | ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)) ),
    c_0_9241,
    [final] ).

cnf(c_0_12179,plain,
    ( c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2)
    | ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2)) ),
    c_0_9242,
    [final] ).

cnf(c_0_12180,plain,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9243,
    [final] ).

cnf(c_0_12181,plain,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    c_0_9244,
    [final] ).

cnf(c_0_12182,plain,
    ( c_less(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ c_less(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9245,
    [final] ).

cnf(c_0_12183,plain,
    ( c_less(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9246,
    [final] ).

cnf(c_0_12184,plain,
    ( c_lessequals(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9247,
    [final] ).

cnf(c_0_12185,plain,
    ( c_lessequals(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_9248,
    [final] ).

cnf(c_0_12186,plain,
    ( c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X1,X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3)) ),
    c_0_9249,
    [final] ).

cnf(c_0_12187,plain,
    ( c_lessequals(X1,c_inter(X2,X3,X4),tc_set(X4))
    | ~ c_lessequals(X1,X2,tc_set(X4))
    | ~ c_lessequals(X1,X3,tc_set(X4)) ),
    c_0_9250,
    [final] ).

cnf(c_0_12188,plain,
    ( ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_9251,
    [final] ).

cnf(c_0_12189,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_9252,
    [final] ).

cnf(c_0_12190,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9253,
    [final] ).

cnf(c_0_12191,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X1,X2,X3),X2,X3) = c_emptyset,
    c_0_9254,
    [final] ).

cnf(c_0_12192,plain,
    c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X1,X2,X3),X2,X3) = c_emptyset,
    c_0_9255,
    [final] ).

cnf(c_0_12193,plain,
    ( c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_9256,
    [final] ).

cnf(c_0_12194,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_lessequals(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9257,
    [final] ).

cnf(c_0_12195,plain,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9258,
    [final] ).

cnf(c_0_12196,plain,
    ( c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_9259,
    [final] ).

cnf(c_0_12197,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Power_Orecpower(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9260,
    [final] ).

cnf(c_0_12198,plain,
    ( c_less(c_0,X1,tc_nat)
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    c_0_9261,
    [final] ).

cnf(c_0_12199,plain,
    ( c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9262,
    [final] ).

cnf(c_0_12200,plain,
    ( c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9263,
    [final] ).

cnf(c_0_12201,plain,
    ( c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9264,
    [final] ).

cnf(c_0_12202,plain,
    ( c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9265,
    [final] ).

cnf(c_0_12203,plain,
    ( c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9266,
    [final] ).

cnf(c_0_12204,plain,
    ( c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9267,
    [final] ).

cnf(c_0_12205,plain,
    ( c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9268,
    [final] ).

cnf(c_0_12206,plain,
    ( c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9269,
    [final] ).

cnf(c_0_12207,plain,
    ( c_less(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    c_0_9270,
    [final] ).

cnf(c_0_12208,plain,
    ( c_lessequals(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    c_0_9271,
    [final] ).

cnf(c_0_12209,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    c_0_9272,
    [final] ).

cnf(c_0_12210,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    c_0_9273,
    [final] ).

cnf(c_0_12211,plain,
    ( X1 = c_emptyset
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9274,
    [final] ).

cnf(c_0_12212,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9275,
    [final] ).

cnf(c_0_12213,plain,
    ( X1 = c_emptyset
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9276,
    [final] ).

cnf(c_0_12214,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9277,
    [final] ).

cnf(c_0_12215,plain,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    c_0_9278,
    [final] ).

cnf(c_0_12216,plain,
    ( c_in(X1,c_SetInterval_OgreaterThanLessThan(X2,X3,X4),X4)
    | ~ c_less(X2,X1,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    c_0_9279,
    [final] ).

cnf(c_0_12217,plain,
    ( c_in(X1,c_SetInterval_OgreaterThanAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ c_less(X2,X1,X4)
    | ~ class_Orderings_Oord(X4) ),
    c_0_9280,
    [final] ).

cnf(c_0_12218,plain,
    ( c_in(X1,c_SetInterval_OatLeastLessThan(X2,X3,X4),X4)
    | ~ c_lessequals(X2,X1,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    c_0_9281,
    [final] ).

cnf(c_0_12219,plain,
    ( c_in(X1,c_SetInterval_OatLeastAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X2,X1,X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    c_0_9282,
    [final] ).

cnf(c_0_12220,plain,
    ( c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9283,
    [final] ).

cnf(c_0_12221,plain,
    ( c_lessequals(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_9284,
    [final] ).

cnf(c_0_12222,plain,
    ( c_less(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_less(X1,X2,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_9285,
    [final] ).

cnf(c_0_12223,plain,
    ( c_less(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_less(X1,X4,X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9286,
    [final] ).

cnf(c_0_12224,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3) ),
    c_0_9287,
    [final] ).

cnf(c_0_12225,plain,
    ( c_Message_Osynth(c_Message_Oanalz(c_insert(X1,X2,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X2))
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    c_0_9288,
    [final] ).

cnf(c_0_12226,plain,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset
    | ~ c_in(X1,X4,X3) ),
    c_0_9289,
    [final] ).

cnf(c_0_12227,plain,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset
    | ~ c_in(X1,X4,X3) ),
    c_0_9290,
    [final] ).

cnf(c_0_12228,plain,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset
    | ~ c_in(X2,X1,X4) ),
    c_0_9291,
    [final] ).

cnf(c_0_12229,plain,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset
    | ~ c_in(X2,X1,X4) ),
    c_0_9292,
    [final] ).

cnf(c_0_12230,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9293,
    [final] ).

cnf(c_0_12231,plain,
    ( c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9294,
    [final] ).

cnf(c_0_12232,plain,
    ( c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9295,
    [final] ).

cnf(c_0_12233,plain,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9296,
    [final] ).

cnf(c_0_12234,plain,
    ( c_divide(c_times(X1,X2,X3),c_times(X4,X2,X3),X3) = c_divide(X1,X4,X3)
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9297,
    [final] ).

cnf(c_0_12235,plain,
    ( c_divide(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) = c_divide(X2,X4,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9298,
    [final] ).

cnf(c_0_12236,plain,
    ( c_HOL_Oabs(c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2),X2) = c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_9299,
    [final] ).

cnf(c_0_12237,plain,
    ( c_divide(c_times(X1,X3,X4),X2,X4) = c_divide(X1,c_divide(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    c_0_9300,
    [final] ).

cnf(c_0_12238,plain,
    ( c_divide(c_divide(X1,X2,X3),X4,X3) = c_divide(X1,c_times(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9301,
    [final] ).

cnf(c_0_12239,plain,
    ( c_in(c_times(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    c_0_9302,
    [final] ).

cnf(c_0_12240,plain,
    ( c_in(c_plus(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    c_0_9303,
    [final] ).

cnf(c_0_12241,plain,
    ( c_in(c_times(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9304,
    [final] ).

cnf(c_0_12242,plain,
    ( c_in(c_minus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9305,
    [final] ).

cnf(c_0_12243,plain,
    ( c_in(c_plus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9306,
    [final] ).

cnf(c_0_12244,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9307,
    [final] ).

cnf(c_0_12245,plain,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInter__iff__1(X1,X2,X3),X3) ),
    c_0_9308,
    [final] ).

cnf(c_0_12246,plain,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3) ),
    c_0_9309,
    [final] ).

cnf(c_0_12247,plain,
    ( c_List_Odistinct(c_append(X1,X2,X3),X3)
    | c_inter(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) != c_emptyset
    | ~ c_List_Odistinct(X1,X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_9310,
    [final] ).

cnf(c_0_12248,plain,
    ( c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_9311,
    [final] ).

cnf(c_0_12249,plain,
    ( c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_nat),tc_IntDef_Oint)) = c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9312,
    [final] ).

cnf(c_0_12250,plain,
    ( c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9313,
    [final] ).

cnf(c_0_12251,plain,
    ( c_minus(c_List_Oset(X2,X3),c_insert(X1,c_emptyset,X3),tc_set(X3)) = c_List_Oset(c_List_Oremove1(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_9314,
    [final] ).

cnf(c_0_12252,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3) ),
    c_0_9315,
    [final] ).

cnf(c_0_12253,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3) ),
    c_0_9316,
    [final] ).

cnf(c_0_12254,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    c_0_9317,
    [final] ).

cnf(c_0_12255,plain,
    c_minus(c_minus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_minus(c_minus(X1,X2,tc_nat),X3,tc_nat),
    c_0_9318,
    [final] ).

cnf(c_0_12256,plain,
    ( c_in(c_List_Onth(X1,X2,X3),c_List_Oset(X1,X3),X3)
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    c_0_9319,
    [final] ).

cnf(c_0_12257,plain,
    ( c_divide(c_times(X1,X4,X3),X2,X3) = c_times(c_divide(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ofield(X3) ),
    c_0_9320,
    [final] ).

cnf(c_0_12258,plain,
    ( c_divide(c_times(X1,X2,X4),X3,X4) = c_times(X1,c_divide(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    c_0_9321,
    [final] ).

cnf(c_0_12259,plain,
    ( c_less(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_less(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9322,
    [final] ).

cnf(c_0_12260,plain,
    ( c_lessequals(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9323,
    [final] ).

cnf(c_0_12261,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_less(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9324,
    [final] ).

cnf(c_0_12262,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_lessequals(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9325,
    [final] ).

cnf(c_0_12263,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9326,
    [final] ).

cnf(c_0_12264,plain,
    c_List_Olast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3),X3) = X2,
    c_0_9327,
    [final] ).

cnf(c_0_12265,plain,
    c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3),X3) = X1,
    c_0_9328,
    [final] ).

cnf(c_0_12266,plain,
    ( c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3)
    | ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3)) ),
    c_0_9329,
    [final] ).

cnf(c_0_12267,plain,
    c_List_Otake(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X1,X3,X4),X4),
    c_0_9330,
    [final] ).

cnf(c_0_12268,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3) ),
    c_0_9331,
    [final] ).

cnf(c_0_12269,plain,
    c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_inter(X1,X3,X2),
    c_0_9332,
    [final] ).

cnf(c_0_12270,plain,
    ( X1 = X2
    | c_IntDef_OAbs__Integ(X1) != c_IntDef_OAbs__Integ(X2)
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    c_0_9333,
    [final] ).

cnf(c_0_12271,plain,
    ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_insert(X2,c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    c_0_9334,
    [final] ).

cnf(c_0_12272,plain,
    ( c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4)
    | X1 = X2 ),
    c_0_9335,
    [final] ).

cnf(c_0_12273,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_insert(X4,X1,X3),X2,tc_set(X3)) ),
    c_0_9336,
    [final] ).

cnf(c_0_12274,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
    c_0_9337,
    [final] ).

cnf(c_0_12275,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_union(X1,X4,X3),X2,tc_set(X3)) ),
    c_0_9338,
    [final] ).

cnf(c_0_12276,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,c_inter(X4,X2,X3),tc_set(X3)) ),
    c_0_9339,
    [final] ).

cnf(c_0_12277,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,c_inter(X2,X4,X3),tc_set(X3)) ),
    c_0_9340,
    [final] ).

cnf(c_0_12278,plain,
    ( c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_1,X2,tc_nat) ),
    c_0_9341,
    [final] ).

cnf(c_0_12279,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    c_0_9342,
    [final] ).

cnf(c_0_12280,plain,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    c_0_9343,
    [final] ).

cnf(c_0_12281,plain,
    c_union(X1,c_insert(X2,X3,X4),X4) = c_insert(X2,c_union(X1,X3,X4),X4),
    c_0_9344,
    [final] ).

cnf(c_0_12282,plain,
    c_union(c_insert(X1,X2,X3),X4,X3) = c_insert(X1,c_union(X2,X4,X3),X3),
    c_0_9345,
    [final] ).

cnf(c_0_12283,plain,
    c_append(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_append(X2,X4,X3),X3),
    c_0_9346,
    [final] ).

cnf(c_0_12284,plain,
    c_List_Oitrev(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Oitrev(X2,c_List_Olist_OCons(X1,X4,X3),X3),
    c_0_9347,
    [final] ).

cnf(c_0_12285,plain,
    c_append(c_append(X1,X2,X3),X4,X3) = c_append(X1,c_append(X2,X4,X3),X3),
    c_0_9348,
    [final] ).

cnf(c_0_12286,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_insert(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_9349,
    [final] ).

cnf(c_0_12287,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_9350,
    [final] ).

cnf(c_0_12288,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_9351,
    [final] ).

cnf(c_0_12289,plain,
    ( c_less(c_minus(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9352,
    [final] ).

cnf(c_0_12290,plain,
    ( c_less(c_div(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_1,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9353,
    [final] ).

cnf(c_0_12291,plain,
    c_List_Otake(X1,c_List_Otake(X2,X3,X4),X4) = c_List_Otake(c_Orderings_Omin(X1,X2,tc_nat),X3,X4),
    c_0_9354,
    [final] ).

cnf(c_0_12292,plain,
    c_List_Otake(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_Orderings_Omin(X1,X2,tc_nat),X3,X4),
    c_0_9355,
    [final] ).

cnf(c_0_12293,plain,
    c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_minus(X2,X1,tc_nat),X3,X4),
    c_0_9356,
    [final] ).

cnf(c_0_12294,plain,
    c_List_Odrop(X1,c_List_Odrop(X2,X3,X4),X4) = c_List_Odrop(c_plus(X1,X2,tc_nat),X3,X4),
    c_0_9357,
    [final] ).

cnf(c_0_12295,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9358,
    [final] ).

cnf(c_0_12296,plain,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_insert(X1,X4,X3),X2,tc_set(X3)) ),
    c_0_9359,
    [final] ).

cnf(c_0_12297,plain,
    ( c_less(c_0,c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9360,
    [final] ).

cnf(c_0_12298,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_9361,
    [final] ).

cnf(c_0_12299,plain,
    ( ~ c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3) ),
    c_0_9362,
    [final] ).

cnf(c_0_12300,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanLessThan(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9363,
    [final] ).

cnf(c_0_12301,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanLessThan(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9364,
    [final] ).

cnf(c_0_12302,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanAtMost(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9365,
    [final] ).

cnf(c_0_12303,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanAtMost(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9366,
    [final] ).

cnf(c_0_12304,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatLeastLessThan(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9367,
    [final] ).

cnf(c_0_12305,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeastLessThan(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9368,
    [final] ).

cnf(c_0_12306,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatLeastAtMost(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9369,
    [final] ).

cnf(c_0_12307,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeastAtMost(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9370,
    [final] ).

cnf(c_0_12308,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9371,
    [final] ).

cnf(c_0_12309,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9372,
    [final] ).

cnf(c_0_12310,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9373,
    [final] ).

cnf(c_0_12311,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9374,
    [final] ).

cnf(c_0_12312,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9375,
    [final] ).

cnf(c_0_12313,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9376,
    [final] ).

cnf(c_0_12314,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9377,
    [final] ).

cnf(c_0_12315,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9378,
    [final] ).

cnf(c_0_12316,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X3)),c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    c_0_9379,
    [final] ).

cnf(c_0_12317,plain,
    ( c_minus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_minus(X1,X2,tc_nat),X3)
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9380,
    [final] ).

cnf(c_0_12318,plain,
    ( c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    c_0_9381,
    [final] ).

cnf(c_0_12319,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    c_0_9382,
    [final] ).

cnf(c_0_12320,plain,
    ( c_less(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ c_less(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9383,
    [final] ).

cnf(c_0_12321,plain,
    ( c_lessequals(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ c_lessequals(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9384,
    [final] ).

cnf(c_0_12322,plain,
    ( c_less(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9385,
    [final] ).

cnf(c_0_12323,plain,
    ( c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9386,
    [final] ).

cnf(c_0_12324,plain,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9387,
    [final] ).

cnf(c_0_12325,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9388,
    [final] ).

cnf(c_0_12326,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9389,
    [final] ).

cnf(c_0_12327,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9390,
    [final] ).

cnf(c_0_12328,plain,
    ( c_minus(c_insert(X1,X2,X3),X4,tc_set(X3)) = c_minus(X2,X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_9391,
    [final] ).

cnf(c_0_12329,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9392,
    [final] ).

cnf(c_0_12330,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9393,
    [final] ).

cnf(c_0_12331,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_9394,
    [final] ).

cnf(c_0_12332,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_9395,
    [final] ).

cnf(c_0_12333,plain,
    c_minus(c_minus(X1,X2,tc_nat),X3,tc_nat) = c_minus(X1,c_plus(X2,X3,tc_nat),tc_nat),
    c_0_9396,
    [final] ).

cnf(c_0_12334,plain,
    ( c_div(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_plus(c_div(X1,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X2 = c_0 ),
    c_0_9397,
    [final] ).

cnf(c_0_12335,plain,
    ( c_div(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_plus(c_div(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X1 = c_0 ),
    c_0_9398,
    [final] ).

cnf(c_0_12336,plain,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9399,
    [final] ).

cnf(c_0_12337,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | c_less(c_0,X2,tc_nat) ),
    c_0_9400,
    [final] ).

cnf(c_0_12338,plain,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    c_0_9401,
    [final] ).

cnf(c_0_12339,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_9402,
    [final] ).

cnf(c_0_12340,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_9403,
    [final] ).

cnf(c_0_12341,plain,
    ( X1 = X2
    | c_in(X1,X3,X4)
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    c_0_9404,
    [final] ).

cnf(c_0_12342,plain,
    ( X1 = X2
    | c_List_Oop_Amem(X2,X3,X4)
    | ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X3,X4),X4) ),
    c_0_9405,
    [final] ).

cnf(c_0_12343,plain,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9406,
    [final] ).

cnf(c_0_12344,plain,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset ),
    c_0_9407,
    [final] ).

cnf(c_0_12345,plain,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset ),
    c_0_9408,
    [final] ).

cnf(c_0_12346,plain,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset ),
    c_0_9409,
    [final] ).

cnf(c_0_12347,plain,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset ),
    c_0_9410,
    [final] ).

cnf(c_0_12348,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X4,X2,X3),X3) ),
    c_0_9411,
    [final] ).

cnf(c_0_12349,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
    c_0_9412,
    [final] ).

cnf(c_0_12350,plain,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9413,
    [final] ).

cnf(c_0_12351,plain,
    c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X1,
    c_0_9414,
    [final] ).

cnf(c_0_12352,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9415,
    [final] ).

cnf(c_0_12353,plain,
    c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil,X3),X3) = c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3),
    c_0_9416,
    [final] ).

cnf(c_0_12354,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9417,
    [final] ).

cnf(c_0_12355,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    c_0_9418,
    [final] ).

cnf(c_0_12356,plain,
    ( c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_0),c_times(X2,X1,tc_nat),tc_nat) ),
    c_0_9419,
    [final] ).

cnf(c_0_12357,plain,
    ( c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat) ),
    c_0_9420,
    [final] ).

cnf(c_0_12358,plain,
    ( c_Orderings_Omin(X1,c_Finite__Set_OMin(X2,X3),X3) = c_Finite__Set_OMin(c_insert(X1,X2,X3),X3)
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9421,
    [final] ).

cnf(c_0_12359,plain,
    ( c_Orderings_Omax(X1,c_Finite__Set_OMax(X2,X3),X3) = c_Finite__Set_OMax(c_insert(X1,X2,X3),X3)
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9422,
    [final] ).

cnf(c_0_12360,plain,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9423,
    [final] ).

cnf(c_0_12361,plain,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(X2,X4,X3) != c_emptyset ),
    c_0_9424,
    [final] ).

cnf(c_0_12362,plain,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(X2,X4,X3) != c_emptyset ),
    c_0_9425,
    [final] ).

cnf(c_0_12363,plain,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,X3,X4) != c_emptyset ),
    c_0_9426,
    [final] ).

cnf(c_0_12364,plain,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,X3,X4) != c_emptyset ),
    c_0_9427,
    [final] ).

cnf(c_0_12365,plain,
    ( c_List_Onth(c_List_Otake(X1,X2,X3),X4,X3) = c_List_Onth(X2,X4,X3)
    | ~ c_less(X4,X1,tc_nat) ),
    c_0_9428,
    [final] ).

cnf(c_0_12366,plain,
    ( c_Finite__Set_Ocard(c_insert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_9429,
    [final] ).

cnf(c_0_12367,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X1,X3),c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    c_0_9430,
    [final] ).

cnf(c_0_12368,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_0,c_minus(X2,X1,tc_nat),tc_nat) ),
    c_0_9431,
    [final] ).

cnf(c_0_12369,plain,
    ( c_inter(c_List_Oset(X1,X2),c_List_Oset(X3,X2),X2) = c_emptyset
    | ~ c_List_Odistinct(c_append(X1,X3,X2),X2) ),
    c_0_9432,
    [final] ).

cnf(c_0_12370,plain,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X3,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    c_0_9433,
    [final] ).

cnf(c_0_12371,plain,
    ( c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist__inter(X2,X4,X3)
    | c_in(X1,c_List_Oset(X4,X3),X3) ),
    c_0_9434,
    [final] ).

cnf(c_0_12372,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_times(X2,X1,tc_nat),tc_nat) ),
    c_0_9435,
    [final] ).

cnf(c_0_12373,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_times(X1,X2,tc_nat),tc_nat) ),
    c_0_9436,
    [final] ).

cnf(c_0_12374,plain,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9437,
    [final] ).

cnf(c_0_12375,plain,
    ( c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9438,
    [final] ).

cnf(c_0_12376,plain,
    ( c_in(c_Main_OUnion__iff__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    c_0_9439,
    [final] ).

cnf(c_0_12377,plain,
    ( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    c_0_9440,
    [final] ).

cnf(c_0_12378,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9441,
    [final] ).

cnf(c_0_12379,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9442,
    [final] ).

cnf(c_0_12380,plain,
    ( X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    c_0_9443,
    [final] ).

cnf(c_0_12381,plain,
    ( c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2)
    | ~ c_in(c_0,X3,tc_nat) ),
    c_0_9444,
    [final] ).

cnf(c_0_12382,plain,
    c_plus(c_plus(c_Nat_Osize(X1,tc_Message_Omsg),c_Nat_Osize(X2,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OMPair(X1,X2),tc_Message_Omsg),
    c_0_9445,
    [final] ).

cnf(c_0_12383,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9446,
    [final] ).

cnf(c_0_12384,plain,
    c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X2,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9447,
    [final] ).

cnf(c_0_12385,plain,
    ( c_in(X1,c_Main_OUnion__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    c_0_9448,
    [final] ).

cnf(c_0_12386,plain,
    ( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    c_0_9449,
    [final] ).

cnf(c_0_12387,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9450,
    [final] ).

cnf(c_0_12388,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    c_0_9451,
    [final] ).

cnf(c_0_12389,plain,
    ( c_append(c_List_Oupt(X1,X2),c_List_Olist_OCons(X2,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X1,c_Suc(X2))
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_9452,
    [final] ).

cnf(c_0_12390,plain,
    ( c_in(c_Message_Omsg_OKey(v_sko__uhi(X1,X2)),X1,tc_Message_Omsg)
    | c_in(X2,c_Message_OkeysFor(X1),tc_nat)
    | ~ c_in(X2,c_Message_OkeysFor(c_Message_Osynth(X1)),tc_nat) ),
    c_0_9453,
    [final] ).

cnf(c_0_12391,plain,
    ( c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)) = c_minus(X1,X3,tc_set(X4))
    | c_in(X2,X1,X4) ),
    c_0_9454,
    [final] ).

cnf(c_0_12392,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9455,
    [final] ).

cnf(c_0_12393,plain,
    ( c_List_Olist_OCons(X1,c_List_Oremdups(X2,X3),X3) = c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3) ),
    c_0_9456,
    [final] ).

cnf(c_0_12394,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9457,
    [final] ).

cnf(c_0_12395,plain,
    ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Event_Obad,tc_Message_Oagent) ),
    c_0_9458,
    [final] ).

cnf(c_0_12396,plain,
    ( c_List_Olast(c_List_Odrop(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | ~ c_less(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    c_0_9459,
    [final] ).

cnf(c_0_12397,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9460,
    [final] ).

cnf(c_0_12398,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    c_0_9461,
    [final] ).

cnf(c_0_12399,plain,
    ( c_List_Otl(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_minus(X1,c_1,tc_nat),X2,X3)
    | X1 = c_0 ),
    c_0_9462,
    [final] ).

cnf(c_0_12400,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3)) ),
    c_0_9463,
    [final] ).

cnf(c_0_12401,plain,
    ( c_divide(c_times(X1,c_0,X2),c_times(X3,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9464,
    [final] ).

cnf(c_0_12402,plain,
    ( c_divide(c_times(c_0,X1,X2),c_times(c_0,X3,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9465,
    [final] ).

cnf(c_0_12403,plain,
    ( c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9466,
    [final] ).

cnf(c_0_12404,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9467,
    [final] ).

cnf(c_0_12405,plain,
    ( c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9468,
    [final] ).

cnf(c_0_12406,plain,
    ( c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_9469,
    [final] ).

cnf(c_0_12407,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9470,
    [final] ).

cnf(c_0_12408,plain,
    ( c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
    | c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3)) ),
    c_0_9471,
    [final] ).

cnf(c_0_12409,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    c_0_9472,
    [final] ).

cnf(c_0_12410,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    c_0_9473,
    [final] ).

cnf(c_0_12411,plain,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg) ),
    c_0_9474,
    [final] ).

cnf(c_0_12412,plain,
    ( c_in(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    c_0_9475,
    [final] ).

cnf(c_0_12413,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9476,
    [final] ).

cnf(c_0_12414,plain,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    c_0_9477,
    [final] ).

cnf(c_0_12415,plain,
    ( c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X3,tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    c_0_9478,
    [final] ).

cnf(c_0_12416,plain,
    ( X1 = X2
    | c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    c_0_9479,
    [final] ).

cnf(c_0_12417,plain,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_9480,
    [final] ).

cnf(c_0_12418,plain,
    ( c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9481,
    [final] ).

cnf(c_0_12419,plain,
    ( c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9482,
    [final] ).

cnf(c_0_12420,plain,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg) ),
    c_0_9483,
    [final] ).

cnf(c_0_12421,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9484,
    [final] ).

cnf(c_0_12422,plain,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9485,
    [final] ).

cnf(c_0_12423,plain,
    c_append(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
    c_0_9486,
    [final] ).

cnf(c_0_12424,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9487,
    [final] ).

cnf(c_0_12425,plain,
    ( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9488,
    [final] ).

cnf(c_0_12426,plain,
    ( c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_9489,
    [final] ).

cnf(c_0_12427,plain,
    ( c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oremdups(X2,X3)
    | ~ c_in(X1,c_List_Oset(X2,X3),X3) ),
    c_0_9490,
    [final] ).

cnf(c_0_12428,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9491,
    [final] ).

cnf(c_0_12429,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_9492,
    [final] ).

cnf(c_0_12430,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_9493,
    [final] ).

cnf(c_0_12431,plain,
    ( c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_9494,
    [final] ).

cnf(c_0_12432,plain,
    ( c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,X3,X4)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    c_0_9495,
    [final] ).

cnf(c_0_12433,plain,
    ( c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9496,
    [final] ).

cnf(c_0_12434,plain,
    ( c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9497,
    [final] ).

cnf(c_0_12435,plain,
    ( c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_9498,
    [final] ).

cnf(c_0_12436,plain,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9499,
    [final] ).

cnf(c_0_12437,plain,
    c_inter(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3) = c_uminus(c_union(X1,X2,X3),tc_set(X3)),
    c_0_9500,
    [final] ).

cnf(c_0_12438,plain,
    c_union(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3) = c_uminus(c_inter(X1,X2,X3),tc_set(X3)),
    c_0_9501,
    [final] ).

cnf(c_0_12439,plain,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_OkeysFor(c_Message_Oanalz(X2)),tc_nat) ),
    c_0_9502,
    [final] ).

cnf(c_0_12440,plain,
    c_plus(c_Nat_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) = c_Nat_Osize(c_append(X1,X2,X3),tc_List_Olist(X3)),
    c_0_9503,
    [final] ).

cnf(c_0_12441,plain,
    ( c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9504,
    [final] ).

cnf(c_0_12442,plain,
    ( c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9505,
    [final] ).

cnf(c_0_12443,plain,
    ( c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9506,
    [final] ).

cnf(c_0_12444,plain,
    ( c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9507,
    [final] ).

cnf(c_0_12445,plain,
    ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) != c_0 ),
    c_0_9508,
    [final] ).

cnf(c_0_12446,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    c_0_9509,
    [final] ).

cnf(c_0_12447,plain,
    ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    c_0_9510,
    [final] ).

cnf(c_0_12448,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9511,
    [final] ).

cnf(c_0_12449,plain,
    ( c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_9512,
    [final] ).

cnf(c_0_12450,plain,
    ( c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_9513,
    [final] ).

cnf(c_0_12451,plain,
    ( X1 = X2
    | ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3) ),
    c_0_9514,
    [final] ).

cnf(c_0_12452,plain,
    ( c_Nat_Opower(c_HOL_Oabs(X1,X2),c_Numeral_Onumber__of(X3,tc_nat),X2) = c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9515,
    [final] ).

cnf(c_0_12453,plain,
    ( c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_9516,
    [final] ).

cnf(c_0_12454,plain,
    ( c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_9517,
    [final] ).

cnf(c_0_12455,plain,
    ( c_less(c_minus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9518,
    [final] ).

cnf(c_0_12456,plain,
    ( c_minus(c_insert(X1,c_emptyset,X2),c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_insert(X1,c_emptyset,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_9519,
    [final] ).

cnf(c_0_12457,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9520,
    [final] ).

cnf(c_0_12458,plain,
    ( c_in(c_Main_OInter__iff__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    c_0_9521,
    [final] ).

cnf(c_0_12459,plain,
    ( c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    c_0_9522,
    [final] ).

cnf(c_0_12460,plain,
    ( c_in(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_9523,
    [final] ).

cnf(c_0_12461,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_9524,
    [final] ).

cnf(c_0_12462,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4) ),
    c_0_9525,
    [final] ).

cnf(c_0_12463,plain,
    ( c_List_Oop_Amem(X1,c_List_Olist_OCons(X2,X3,X4),X4)
    | ~ c_List_Oop_Amem(X1,X3,X4) ),
    c_0_9526,
    [final] ).

cnf(c_0_12464,plain,
    c_Public_Okeymode_Okeymode__rec(X1,X2,c_Public_Okeymode_OEncryption,X3) = X2,
    c_0_9527,
    [final] ).

cnf(c_0_12465,plain,
    c_Public_Okeymode_Okeymode__rec(X1,X2,c_Public_Okeymode_OSignature,X3) = X1,
    c_0_9528,
    [final] ).

cnf(c_0_12466,plain,
    c_Public_Okeymode_Okeymode__case(X1,X2,c_Public_Okeymode_OEncryption,X3) = X2,
    c_0_9529,
    [final] ).

cnf(c_0_12467,plain,
    c_Public_Okeymode_Okeymode__case(X1,X2,c_Public_Okeymode_OSignature,X3) = X1,
    c_0_9530,
    [final] ).

cnf(c_0_12468,plain,
    c_Relation_OImage(c_Relation_OId,X1,X2,X2) = X1,
    c_0_9531,
    [final] ).

cnf(c_0_12469,plain,
    c_Numeral_Obit_Obit__rec(X1,X2,c_Numeral_Obit_OB1,X3) = X2,
    c_0_9532,
    [final] ).

cnf(c_0_12470,plain,
    c_Numeral_Obit_Obit__rec(X1,X2,c_Numeral_Obit_OB0,X3) = X1,
    c_0_9533,
    [final] ).

cnf(c_0_12471,plain,
    c_Numeral_Obit_Obit__case(X1,X2,c_Numeral_Obit_OB1,X3) = X2,
    c_0_9534,
    [final] ).

cnf(c_0_12472,plain,
    c_Numeral_Obit_Obit__case(X1,X2,c_Numeral_Obit_OB0,X3) = X1,
    c_0_9535,
    [final] ).

cnf(c_0_12473,plain,
    c_Extraction_Osumbool_Osumbool__rec(X1,X2,c_Extraction_Osumbool_ORight,X3) = X2,
    c_0_9536,
    [final] ).

cnf(c_0_12474,plain,
    c_Extraction_Osumbool_Osumbool__rec(X1,X2,c_Extraction_Osumbool_OLeft,X3) = X1,
    c_0_9537,
    [final] ).

cnf(c_0_12475,plain,
    c_Extraction_Osumbool_Osumbool__case(X1,X2,c_Extraction_Osumbool_ORight,X3) = X2,
    c_0_9538,
    [final] ).

cnf(c_0_12476,plain,
    c_Extraction_Osumbool_Osumbool__case(X1,X2,c_Extraction_Osumbool_OLeft,X3) = X1,
    c_0_9539,
    [final] ).

cnf(c_0_12477,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X2,tc_nat),
    c_0_9540,
    [final] ).

cnf(c_0_12478,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X1,tc_nat),
    c_0_9541,
    [final] ).

cnf(c_0_12479,plain,
    c_Relation_OImage(X1,c_emptyset,X2,X3) = c_emptyset,
    c_0_9542,
    [final] ).

cnf(c_0_12480,plain,
    c_List_Ozip(c_List_Olist_ONil,X1,X2,X3) = c_List_Olist_ONil,
    c_0_9543,
    [final] ).

cnf(c_0_12481,plain,
    c_List_Ozip(X1,c_List_Olist_ONil,X2,X3) = c_List_Olist_ONil,
    c_0_9544,
    [final] ).

cnf(c_0_12482,plain,
    ( c_List_Onth(c_List_Oreplicate(X1,X2,X3),X4,X3) = X2
    | ~ c_less(X4,X1,tc_nat) ),
    c_0_9545,
    [final] ).

cnf(c_0_12483,plain,
    c_List_Olist__update(c_List_Olist_ONil,X1,X2,X3) = c_List_Olist_ONil,
    c_0_9546,
    [final] ).

cnf(c_0_12484,plain,
    c_Datatype__Universe_Ontrunc(c_0,X1,X2,X3) = c_emptyset,
    c_0_9547,
    [final] ).

cnf(c_0_12485,plain,
    c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) = c_UNIV,
    c_0_9548,
    [final] ).

cnf(c_0_12486,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9549,
    [final] ).

cnf(c_0_12487,plain,
    ( c_plus(X1,c_minus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_9550,
    [final] ).

cnf(c_0_12488,plain,
    ( c_plus(c_minus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_9551,
    [final] ).

cnf(c_0_12489,plain,
    ( c_minus(X1,c_minus(X1,X2,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_9552,
    [final] ).

cnf(c_0_12490,plain,
    ( c_times(c_HOL_Oinverse(X1,X3),c_HOL_Oinverse(X2,X3),X3) = c_HOL_Oinverse(c_times(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9553,
    [final] ).

cnf(c_0_12491,plain,
    ( c_divide(c_HOL_Oabs(X1,X3),c_HOL_Oabs(X2,X3),X3) = c_HOL_Oabs(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9554,
    [final] ).

cnf(c_0_12492,plain,
    ( c_lessequals(c_Suc(c_0),c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat) ),
    c_0_9555,
    [final] ).

cnf(c_0_12493,plain,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,X1,tc_nat),tc_nat) ),
    c_0_9556,
    [final] ).

cnf(c_0_12494,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9557,
    [final] ).

cnf(c_0_12495,plain,
    c_minus(c_minus(X1,X2,tc_set(X3)),X2,tc_set(X3)) = c_minus(X1,X2,tc_set(X3)),
    c_0_9558,
    [final] ).

cnf(c_0_12496,plain,
    c_union(c_Union(X1,X3),c_Union(X2,X3),X3) = c_Union(c_union(X1,X2,tc_set(X3)),X3),
    c_0_9559,
    [final] ).

cnf(c_0_12497,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9560,
    [final] ).

cnf(c_0_12498,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9561,
    [final] ).

cnf(c_0_12499,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    c_0_9562,
    [final] ).

cnf(c_0_12500,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    c_0_9563,
    [final] ).

cnf(c_0_12501,plain,
    ( c_less(c_0,c_minus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(X2,X1,tc_nat) ),
    c_0_9564,
    [final] ).

cnf(c_0_12502,plain,
    c_append(c_List_Oconcat(X1,X3),c_List_Oconcat(X2,X3),X3) = c_List_Oconcat(c_append(X1,X2,tc_List_Olist(X3)),X3),
    c_0_9565,
    [final] ).

cnf(c_0_12503,plain,
    ( c_div(c_times(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9566,
    [final] ).

cnf(c_0_12504,plain,
    ( c_div(c_times(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9567,
    [final] ).

cnf(c_0_12505,plain,
    ( c_append(c_List_Obutlast(X1,X2),c_List_Olist_OCons(c_List_Olast(X1,X2),c_List_Olist_ONil,X2),X2) = X1
    | X1 = c_List_Olist_ONil ),
    c_0_9568,
    [final] ).

cnf(c_0_12506,plain,
    ( c_less(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint) ),
    c_0_9569,
    [final] ).

cnf(c_0_12507,plain,
    ( c_less(X1,c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(X1,c_0,tc_IntDef_Oint) ),
    c_0_9570,
    [final] ).

cnf(c_0_12508,plain,
    ( c_less(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9571,
    [final] ).

cnf(c_0_12509,plain,
    ( c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9572,
    [final] ).

cnf(c_0_12510,plain,
    ( c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    c_0_9573,
    [final] ).

cnf(c_0_12511,plain,
    ( c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(X1,X2,tc_IntDef_Oint) ),
    c_0_9574,
    [final] ).

cnf(c_0_12512,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9575,
    [final] ).

cnf(c_0_12513,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    c_0_9576,
    [final] ).

cnf(c_0_12514,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    c_0_9577,
    [final] ).

cnf(c_0_12515,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    c_0_9578,
    [final] ).

cnf(c_0_12516,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    c_0_9579,
    [final] ).

cnf(c_0_12517,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_9580,
    [final] ).

cnf(c_0_12518,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9581,
    [final] ).

cnf(c_0_12519,plain,
    ( c_lessequals(c_0,c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint) ),
    c_0_9582,
    [final] ).

cnf(c_0_12520,plain,
    ( c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(X2,c_0,tc_IntDef_Oint) ),
    c_0_9583,
    [final] ).

cnf(c_0_12521,plain,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_9584,
    [final] ).

cnf(c_0_12522,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9585,
    [final] ).

cnf(c_0_12523,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat) ),
    c_0_9586,
    [final] ).

cnf(c_0_12524,plain,
    ( c_LOrder_Ojoin(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_LOrder_Omeet(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group(X3) ),
    c_0_9587,
    [final] ).

cnf(c_0_12525,plain,
    ( c_LOrder_Omeet(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_LOrder_Ojoin(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group(X3) ),
    c_0_9588,
    [final] ).

cnf(c_0_12526,plain,
    ( c_plus(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_plus(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_9589,
    [final] ).

cnf(c_0_12527,plain,
    ( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
    | ~ c_in(X1,X2,tc_prod(X3,X3)) ),
    c_0_9590,
    [final] ).

cnf(c_0_12528,plain,
    c_inter(c_Pow(X1,X3),c_Pow(X2,X3),tc_set(X3)) = c_Pow(c_inter(X1,X2,X3),X3),
    c_0_9591,
    [final] ).

cnf(c_0_12529,plain,
    c_inter(c_List_Olists(X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) = c_List_Olists(c_inter(X1,X2,X3),X3),
    c_0_9592,
    [final] ).

cnf(c_0_12530,plain,
    ( c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2))
    | ~ c_lessequals(X3,X1,tc_set(X2)) ),
    c_0_9593,
    [final] ).

cnf(c_0_12531,plain,
    ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3)
    | c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    c_0_9594,
    [final] ).

cnf(c_0_12532,plain,
    ( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | ~ c_in(X1,X2,X3) ),
    c_0_9595,
    [final] ).

cnf(c_0_12533,plain,
    ( c_times(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2),X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9596,
    [final] ).

cnf(c_0_12534,plain,
    c_uminus(c_minus(X1,X2,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X1,tc_set(X3)),X2,X3),
    c_0_9597,
    [final] ).

cnf(c_0_12535,plain,
    ( c_times(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_times(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    c_0_9598,
    [final] ).

cnf(c_0_12536,plain,
    ( c_plus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_plus(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    c_0_9599,
    [final] ).

cnf(c_0_12537,plain,
    ( c_times(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_times(X1,X2,tc_IntDef_Oint),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9600,
    [final] ).

cnf(c_0_12538,plain,
    ( c_minus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_minus(X1,X2,tc_IntDef_Oint),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9601,
    [final] ).

cnf(c_0_12539,plain,
    ( c_plus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_plus(X1,X2,tc_IntDef_Oint),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_9602,
    [final] ).

cnf(c_0_12540,plain,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9603,
    [final] ).

cnf(c_0_12541,plain,
    ( c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
    | ~ c_less(c_0,X2,tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    c_0_9604,
    [final] ).

cnf(c_0_12542,plain,
    ( c_divide(X1,c_times(X2,X1,X3),X3) = c_divide(c_1,X2,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9605,
    [final] ).

cnf(c_0_12543,plain,
    ( c_divide(X1,c_times(X1,X2,X3),X3) = c_divide(c_1,X2,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9606,
    [final] ).

cnf(c_0_12544,plain,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_9607,
    [final] ).

cnf(c_0_12545,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_9608,
    [final] ).

cnf(c_0_12546,plain,
    c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat),
    c_0_9609,
    [final] ).

cnf(c_0_12547,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9610,
    [final] ).

cnf(c_0_12548,plain,
    ( c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_uminus(c_Nat_Opower(X1,X3,X2),X2)
    | c_Parity_Oeven(X3,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9611,
    [final] ).

cnf(c_0_12549,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_9612,
    [final] ).

cnf(c_0_12550,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_9613,
    [final] ).

cnf(c_0_12551,plain,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_9614,
    [final] ).

cnf(c_0_12552,plain,
    ( c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_9615,
    [final] ).

cnf(c_0_12553,plain,
    c_Message_Oanalz(c_union(c_Message_Oanalz(X1),X2,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X1,X2,tc_Message_Omsg)),
    c_0_9616,
    [final] ).

cnf(c_0_12554,plain,
    c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
    c_0_9617,
    [final] ).

cnf(c_0_12555,plain,
    c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
    c_0_9618,
    [final] ).

cnf(c_0_12556,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9619,
    [final] ).

cnf(c_0_12557,plain,
    c_union(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) = c_List_Oset(c_append(X1,X2,X3),X3),
    c_0_9620,
    [final] ).

cnf(c_0_12558,plain,
    c_append(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3) = c_List_Orev(c_append(X1,X2,X3),X3),
    c_0_9621,
    [final] ).

cnf(c_0_12559,plain,
    ( c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9622,
    [final] ).

cnf(c_0_12560,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9623,
    [final] ).

cnf(c_0_12561,plain,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    c_0_9624,
    [final] ).

cnf(c_0_12562,plain,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    c_0_9625,
    [final] ).

cnf(c_0_12563,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X1),c_Message_OkeysFor(X3),tc_nat),
    c_0_9626,
    [final] ).

cnf(c_0_12564,plain,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X2)),tc_Message_Omsg) ),
    c_0_9627,
    [final] ).

cnf(c_0_12565,plain,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_9628,
    [final] ).

cnf(c_0_12566,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,X1,tc_IntDef_Oint)),
    c_0_9629,
    [final] ).

cnf(c_0_12567,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,X1,tc_IntDef_Oint)),
    c_0_9630,
    [final] ).

cnf(c_0_12568,plain,
    ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),c_0,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9631,
    [final] ).

cnf(c_0_12569,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat) ),
    c_0_9632,
    [final] ).

cnf(c_0_12570,plain,
    ( c_Orderings_Omax(X1,c_Orderings_Omax(X1,X2,X3),X3) = c_Orderings_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9633,
    [final] ).

cnf(c_0_12571,plain,
    ( c_Orderings_Omin(X1,c_Orderings_Omin(X1,X2,X3),X3) = c_Orderings_Omin(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_9634,
    [final] ).

cnf(c_0_12572,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    c_0_9635,
    [final] ).

cnf(c_0_12573,plain,
    ( c_in(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    c_0_9636,
    [final] ).

cnf(c_0_12574,plain,
    c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_Suc(X1),X2,X3),
    c_0_9637,
    [final] ).

cnf(c_0_12575,plain,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X3) = c_List_Onth(X2,X4,X3),
    c_0_9638,
    [final] ).

cnf(c_0_12576,plain,
    c_List_Odrop(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(X1,X3,X4),
    c_0_9639,
    [final] ).

cnf(c_0_12577,plain,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0 ),
    c_0_9640,
    [final] ).

cnf(c_0_12578,plain,
    c_Nat_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X2,tc_List_Olist(X3)),c_Suc(c_0),tc_nat),
    c_0_9641,
    [final] ).

cnf(c_0_12579,plain,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_uminus(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9642,
    [final] ).

cnf(c_0_12580,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_Numeral_Onumber__of(X3,X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9643,
    [final] ).

cnf(c_0_12581,plain,
    ( c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    c_0_9644,
    [final] ).

cnf(c_0_12582,plain,
    ( c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    c_0_9645,
    [final] ).

cnf(c_0_12583,plain,
    c_Nat_Osize(c_List_Otake(X1,X2,X3),tc_List_Olist(X3)) = c_Orderings_Omin(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    c_0_9646,
    [final] ).

cnf(c_0_12584,plain,
    c_Nat_Osize(c_List_Odrop(X1,X2,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    c_0_9647,
    [final] ).

cnf(c_0_12585,plain,
    ( c_minus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9648,
    [final] ).

cnf(c_0_12586,plain,
    ( c_less(c_uminus(c_1,X1),X2,X1)
    | ~ c_less(c_uminus(X2,X1),c_1,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    c_0_9649,
    [final] ).

cnf(c_0_12587,plain,
    ( c_lessequals(c_uminus(c_1,X1),X2,X1)
    | ~ c_lessequals(c_uminus(X2,X1),c_1,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    c_0_9650,
    [final] ).

cnf(c_0_12588,plain,
    ( c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(c_divide(c_1,X2,X1),X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_9651,
    [final] ).

cnf(c_0_12589,plain,
    ( c_less(X1,c_uminus(c_1,X2),X2)
    | ~ c_less(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_9652,
    [final] ).

cnf(c_0_12590,plain,
    ( c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_9653,
    [final] ).

cnf(c_0_12591,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_9654,
    [final] ).

cnf(c_0_12592,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_9655,
    [final] ).

cnf(c_0_12593,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    c_0_9656,
    [final] ).

cnf(c_0_12594,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    c_0_9657,
    [final] ).

cnf(c_0_12595,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_9658,
    [final] ).

cnf(c_0_12596,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_9659,
    [final] ).

cnf(c_0_12597,plain,
    ( c_less(c_uminus(X1,X2),c_1,X2)
    | ~ c_less(c_uminus(c_1,X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_9660,
    [final] ).

cnf(c_0_12598,plain,
    ( c_lessequals(c_uminus(X1,X2),c_1,X2)
    | ~ c_lessequals(c_uminus(c_1,X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_9661,
    [final] ).

cnf(c_0_12599,plain,
    ( c_less(c_1,c_uminus(X1,X2),X2)
    | ~ c_less(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_9662,
    [final] ).

cnf(c_0_12600,plain,
    ( c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_9663,
    [final] ).

cnf(c_0_12601,plain,
    c_union(X1,c_union(X2,X1,X3),X3) = c_union(X2,X1,X3),
    c_0_9664,
    [final] ).

cnf(c_0_12602,plain,
    c_insert(X1,c_insert(X1,X2,X3),X3) = c_insert(X1,X2,X3),
    c_0_9665,
    [final] ).

cnf(c_0_12603,plain,
    c_times(X1,c_Nat_Opower(X1,X2,tc_nat),tc_nat) = c_Nat_Opower(X1,c_Suc(X2),tc_nat),
    c_0_9666,
    [final] ).

cnf(c_0_12604,plain,
    c_plus(X2,c_times(X1,X2,tc_nat),tc_nat) = c_times(c_Suc(X1),X2,tc_nat),
    c_0_9667,
    [final] ).

cnf(c_0_12605,plain,
    c_plus(X1,c_times(X1,X2,tc_nat),tc_nat) = c_times(X1,c_Suc(X2),tc_nat),
    c_0_9668,
    [final] ).

cnf(c_0_12606,plain,
    c_times(X1,c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X1,c_Suc(X2),tc_IntDef_Oint),
    c_0_9669,
    [final] ).

cnf(c_0_12607,plain,
    ( c_divide(X1,c_uminus(X2,X3),X3) = c_uminus(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9670,
    [final] ).

cnf(c_0_12608,plain,
    c_Divides_Oop_Amod(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9671,
    [final] ).

cnf(c_0_12609,plain,
    c_Union(c_insert(X1,X2,tc_set(X3)),X3) = c_union(X1,c_Union(X2,X3),X3),
    c_0_9672,
    [final] ).

cnf(c_0_12610,plain,
    c_Inter(c_insert(X1,X2,tc_set(X3)),X3) = c_inter(X1,c_Inter(X2,X3),X3),
    c_0_9673,
    [final] ).

cnf(c_0_12611,plain,
    c_List_Olistset(c_List_Olist_OCons(X1,X2,tc_set(X3)),X3) = c_List_Oset__Cons(X1,c_List_Olistset(X2,X3),X3),
    c_0_9674,
    [final] ).

cnf(c_0_12612,plain,
    c_List_Oconcat(c_List_Olist_OCons(X1,X2,tc_List_Olist(X3)),X3) = c_append(X1,c_List_Oconcat(X2,X3),X3),
    c_0_9675,
    [final] ).

cnf(c_0_12613,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    c_0_9676,
    [final] ).

cnf(c_0_12614,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9677,
    [final] ).

cnf(c_0_12615,plain,
    c_plus(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(X1)),
    c_0_9678,
    [final] ).

cnf(c_0_12616,plain,
    c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1,tc_nat) = c_Suc(c_Suc(X1)),
    c_0_9679,
    [final] ).

cnf(c_0_12617,plain,
    ( c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_ONil
    | c_in(c_0,X3,tc_nat) ),
    c_0_9680,
    [final] ).

cnf(c_0_12618,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),
    c_0_9681,
    [final] ).

cnf(c_0_12619,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),
    c_0_9682,
    [final] ).

cnf(c_0_12620,plain,
    c_Divides_Oop_Amod(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),
    c_0_9683,
    [final] ).

cnf(c_0_12621,plain,
    c_Divides_Oop_Amod(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    c_0_9684,
    [final] ).

cnf(c_0_12622,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    c_0_9685,
    [final] ).

cnf(c_0_12623,plain,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_nat),X1,tc_nat) = c_Divides_Oop_Amod(X2,X1,tc_nat),
    c_0_9686,
    [final] ).

cnf(c_0_12624,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9687,
    [final] ).

cnf(c_0_12625,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat) ),
    c_0_9688,
    [final] ).

cnf(c_0_12626,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9689,
    [final] ).

cnf(c_0_12627,plain,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMin(X1,X2),c_Finite__Set_OMax(X1,X2),X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9690,
    [final] ).

cnf(c_0_12628,plain,
    ( c_times(X1,c_uminus(X2,X3),X3) = c_uminus(c_times(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    c_0_9691,
    [final] ).

cnf(c_0_12629,plain,
    ( c_times(c_uminus(X1,X2),X3,X2) = c_uminus(c_times(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Oring(X2) ),
    c_0_9692,
    [final] ).

cnf(c_0_12630,plain,
    ( c_divide(c_uminus(X1,X2),X3,X2) = c_uminus(c_divide(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    c_0_9693,
    [final] ).

cnf(c_0_12631,plain,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_0
    | ~ class_Power_Orecpower(X1) ),
    c_0_9694,
    [final] ).

cnf(c_0_12632,plain,
    ( c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_1
    | ~ class_Power_Orecpower(X1) ),
    c_0_9695,
    [final] ).

cnf(c_0_12633,plain,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9696,
    [final] ).

cnf(c_0_12634,plain,
    ( c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9697,
    [final] ).

cnf(c_0_12635,plain,
    ( c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9698,
    [final] ).

cnf(c_0_12636,plain,
    ( c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_9699,
    [final] ).

cnf(c_0_12637,plain,
    ( c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_9700,
    [final] ).

cnf(c_0_12638,plain,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Numeral_Onumber__of(X4,tc_nat),X3) = X1
    | c_Numeral_Onumber__of(X4,tc_nat) != c_0 ),
    c_0_9701,
    [final] ).

cnf(c_0_12639,plain,
    ( c_Message_Oparts(c_insert(X1,X2,tc_Message_Omsg)) = c_Message_Oparts(X2)
    | ~ c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    c_0_9702,
    [final] ).

cnf(c_0_12640,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    c_0_9703,
    [final] ).

cnf(c_0_12641,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate(X3,X1,X2),X2) ),
    c_0_9704,
    [final] ).

cnf(c_0_12642,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_append(X3,X1,X2),X2) ),
    c_0_9705,
    [final] ).

cnf(c_0_12643,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_append(X1,X3,X2),X2) ),
    c_0_9706,
    [final] ).

cnf(c_0_12644,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X3,X1,X2),X2) ),
    c_0_9707,
    [final] ).

cnf(c_0_12645,plain,
    ( c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_ONil
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    c_0_9708,
    [final] ).

cnf(c_0_12646,plain,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9709,
    [final] ).

cnf(c_0_12647,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9710,
    [final] ).

cnf(c_0_12648,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9711,
    [final] ).

cnf(c_0_12649,plain,
    ( c_Message_OinvKey(v_sko__uhi(X2,X1)) = X1
    | c_in(X1,c_Message_OkeysFor(X2),tc_nat)
    | ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
    c_0_9712,
    [final] ).

cnf(c_0_12650,plain,
    ( c_append(c_List_Otl(X1,X3),X2,X3) = c_List_Otl(c_append(X1,X2,X3),X3)
    | X1 = c_List_Olist_ONil ),
    c_0_9713,
    [final] ).

cnf(c_0_12651,plain,
    ( c_List_Olist_OCons(X1,c_List_Obutlast(X2,X3),X3) = c_List_Obutlast(c_List_Olist_OCons(X1,X2,X3),X3)
    | X2 = c_List_Olist_ONil ),
    c_0_9714,
    [final] ).

cnf(c_0_12652,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9715,
    [final] ).

cnf(c_0_12653,plain,
    c_insert(X1,c_List_Oset(X2,X3),X3) = c_List_Oset(c_List_Olist_OCons(X1,X2,X3),X3),
    c_0_9716,
    [final] ).

cnf(c_0_12654,plain,
    c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9717,
    [final] ).

cnf(c_0_12655,plain,
    ( c_lessequals(c_OrderedGroup_Opprt(X1,X2),c_OrderedGroup_Opprt(X3,X2),X2)
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_9718,
    [final] ).

cnf(c_0_12656,plain,
    ( c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_OrderedGroup_Onprt(X3,X2),X2)
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_9719,
    [final] ).

cnf(c_0_12657,plain,
    ( c_less(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9720,
    [final] ).

cnf(c_0_12658,plain,
    ( c_lessequals(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9721,
    [final] ).

cnf(c_0_12659,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X3),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9722,
    [final] ).

cnf(c_0_12660,plain,
    ( c_List_Otake(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    c_0_9723,
    [final] ).

cnf(c_0_12661,plain,
    ( c_List_Orotate(X1,X2,X3) = X2
    | c_Divides_Oop_Amod(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) != c_0 ),
    c_0_9724,
    [final] ).

cnf(c_0_12662,plain,
    ( c_List_Odrop(X1,X2,X3) = c_List_Olist_ONil
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    c_0_9725,
    [final] ).

cnf(c_0_12663,plain,
    c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9726,
    [final] ).

cnf(c_0_12664,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9727,
    [final] ).

cnf(c_0_12665,plain,
    ( c_less(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ c_less(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_9728,
    [final] ).

cnf(c_0_12666,plain,
    ( c_lessequals(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_9729,
    [final] ).

cnf(c_0_12667,plain,
    ( c_less(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ c_less(X1,X3,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9730,
    [final] ).

cnf(c_0_12668,plain,
    ( c_lessequals(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ c_lessequals(X1,X3,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9731,
    [final] ).

cnf(c_0_12669,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    c_0_9732,
    [final] ).

cnf(c_0_12670,plain,
    ( X1 = X2
    | ~ c_in(X2,X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    c_0_9733,
    [final] ).

cnf(c_0_12671,plain,
    ( c_List_Orotate(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),c_1,tc_nat) ),
    c_0_9734,
    [final] ).

cnf(c_0_12672,plain,
    c_List_Odrop(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(c_plus(X2,X1,tc_nat),X3),
    c_0_9735,
    [final] ).

cnf(c_0_12673,plain,
    ( c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_9736,
    [final] ).

cnf(c_0_12674,plain,
    ( ~ c_lessequals(v_sko__urX(X1),X2,tc_nat)
    | ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(X1),tc_Message_Omsg) ),
    c_0_9737,
    [final] ).

cnf(c_0_12675,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9738,
    [final] ).

cnf(c_0_12676,plain,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    c_0_9739,
    [final] ).

cnf(c_0_12677,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9740,
    [final] ).

cnf(c_0_12678,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9741,
    [final] ).

cnf(c_0_12679,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9742,
    [final] ).

cnf(c_0_12680,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    c_0_9743,
    [final] ).

cnf(c_0_12681,plain,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Event_Oused(X2),tc_Message_Omsg) ),
    c_0_9744,
    [final] ).

cnf(c_0_12682,plain,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Event_Oused(X2),tc_Message_Omsg) ),
    c_0_9745,
    [final] ).

cnf(c_0_12683,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    c_0_9746,
    [final] ).

cnf(c_0_12684,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    c_0_9747,
    [final] ).

cnf(c_0_12685,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oparts(X2),tc_Message_Omsg) ),
    c_0_9748,
    [final] ).

cnf(c_0_12686,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
    c_0_9749,
    [final] ).

cnf(c_0_12687,plain,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9750,
    [final] ).

cnf(c_0_12688,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9751,
    [final] ).

cnf(c_0_12689,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9752,
    [final] ).

cnf(c_0_12690,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9753,
    [final] ).

cnf(c_0_12691,plain,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X2,X1,tc_set(X3)) ),
    c_0_9754,
    [final] ).

cnf(c_0_12692,plain,
    ( c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_9755,
    [final] ).

cnf(c_0_12693,plain,
    ~ c_List_Onull(c_List_Olist_OCons(X1,X2,X3),X3),
    c_0_9756,
    [final] ).

cnf(c_0_12694,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9757,
    [final] ).

cnf(c_0_12695,plain,
    ( c_HOL_Oinverse(c_divide(X1,X2,X3),X3) = c_divide(X2,X1,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9758,
    [final] ).

cnf(c_0_12696,plain,
    ( X1 = c_0
    | X2 = X3
    | c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    c_0_9759,
    [final] ).

cnf(c_0_12697,plain,
    ( X1 = c_0
    | X2 = X3
    | c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    c_0_9760,
    [final] ).

cnf(c_0_12698,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9761,
    [final] ).

cnf(c_0_12699,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9762,
    [final] ).

cnf(c_0_12700,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9763,
    [final] ).

cnf(c_0_12701,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9764,
    [final] ).

cnf(c_0_12702,plain,
    ( c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1),X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_9765,
    [final] ).

cnf(c_0_12703,plain,
    ( c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9766,
    [final] ).

cnf(c_0_12704,plain,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9767,
    [final] ).

cnf(c_0_12705,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    c_0_9768,
    [final] ).

cnf(c_0_12706,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    c_0_9769,
    [final] ).

cnf(c_0_12707,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    c_0_9770,
    [final] ).

cnf(c_0_12708,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    c_0_9771,
    [final] ).

cnf(c_0_12709,plain,
    c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    c_0_9772,
    [final] ).

cnf(c_0_12710,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    c_0_9773,
    [final] ).

cnf(c_0_12711,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    c_0_9774,
    [final] ).

cnf(c_0_12712,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    c_0_9775,
    [final] ).

cnf(c_0_12713,plain,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    c_0_9776,
    [final] ).

cnf(c_0_12714,plain,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9777,
    [final] ).

cnf(c_0_12715,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9778,
    [final] ).

cnf(c_0_12716,plain,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9779,
    [final] ).

cnf(c_0_12717,plain,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9780,
    [final] ).

cnf(c_0_12718,plain,
    c_Transitive__Closure_Otrancl(c_union(X1,c_Relation_OId,tc_prod(X2,X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    c_0_9781,
    [final] ).

cnf(c_0_12719,plain,
    c_Transitive__Closure_Ortrancl(c_union(X1,c_Relation_OId,tc_prod(X2,X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    c_0_9782,
    [final] ).

cnf(c_0_12720,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_9783,
    [final] ).

cnf(c_0_12721,plain,
    ( c_less(X1,c_0,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9784,
    [final] ).

cnf(c_0_12722,plain,
    ( c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9785,
    [final] ).

cnf(c_0_12723,plain,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9786,
    [final] ).

cnf(c_0_12724,plain,
    ( c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9787,
    [final] ).

cnf(c_0_12725,plain,
    ( X1 = c_emptyset
    | c_in(c_Finite__Set_OMin(X1,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9788,
    [final] ).

cnf(c_0_12726,plain,
    ( X1 = c_emptyset
    | c_in(c_Finite__Set_OMax(X1,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_9789,
    [final] ).

cnf(c_0_12727,plain,
    ( c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    c_0_9790,
    [final] ).

cnf(c_0_12728,plain,
    ( c_uminus(c_minus(X1,X2,X3),X3) = c_minus(X2,X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_9791,
    [final] ).

cnf(c_0_12729,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X2,X1,X4) != c_times(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    c_0_9792,
    [final] ).

cnf(c_0_12730,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X1,X2,X4) != c_times(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    c_0_9793,
    [final] ).

cnf(c_0_12731,plain,
    c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oused(X3),tc_Message_Omsg),
    c_0_9794,
    [final] ).

cnf(c_0_12732,plain,
    c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_OinitState(X2),tc_Message_Omsg),
    c_0_9795,
    [final] ).

cnf(c_0_12733,plain,
    c_List_Orotate1(c_List_Orotate(X1,X2,X3),X3) = c_List_Orotate(c_Suc(X1),X2,X3),
    c_0_9796,
    [final] ).

cnf(c_0_12734,plain,
    c_lessequals(c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)),c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat),
    c_0_9797,
    [final] ).

cnf(c_0_12735,plain,
    ( X1 = X2
    | c_plus(X1,X3,X4) != c_plus(X2,X3,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    c_0_9798,
    [final] ).

cnf(c_0_12736,plain,
    ( X1 = X2
    | c_plus(X3,X1,X4) != c_plus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    c_0_9799,
    [final] ).

cnf(c_0_12737,plain,
    c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3),
    c_0_9800,
    [final] ).

cnf(c_0_12738,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    c_0_9801,
    [final] ).

cnf(c_0_12739,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    c_0_9802,
    [final] ).

cnf(c_0_12740,plain,
    ( c_times(X1,c_divide(X2,X1,X3),X3) = X2
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9803,
    [final] ).

cnf(c_0_12741,plain,
    ( c_times(c_divide(X1,X2,X3),X2,X3) = X1
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9804,
    [final] ).

cnf(c_0_12742,plain,
    ( c_divide(c_times(X1,X2,X3),X2,X3) = X1
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9805,
    [final] ).

cnf(c_0_12743,plain,
    ( c_divide(c_times(X1,X2,X3),X1,X3) = X2
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_9806,
    [final] ).

cnf(c_0_12744,plain,
    ( c_minus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9807,
    [final] ).

cnf(c_0_12745,plain,
    ( c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),X3,tc_nat)
    | c_List_Odrop(X3,X1,X2) != c_List_Olist_ONil ),
    c_0_9808,
    [final] ).

cnf(c_0_12746,plain,
    ( c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9809,
    [final] ).

cnf(c_0_12747,plain,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9810,
    [final] ).

cnf(c_0_12748,plain,
    ( c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9811,
    [final] ).

cnf(c_0_12749,plain,
    ( c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9812,
    [final] ).

cnf(c_0_12750,plain,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(c_Message_Oagent_OSpy,X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    c_0_9813,
    [final] ).

cnf(c_0_12751,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,c_Suc(X1),tc_nat),
    c_0_9814,
    [final] ).

cnf(c_0_12752,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat) = c_minus(c_Suc(X2),X1,tc_nat),
    c_0_9815,
    [final] ).

cnf(c_0_12753,plain,
    ( c_List_Oset(c_List_Oreplicate(X1,X2,X3),X3) = c_insert(X2,c_emptyset,X3)
    | X1 = c_0 ),
    c_0_9816,
    [final] ).

cnf(c_0_12754,plain,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    c_0_9817,
    [final] ).

cnf(c_0_12755,plain,
    ( c_divide(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_divide(X1,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9818,
    [final] ).

cnf(c_0_12756,plain,
    ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9819,
    [final] ).

cnf(c_0_12757,plain,
    ( c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    c_0_9820,
    [final] ).

cnf(c_0_12758,plain,
    ( c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    c_0_9821,
    [final] ).

cnf(c_0_12759,plain,
    ( c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    c_0_9822,
    [final] ).

cnf(c_0_12760,plain,
    ( c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9823,
    [final] ).

cnf(c_0_12761,plain,
    ( c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9824,
    [final] ).

cnf(c_0_12762,plain,
    ( c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9825,
    [final] ).

cnf(c_0_12763,plain,
    ( c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_9826,
    [final] ).

cnf(c_0_12764,plain,
    c_inter(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_emptyset,
    c_0_9827,
    [final] ).

cnf(c_0_12765,plain,
    ( c_List_Olast(c_List_Oupt(X1,X2),tc_nat) = c_minus(X2,c_1,tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_9828,
    [final] ).

cnf(c_0_12766,plain,
    ( X1 = X2
    | c_Event_Oevent_OSays(X3,X4,X1) != c_Event_Oevent_OSays(X5,X6,X2) ),
    c_0_9829,
    [final] ).

cnf(c_0_12767,plain,
    ( X1 = X2
    | c_Event_Oevent_OSays(X3,X1,X4) != c_Event_Oevent_OSays(X5,X2,X6) ),
    c_0_9830,
    [final] ).

cnf(c_0_12768,plain,
    ( X1 = X2
    | c_Event_Oevent_OSays(X1,X3,X4) != c_Event_Oevent_OSays(X2,X5,X6) ),
    c_0_9831,
    [final] ).

cnf(c_0_12769,plain,
    ( X1 = X2
    | c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4) ),
    c_0_9832,
    [final] ).

cnf(c_0_12770,plain,
    ( X1 = X2
    | c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4) ),
    c_0_9833,
    [final] ).

cnf(c_0_12771,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9834,
    [final] ).

cnf(c_0_12772,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X3,X2,X4) ),
    c_0_9835,
    [final] ).

cnf(c_0_12773,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    c_0_9836,
    [final] ).

cnf(c_0_12774,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    c_0_9837,
    [final] ).

cnf(c_0_12775,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X3,X4) ),
    c_0_9838,
    [final] ).

cnf(c_0_12776,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4) ),
    c_0_9839,
    [final] ).

cnf(c_0_12777,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4) ),
    c_0_9840,
    [final] ).

cnf(c_0_12778,plain,
    ( X1 = X2
    | c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4) ),
    c_0_9841,
    [final] ).

cnf(c_0_12779,plain,
    ( X1 = X2
    | c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4) ),
    c_0_9842,
    [final] ).

cnf(c_0_12780,plain,
    ( X1 = X2
    | c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4) ),
    c_0_9843,
    [final] ).

cnf(c_0_12781,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    c_0_9844,
    [final] ).

cnf(c_0_12782,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9845,
    [final] ).

cnf(c_0_12783,plain,
    c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg) = c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)),
    c_0_9846,
    [final] ).

cnf(c_0_12784,plain,
    c_union(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_nat) = c_Message_OkeysFor(c_union(X1,X2,tc_Message_Omsg)),
    c_0_9847,
    [final] ).

cnf(c_0_12785,plain,
    c_Orderings_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omin(X1,X2,tc_nat)),
    c_0_9848,
    [final] ).

cnf(c_0_12786,plain,
    c_Orderings_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omax(X1,X2,tc_nat)),
    c_0_9849,
    [final] ).

cnf(c_0_12787,plain,
    ( c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9850,
    [final] ).

cnf(c_0_12788,plain,
    c_plus(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(X1,X2,tc_nat)),
    c_0_9851,
    [final] ).

cnf(c_0_12789,plain,
    ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X1,X2)),c_Message_OsymKeys,tc_nat),
    c_0_9852,
    [final] ).

cnf(c_0_12790,plain,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Osynth(X2)),tc_Message_Omsg) ),
    c_0_9853,
    [final] ).

cnf(c_0_12791,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_Message_Oparts(X2)),tc_Message_Omsg) ),
    c_0_9854,
    [final] ).

cnf(c_0_12792,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oanalz(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    c_0_9855,
    [final] ).

cnf(c_0_12793,plain,
    ( c_times(c_0,c_divide(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9856,
    [final] ).

cnf(c_0_12794,plain,
    ( c_times(c_divide(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9857,
    [final] ).

cnf(c_0_12795,plain,
    ( c_divide(c_times(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9858,
    [final] ).

cnf(c_0_12796,plain,
    ( c_divide(c_0,c_times(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9859,
    [final] ).

cnf(c_0_12797,plain,
    ( c_divide(c_times(c_0,X1,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9860,
    [final] ).

cnf(c_0_12798,plain,
    ( c_divide(c_0,c_times(c_0,X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_9861,
    [final] ).

cnf(c_0_12799,plain,
    c_Sum__Type_OInr(X1,X2,X3) != c_Sum__Type_OInl(X4,X3,X2),
    c_0_9862,
    [final] ).

cnf(c_0_12800,plain,
    c_Sum__Type_OInl(X1,X2,X3) != c_Sum__Type_OInr(X4,X3,X2),
    c_0_9863,
    [final] ).

cnf(c_0_12801,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
    c_0_9864,
    [final] ).

cnf(c_0_12802,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
    c_0_9865,
    [final] ).

cnf(c_0_12803,plain,
    c_Datatype__Universe_OIn1(X1,X2,X3) != c_Datatype__Universe_OIn0(X4,X2,X3),
    c_0_9866,
    [final] ).

cnf(c_0_12804,plain,
    c_Datatype__Universe_OIn0(X1,X2,X3) != c_Datatype__Universe_OIn1(X4,X2,X3),
    c_0_9867,
    [final] ).

cnf(c_0_12805,plain,
    ( c_in(c_Message_OinvKey(X1),c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    c_0_9868,
    [final] ).

cnf(c_0_12806,plain,
    ( X1 = X2
    | c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4) ),
    c_0_9869,
    [final] ).

cnf(c_0_12807,plain,
    ( X1 = X2
    | c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3) ),
    c_0_9870,
    [final] ).

cnf(c_0_12808,plain,
    ( c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    c_0_9871,
    [final] ).

cnf(c_0_12809,plain,
    ( c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    c_0_9872,
    [final] ).

cnf(c_0_12810,plain,
    ( c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    c_0_9873,
    [final] ).

cnf(c_0_12811,plain,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),
    c_0_9874,
    [final] ).

cnf(c_0_12812,plain,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),
    c_0_9875,
    [final] ).

cnf(c_0_12813,plain,
    ( c_less(c_uminus(X1,X2),c_0,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9876,
    [final] ).

cnf(c_0_12814,plain,
    ( c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9877,
    [final] ).

cnf(c_0_12815,plain,
    ( c_less(c_0,c_uminus(X1,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9878,
    [final] ).

cnf(c_0_12816,plain,
    ( c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_9879,
    [final] ).

cnf(c_0_12817,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X2,X1,tc_nat) != c_times(X3,X1,tc_nat) ),
    c_0_9880,
    [final] ).

cnf(c_0_12818,plain,
    ( X1 = c_0
    | X2 = X3
    | c_times(X1,X2,tc_nat) != c_times(X1,X3,tc_nat) ),
    c_0_9881,
    [final] ).

cnf(c_0_12819,plain,
    ( c_in(c_uminus(X1,X2),c_IntDef_OInts,X2)
    | ~ c_in(X1,c_IntDef_OInts,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    c_0_9882,
    [final] ).

cnf(c_0_12820,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),X3),X3)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    c_0_9883,
    [final] ).

cnf(c_0_12821,plain,
    ( c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_Nat_Opower(X1,X3,X2)
    | ~ c_Parity_Oeven(X3,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9884,
    [final] ).

cnf(c_0_12822,plain,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
    c_0_9885,
    [final] ).

cnf(c_0_12823,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
    c_0_9886,
    [final] ).

cnf(c_0_12824,plain,
    ( X1 = X2
    | c_plus(X1,X3,tc_nat) != c_plus(X2,X3,tc_nat) ),
    c_0_9887,
    [final] ).

cnf(c_0_12825,plain,
    ( X1 = X2
    | c_plus(X3,X1,tc_nat) != c_plus(X3,X2,tc_nat) ),
    c_0_9888,
    [final] ).

cnf(c_0_12826,plain,
    ( X1 = X2
    | c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3) ),
    c_0_9889,
    [final] ).

cnf(c_0_12827,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | c_Numeral_Onumber__of(X1,X3) != c_Numeral_Onumber__of(X2,X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    c_0_9890,
    [final] ).

cnf(c_0_12828,plain,
    ( c_times(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_times(X1,X3,X2)
    | ~ class_Ring__and__Field_Oring(X2) ),
    c_0_9891,
    [final] ).

cnf(c_0_12829,plain,
    ( c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_9892,
    [final] ).

cnf(c_0_12830,plain,
    ( c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9893,
    [final] ).

cnf(c_0_12831,plain,
    ( c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9894,
    [final] ).

cnf(c_0_12832,plain,
    ( c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ c_less(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9895,
    [final] ).

cnf(c_0_12833,plain,
    ( c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_9896,
    [final] ).

cnf(c_0_12834,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9897,
    [final] ).

cnf(c_0_12835,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9898,
    [final] ).

cnf(c_0_12836,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9899,
    [final] ).

cnf(c_0_12837,plain,
    ( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    c_0_9900,
    [final] ).

cnf(c_0_12838,plain,
    c_Suc(c_plus(X1,X2,tc_nat)) = c_plus(c_Suc(X1),X2,tc_nat),
    c_0_9901,
    [final] ).

cnf(c_0_12839,plain,
    c_Suc(c_plus(X1,X2,tc_nat)) = c_plus(X1,c_Suc(X2),tc_nat),
    c_0_9902,
    [final] ).

cnf(c_0_12840,plain,
    ( c_minus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9903,
    [final] ).

cnf(c_0_12841,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9904,
    [final] ).

cnf(c_0_12842,plain,
    ( c_plus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9905,
    [final] ).

cnf(c_0_12843,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    c_0_9906,
    [final] ).

cnf(c_0_12844,plain,
    ( c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | ~ c_in(X1,c_Message_OkeysFor(X2),tc_nat) ),
    c_0_9907,
    [final] ).

cnf(c_0_12845,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9908,
    [final] ).

cnf(c_0_12846,plain,
    c_Message_OkeysFor(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)) = c_Message_OkeysFor(X3),
    c_0_9909,
    [final] ).

cnf(c_0_12847,plain,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oused(X3),
    c_0_9910,
    [final] ).

cnf(c_0_12848,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)) = c_Message_OkeysFor(X3),
    c_0_9911,
    [final] ).

cnf(c_0_12849,plain,
    ( c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0 ),
    c_0_9912,
    [final] ).

cnf(c_0_12850,plain,
    ( c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0 ),
    c_0_9913,
    [final] ).

cnf(c_0_12851,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X3)),tc_Message_Omsg),
    c_0_9914,
    [final] ).

cnf(c_0_12852,plain,
    ( c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    c_0_9915,
    [final] ).

cnf(c_0_12853,plain,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    c_0_9916,
    [final] ).

cnf(c_0_12854,plain,
    c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
    c_0_9917,
    [final] ).

cnf(c_0_12855,plain,
    c_List_Oremove1(X1,c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    c_0_9918,
    [final] ).

cnf(c_0_12856,plain,
    c_in(X1,c_insert(X1,X2,X3),X3),
    c_0_9919,
    [final] ).

cnf(c_0_12857,plain,
    c_List_Oop_Amem(X1,c_List_Olist_OCons(X1,X2,X3),X3),
    c_0_9920,
    [final] ).

cnf(c_0_12858,plain,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_0,X3) = X1,
    c_0_9921,
    [final] ).

cnf(c_0_12859,plain,
    ( c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    c_0_9922,
    [final] ).

cnf(c_0_12860,plain,
    ( c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    c_0_9923,
    [final] ).

cnf(c_0_12861,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_9924,
    [final] ).

cnf(c_0_12862,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_9925,
    [final] ).

cnf(c_0_12863,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_9926,
    [final] ).

cnf(c_0_12864,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_9927,
    [final] ).

cnf(c_0_12865,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_9928,
    [final] ).

cnf(c_0_12866,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_9929,
    [final] ).

cnf(c_0_12867,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_9930,
    [final] ).

cnf(c_0_12868,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_9931,
    [final] ).

cnf(c_0_12869,plain,
    ( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) != c_List_Orev(X1,X3) ),
    c_0_9932,
    [final] ).

cnf(c_0_12870,plain,
    ( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) ),
    c_0_9933,
    [final] ).

cnf(c_0_12871,plain,
    ( c_div(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
    | X1 = c_0 ),
    c_0_9934,
    [final] ).

cnf(c_0_12872,plain,
    ( c_div(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = X1
    | X2 = c_0 ),
    c_0_9935,
    [final] ).

cnf(c_0_12873,plain,
    ( X1 = X2
    | c_less(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    c_0_9936,
    [final] ).

cnf(c_0_12874,plain,
    ( c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg) ),
    c_0_9937,
    [final] ).

cnf(c_0_12875,plain,
    ( c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg) ),
    c_0_9938,
    [final] ).

cnf(c_0_12876,plain,
    ( c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    c_0_9939,
    [final] ).

cnf(c_0_12877,plain,
    c_in(X1,c_insert(X1,c_emptyset,X2),X2),
    c_0_9940,
    [final] ).

cnf(c_0_12878,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_9941,
    [final] ).

cnf(c_0_12879,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    c_0_9942,
    [final] ).

cnf(c_0_12880,plain,
    ( c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_9943,
    [final] ).

cnf(c_0_12881,plain,
    c_lessequals(X1,c_plus(X2,X1,tc_nat),tc_nat),
    c_0_9944,
    [final] ).

cnf(c_0_12882,plain,
    c_lessequals(X1,c_plus(X1,X2,tc_nat),tc_nat),
    c_0_9945,
    [final] ).

cnf(c_0_12883,plain,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    c_0_9946,
    [final] ).

cnf(c_0_12884,plain,
    c_lessequals(c_minus(X1,X2,tc_nat),X1,tc_nat),
    c_0_9947,
    [final] ).

cnf(c_0_12885,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_0,
    c_0_9948,
    [final] ).

cnf(c_0_12886,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_0,
    c_0_9949,
    [final] ).

cnf(c_0_12887,plain,
    c_div(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_0,
    c_0_9950,
    [final] ).

cnf(c_0_12888,plain,
    c_div(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) = c_0,
    c_0_9951,
    [final] ).

cnf(c_0_12889,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_nat),X2,tc_nat) = c_0,
    c_0_9952,
    [final] ).

cnf(c_0_12890,plain,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_nat),X1,tc_nat) = c_0,
    c_0_9953,
    [final] ).

cnf(c_0_12891,plain,
    c_lessequals(c_div(X1,X2,tc_nat),X1,tc_nat),
    c_0_9954,
    [final] ).

cnf(c_0_12892,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9955,
    [final] ).

cnf(c_0_12893,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9956,
    [final] ).

cnf(c_0_12894,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_nat),tc_nat),
    c_0_9957,
    [final] ).

cnf(c_0_12895,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_nat),tc_nat),
    c_0_9958,
    [final] ).

cnf(c_0_12896,plain,
    ( c_minus(X1,X2,tc_set(X3)) = c_emptyset
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    c_0_9959,
    [final] ).

cnf(c_0_12897,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_minus(X1,X2,tc_set(X3)) != c_emptyset ),
    c_0_9960,
    [final] ).

cnf(c_0_12898,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X1,X2,tc_set(X3)) ),
    c_0_9961,
    [final] ).

cnf(c_0_12899,plain,
    ( c_List_Orotate1(X1,X2) = X1
    | ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat) ),
    c_0_9962,
    [final] ).

cnf(c_0_12900,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_9963,
    [final] ).

cnf(c_0_12901,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_9964,
    [final] ).

cnf(c_0_12902,plain,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat) ),
    c_0_9965,
    [final] ).

cnf(c_0_12903,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    c_0_9966,
    [final] ).

cnf(c_0_12904,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    c_0_9967,
    [final] ).

cnf(c_0_12905,plain,
    ( c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9968,
    [final] ).

cnf(c_0_12906,plain,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9969,
    [final] ).

cnf(c_0_12907,plain,
    ( c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9970,
    [final] ).

cnf(c_0_12908,plain,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Onat(X2),c_IntDef_Onat(X1),tc_nat) ),
    c_0_9971,
    [final] ).

cnf(c_0_12909,plain,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9972,
    [final] ).

cnf(c_0_12910,plain,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9973,
    [final] ).

cnf(c_0_12911,plain,
    c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_inter(X1,X2,X3),
    c_0_9974,
    [final] ).

cnf(c_0_12912,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    c_0_9975,
    [final] ).

cnf(c_0_12913,plain,
    ( c_less(c_0,X1,tc_nat)
    | c_Nat_Opower(X2,X1,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_9976,
    [final] ).

cnf(c_0_12914,plain,
    c_less(c_0,c_Nat_Opower(X1,c_0,tc_nat),tc_nat),
    c_0_9977,
    [final] ).

cnf(c_0_12915,plain,
    c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
    c_0_9978,
    [final] ).

cnf(c_0_12916,plain,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_9979,
    [final] ).

cnf(c_0_12917,plain,
    ( c_less(c_1,X1,tc_IntDef_Oint)
    | ~ c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat) ),
    c_0_9980,
    [final] ).

cnf(c_0_12918,plain,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9981,
    [final] ).

cnf(c_0_12919,plain,
    ( c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_9982,
    [final] ).

cnf(c_0_12920,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_9983,
    [final] ).

cnf(c_0_12921,plain,
    ( c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_9984,
    [final] ).

cnf(c_0_12922,plain,
    ( c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_9985,
    [final] ).

cnf(c_0_12923,plain,
    ( c_Nat_Opower(c_0,X1,X2) = c_0
    | ~ c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    c_0_9986,
    [final] ).

cnf(c_0_12924,plain,
    ~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_9987,
    [final] ).

cnf(c_0_12925,plain,
    ( c_SetInterval_OgreaterThanAtMost(X1,X2,X3) = c_emptyset
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_9988,
    [final] ).

cnf(c_0_12926,plain,
    ( c_SetInterval_OatLeastLessThan(X1,X2,X3) = c_emptyset
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_9989,
    [final] ).

cnf(c_0_12927,plain,
    ( c_SetInterval_OatLeastAtMost(X1,X2,X3) = c_emptyset
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_9990,
    [final] ).

cnf(c_0_12928,plain,
    ( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    c_0_9991,
    [final] ).

cnf(c_0_12929,plain,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_9992,
    [final] ).

cnf(c_0_12930,plain,
    c_Nat_Osize(c_List_Orotate(X1,X2,X3),tc_List_Olist(X3)) = c_Nat_Osize(X2,tc_List_Olist(X3)),
    c_0_9993,
    [final] ).

cnf(c_0_12931,plain,
    c_Nat_Osize(c_Sum__Type_OInr(X1,X2,X3),tc_sum(X3,X2)) = c_0,
    c_0_9994,
    [final] ).

cnf(c_0_12932,plain,
    c_Nat_Osize(c_Sum__Type_OInl(X1,X2,X3),tc_sum(X2,X3)) = c_0,
    c_0_9995,
    [final] ).

cnf(c_0_12933,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_less(X1,c_Suc(X2),tc_nat) ),
    c_0_9996,
    [final] ).

cnf(c_0_12934,plain,
    ( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    c_0_9997,
    [final] ).

cnf(c_0_12935,plain,
    ( c_List_Odistinct(c_List_Otake(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_9998,
    [final] ).

cnf(c_0_12936,plain,
    ( c_List_Odistinct(c_List_Osublist(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X1,X3) ),
    c_0_9999,
    [final] ).

cnf(c_0_12937,plain,
    ( c_List_Odistinct(c_List_Orotate(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_10000,
    [final] ).

cnf(c_0_12938,plain,
    ( c_List_Odistinct(c_List_Oremove1(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_10001,
    [final] ).

cnf(c_0_12939,plain,
    ( c_List_Odistinct(c_List_Odrop(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    c_0_10002,
    [final] ).

cnf(c_0_12940,plain,
    ( c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat)
    | ~ c_less(c_1,X1,tc_IntDef_Oint) ),
    c_0_10003,
    [final] ).

cnf(c_0_12941,plain,
    ( c_less(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_10004,
    [final] ).

cnf(c_0_12942,plain,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    c_0_10005,
    [final] ).

cnf(c_0_12943,plain,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    c_0_10006,
    [final] ).

cnf(c_0_12944,plain,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    c_0_10007,
    [final] ).

cnf(c_0_12945,plain,
    c_plus(c_Binomial_Obinomial(X1,X2),c_Binomial_Obinomial(X1,c_Suc(X2)),tc_nat) = c_Binomial_Obinomial(c_Suc(X1),c_Suc(X2)),
    c_0_10008,
    [final] ).

cnf(c_0_12946,plain,
    ( c_in(X1,c_Message_OsymKeys,tc_nat)
    | ~ c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat) ),
    c_0_10009,
    [final] ).

cnf(c_0_12947,plain,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_0,c_IntDef_Onat(X1),tc_nat) ),
    c_0_10010,
    [final] ).

cnf(c_0_12948,plain,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint) ),
    c_0_10011,
    [final] ).

cnf(c_0_12949,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_10012,
    [final] ).

cnf(c_0_12950,plain,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(X2,tc_nat) ),
    c_0_10013,
    [final] ).

cnf(c_0_12951,plain,
    ( c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_10014,
    [final] ).

cnf(c_0_12952,plain,
    ( X1 = c_Datatype_Ooption_OSome(X2,X3)
    | ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3) ),
    c_0_10015,
    [final] ).

cnf(c_0_12953,plain,
    ( c_minus(X1,c_uminus(X2,X3),X3) = c_plus(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_10016,
    [final] ).

cnf(c_0_12954,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10017,
    [final] ).

cnf(c_0_12955,plain,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_in(c_Main_Oconcat__eq__Nil__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2)) ),
    c_0_10018,
    [final] ).

cnf(c_0_12956,plain,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_in(c_Main_ONil__eq__concat__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2)) ),
    c_0_10019,
    [final] ).

cnf(c_0_12957,plain,
    ( c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat)
    | ~ c_in(X1,c_Message_OsymKeys,tc_nat) ),
    c_0_10020,
    [final] ).

cnf(c_0_12958,plain,
    ( c_less(c_0,c_IntDef_Onat(X1),tc_nat)
    | ~ c_less(c_0,X1,tc_IntDef_Oint) ),
    c_0_10021,
    [final] ).

cnf(c_0_12959,plain,
    ( c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_10022,
    [final] ).

cnf(c_0_12960,plain,
    ( X1 = c_0
    | c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_10023,
    [final] ).

cnf(c_0_12961,plain,
    ( c_Divides_Oop_Amod(X1,X2,tc_nat) = X1
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_10024,
    [final] ).

cnf(c_0_12962,plain,
    ( c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) = c_Suc(c_0)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10025,
    [final] ).

cnf(c_0_12963,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10026,
    [final] ).

cnf(c_0_12964,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10027,
    [final] ).

cnf(c_0_12965,plain,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint) ),
    c_0_10028,
    [final] ).

cnf(c_0_12966,plain,
    ( c_minus(X1,X2,tc_nat) = c_0
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_10029,
    [final] ).

cnf(c_0_12967,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_minus(X1,X2,tc_nat) != c_0 ),
    c_0_10030,
    [final] ).

cnf(c_0_12968,plain,
    ( c_div(X1,X2,tc_nat) = c_0
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_10031,
    [final] ).

cnf(c_0_12969,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    c_0_10032,
    [final] ).

cnf(c_0_12970,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    c_0_10033,
    [final] ).

cnf(c_0_12971,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    c_0_10034,
    [final] ).

cnf(c_0_12972,plain,
    ( c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    c_0_10035,
    [final] ).

cnf(c_0_12973,plain,
    ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),tc_nat),
    c_0_10036,
    [final] ).

cnf(c_0_12974,plain,
    ( c_List_Olast(c_append(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil ),
    c_0_10037,
    [final] ).

cnf(c_0_12975,plain,
    ( c_List_Olast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil ),
    c_0_10038,
    [final] ).

cnf(c_0_12976,plain,
    ( c_List_Ohd(c_append(X1,X2,X3),X3) = c_List_Ohd(X1,X3)
    | X1 = c_List_Olist_ONil ),
    c_0_10039,
    [final] ).

cnf(c_0_12977,plain,
    ( X1 = c_0
    | c_LOrder_Omeet(X1,c_uminus(X1,X2),X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10040,
    [final] ).

cnf(c_0_12978,plain,
    ( X1 = c_0
    | c_LOrder_Ojoin(X1,c_uminus(X1,X2),X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10041,
    [final] ).

cnf(c_0_12979,plain,
    c_Nat_Osize(c_List_Otl(X1,X2),tc_List_Olist(X2)) = c_minus(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat),
    c_0_10042,
    [final] ).

cnf(c_0_12980,plain,
    c_Nat_Osize(c_List_Obutlast(X1,X2),tc_List_Olist(X2)) = c_minus(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat),
    c_0_10043,
    [final] ).

cnf(c_0_12981,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) = c_plus(c_1,c_1,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10044,
    [final] ).

cnf(c_0_12982,plain,
    c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
    c_0_10045,
    [final] ).

cnf(c_0_12983,plain,
    c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
    c_0_10046,
    [final] ).

cnf(c_0_12984,plain,
    c_List_Oset(c_List_Orotate(X1,X2,X3),X3) = c_List_Oset(X2,X3),
    c_0_10047,
    [final] ).

cnf(c_0_12985,plain,
    c_append(c_List_Orev(X1,X3),X2,X3) = c_List_Oitrev(X1,X2,X3),
    c_0_10048,
    [final] ).

cnf(c_0_12986,plain,
    ( c_div(X1,X1,tc_nat) = c_1
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_10049,
    [final] ).

cnf(c_0_12987,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10050,
    [final] ).

cnf(c_0_12988,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg),
    c_0_10051,
    [final] ).

cnf(c_0_12989,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_HOL_Oabs(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10052,
    [final] ).

cnf(c_0_12990,plain,
    ( c_divide(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_HOL_Oinverse(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_10053,
    [final] ).

cnf(c_0_12991,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_10054,
    [final] ).

cnf(c_0_12992,plain,
    c_in(X1,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2),X2),
    c_0_10055,
    [final] ).

cnf(c_0_12993,plain,
    c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X3) = c_List_Otake(X2,X1,X3),
    c_0_10056,
    [final] ).

cnf(c_0_12994,plain,
    c_List_Olast(c_append(X1,c_List_Olist_ONil,X2),X2) = c_List_Olast(X1,X2),
    c_0_10057,
    [final] ).

cnf(c_0_12995,plain,
    ( ~ c_less(c_HOL_Oabs(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10058,
    [final] ).

cnf(c_0_12996,plain,
    ( ~ c_less(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_10059,
    [final] ).

cnf(c_0_12997,plain,
    ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    c_0_10060,
    [final] ).

cnf(c_0_12998,plain,
    c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
    c_0_10061,
    [final] ).

cnf(c_0_12999,plain,
    c_Nat_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    c_0_10062,
    [final] ).

cnf(c_0_13000,plain,
    ( ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_10063,
    [final] ).

cnf(c_0_13001,plain,
    ( c_Finite__Set_OMin(c_insert(X1,c_emptyset,X2),X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10064,
    [final] ).

cnf(c_0_13002,plain,
    ( c_Finite__Set_OMax(c_insert(X1,c_emptyset,X2),X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10065,
    [final] ).

cnf(c_0_13003,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X1,X2),c_Numeral_Obit_OB0),X2) = c_Numeral_Obin__mult(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),
    c_0_10066,
    [final] ).

cnf(c_0_13004,plain,
    ( c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_10067,
    [final] ).

cnf(c_0_13005,plain,
    ( c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_10068,
    [final] ).

cnf(c_0_13006,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    c_0_10069,
    [final] ).

cnf(c_0_13007,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    c_0_10070,
    [final] ).

cnf(c_0_13008,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    c_0_10071,
    [final] ).

cnf(c_0_13009,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    c_0_10072,
    [final] ).

cnf(c_0_13010,plain,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    c_0_10073,
    [final] ).

cnf(c_0_13011,plain,
    ( c_List_Olast(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_0 ),
    c_0_10074,
    [final] ).

cnf(c_0_13012,plain,
    ( c_List_Ohd(c_List_Oupt(X1,X2),tc_nat) = X1
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_10075,
    [final] ).

cnf(c_0_13013,plain,
    ( c_List_Ohd(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_0 ),
    c_0_10076,
    [final] ).

cnf(c_0_13014,plain,
    ~ c_in(c_Public_OpublicKey(X1,X2),c_Message_OsymKeys,tc_nat),
    c_0_10077,
    [final] ).

cnf(c_0_13015,plain,
    ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Oparts(c_Event_OinitState(X2)),tc_Message_Omsg),
    c_0_10078,
    [final] ).

cnf(c_0_13016,plain,
    c_List_Otl(c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    c_0_10079,
    [final] ).

cnf(c_0_13017,plain,
    c_List_Ohd(c_List_Olist_OCons(X1,X2,X3),X3) = X1,
    c_0_10080,
    [final] ).

cnf(c_0_13018,plain,
    ( c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    c_0_10081,
    [final] ).

cnf(c_0_13019,plain,
    ( c_divide(X1,c_0,X2) = c_divide(X3,c_0,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10082,
    [final] ).

cnf(c_0_13020,plain,
    ( c_divide(c_0,X1,X2) = c_divide(c_0,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10083,
    [final] ).

cnf(c_0_13021,plain,
    ( c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_10084,
    [final] ).

cnf(c_0_13022,plain,
    ( c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_10085,
    [final] ).

cnf(c_0_13023,plain,
    ( X1 = c_emptyset
    | c_Union(X2,X3) != c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    c_0_10086,
    [final] ).

cnf(c_0_13024,plain,
    ( X1 = c_emptyset
    | c_Union(X2,X3) != c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    c_0_10087,
    [final] ).

cnf(c_0_13025,plain,
    ( X1 = c_UNIV
    | c_Inter(X2,X3) != c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    c_0_10088,
    [final] ).

cnf(c_0_13026,plain,
    ( X1 = c_UNIV
    | c_Inter(X2,X3) != c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    c_0_10089,
    [final] ).

cnf(c_0_13027,plain,
    c_Nat_Osize(c_Event_Oevent_OSays(X1,X2,X3),tc_Event_Oevent) = c_0,
    c_0_10090,
    [final] ).

cnf(c_0_13028,plain,
    ( c_List_Oremdups(X1,X2) = X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    c_0_10091,
    [final] ).

cnf(c_0_13029,plain,
    ( c_HOL_Oabs(X1,X2) = c_uminus(X1,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10092,
    [final] ).

cnf(c_0_13030,plain,
    c_union(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId,tc_prod(X2,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    c_0_10093,
    [final] ).

cnf(c_0_13031,plain,
    c_Set_Ocontents(c_insert(X1,c_emptyset,X2),X2) = X1,
    c_0_10094,
    [final] ).

cnf(c_0_13032,plain,
    c_List_Olast(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = X1,
    c_0_10095,
    [final] ).

cnf(c_0_13033,plain,
    ( X1 = c_0
    | ~ c_less(c_HOL_Oabs(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    c_0_10096,
    [final] ).

cnf(c_0_13034,plain,
    c_less(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    c_0_10097,
    [final] ).

cnf(c_0_13035,plain,
    c_minus(c_Suc(X1),c_Suc(X2),tc_nat) = c_minus(X1,X2,tc_nat),
    c_0_10098,
    [final] ).

cnf(c_0_13036,plain,
    c_List_Obutlast(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_ONil,
    c_0_10099,
    [final] ).

cnf(c_0_13037,plain,
    ( X1 = c_emptyset
    | c_Finite__Set_Ocard(X1,X2) != c_0
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_10100,
    [final] ).

cnf(c_0_13038,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_Oused(X3),tc_Message_Omsg),
    c_0_10101,
    [final] ).

cnf(c_0_13039,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_OinitState(X3),tc_Message_Omsg),
    c_0_10102,
    [final] ).

cnf(c_0_13040,plain,
    c_Nat_Osize(c_Message_Omsg_OCrypt(X1,X2),tc_Message_Omsg) = c_plus(c_Nat_Osize(X2,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    c_0_10103,
    [final] ).

cnf(c_0_13041,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10104,
    [final] ).

cnf(c_0_13042,plain,
    ( c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_uminus(c_1,X1)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_10105,
    [final] ).

cnf(c_0_13043,plain,
    ( c_SetInterval_OatLeastAtMost(X1,X1,X2) = c_insert(X1,c_emptyset,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_10106,
    [final] ).

cnf(c_0_13044,plain,
    ( c_times(X1,c_0,X2) = c_times(X3,c_0,X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    c_0_10107,
    [final] ).

cnf(c_0_13045,plain,
    ( c_times(c_0,X1,X2) = c_times(c_0,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    c_0_10108,
    [final] ).

cnf(c_0_13046,plain,
    ( c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10109,
    [final] ).

cnf(c_0_13047,plain,
    ( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_1
    | ~ c_Parity_Oeven(X2,tc_nat)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10110,
    [final] ).

cnf(c_0_13048,plain,
    ( c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_1
    | ~ c_Parity_Oeven(X2,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_10111,
    [final] ).

cnf(c_0_13049,plain,
    c_Nat_Opower(X1,c_1,tc_set(tc_prod(X2,X2))) = X1,
    c_0_10112,
    [final] ).

cnf(c_0_13050,plain,
    c_Nat_Opower(X1,c_0,tc_set(tc_prod(X2,X2))) = c_Relation_OId,
    c_0_10113,
    [final] ).

cnf(c_0_13051,plain,
    c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
    c_0_10114,
    [final] ).

cnf(c_0_13052,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),c_Numeral_OBit(X2,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,c_Numeral_Obin__succ(X2)),c_Numeral_Obit_OB0),
    c_0_10115,
    [final] ).

cnf(c_0_13053,plain,
    ( c_List_Olist_OCons(c_List_Ohd(X1,X2),c_List_Otl(X1,X2),X2) = X1
    | X1 = c_List_Olist_ONil ),
    c_0_10116,
    [final] ).

cnf(c_0_13054,plain,
    ( X1 = c_List_Olist_ONil
    | c_in(c_List_Olast(X1,X2),c_List_Oset(X1,X2),X2) ),
    c_0_10117,
    [final] ).

cnf(c_0_13055,plain,
    ( X1 = c_List_Olist_ONil
    | c_in(c_List_Ohd(X1,X2),c_List_Oset(X1,X2),X2) ),
    c_0_10118,
    [final] ).

cnf(c_0_13056,plain,
    c_Event_Oevent_ONotes(X1,X2) != c_Event_Oevent_OSays(X3,X4,X5),
    c_0_10119,
    [final] ).

cnf(c_0_13057,plain,
    c_Event_Oevent_OSays(X1,X2,X3) != c_Event_Oevent_ONotes(X4,X5),
    c_0_10120,
    [final] ).

cnf(c_0_13058,plain,
    c_Event_Oevent_OGets(X1,X2) != c_Event_Oevent_OSays(X3,X4,X5),
    c_0_10121,
    [final] ).

cnf(c_0_13059,plain,
    c_Event_Oevent_OSays(X1,X2,X3) != c_Event_Oevent_OGets(X4,X5),
    c_0_10122,
    [final] ).

cnf(c_0_13060,plain,
    ( c_OrderedGroup_Opprt(X1,X2) = X1
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10123,
    [final] ).

cnf(c_0_13061,plain,
    ( c_OrderedGroup_Onprt(X1,X2) = X1
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10124,
    [final] ).

cnf(c_0_13062,plain,
    ( c_HOL_Oabs(X1,X2) = X1
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10125,
    [final] ).

cnf(c_0_13063,plain,
    ( c_plus(c_NatArith_Oof__nat(X1,X2),c_1,X2) = c_NatArith_Oof__nat(c_Suc(X1),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2) ),
    c_0_10126,
    [final] ).

cnf(c_0_13064,plain,
    ( c_OrderedGroup_Opprt(X1,X2) = c_0
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10127,
    [final] ).

cnf(c_0_13065,plain,
    ( c_OrderedGroup_Onprt(X1,X2) = c_0
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10128,
    [final] ).

cnf(c_0_13066,plain,
    ( c_Finite__Set_Ocard(c_emptyset,X1) = c_0
    | ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
    c_0_10129,
    [final] ).

cnf(c_0_13067,plain,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_1
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ class_Power_Orecpower(X2) ),
    c_0_10130,
    [final] ).

cnf(c_0_13068,plain,
    ( X1 = c_0
    | X2 = c_0
    | c_divide(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_10131,
    [final] ).

cnf(c_0_13069,plain,
    ( X1 = X2
    | c_divide(X1,X2,X3) != c_1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_10132,
    [final] ).

cnf(c_0_13070,plain,
    ( X1 = X2
    | c_divide(X2,X1,X3) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_10133,
    [final] ).

cnf(c_0_13071,plain,
    ( X1 = X2
    | c_divide(X2,X1,X3) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_10134,
    [final] ).

cnf(c_0_13072,plain,
    ( X1 = X2
    | c_divide(X1,X2,X3) != c_1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_10135,
    [final] ).

cnf(c_0_13073,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),c_Numeral_OBit(X2,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,X2),X3),
    c_0_10136,
    [final] ).

cnf(c_0_13074,plain,
    c_times(X1,c_0,tc_nat) = c_times(X2,c_0,tc_nat),
    c_0_10137,
    [final] ).

cnf(c_0_13075,plain,
    c_times(c_0,X1,tc_nat) = c_times(c_0,X2,tc_nat),
    c_0_10138,
    [final] ).

cnf(c_0_13076,plain,
    ( X1 = c_0
    | c_Nat_Opower(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    c_0_10139,
    [final] ).

cnf(c_0_13077,plain,
    ( c_Union(X1,X2) = c_emptyset
    | c_in(c_Main_Oempty__Union__conv__1(X1,X2),X1,tc_set(X2)) ),
    c_0_10140,
    [final] ).

cnf(c_0_13078,plain,
    ( c_Union(X1,X2) = c_emptyset
    | c_in(c_Main_OUnion__empty__conv__1(X1,X2),X1,tc_set(X2)) ),
    c_0_10141,
    [final] ).

cnf(c_0_13079,plain,
    ( c_Inter(X1,X2) = c_UNIV
    | c_in(c_Main_OInter__UNIV__conv__2__1(X1,X2),X1,tc_set(X2)) ),
    c_0_10142,
    [final] ).

cnf(c_0_13080,plain,
    ( c_Inter(X1,X2) = c_UNIV
    | c_in(c_Main_OInter__UNIV__conv__1__1(X1,X2),X1,tc_set(X2)) ),
    c_0_10143,
    [final] ).

cnf(c_0_13081,plain,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oint(X2) != c_Numeral_Onumber__of(X1,tc_IntDef_Oint) ),
    c_0_10144,
    [final] ).

cnf(c_0_13082,plain,
    ( c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10145,
    [final] ).

cnf(c_0_13083,plain,
    ( c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_uminus(X3,X2) != c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    c_0_10146,
    [final] ).

cnf(c_0_13084,plain,
    ( X1 = c_uminus(c_Numeral_Onumber__of(X2,X3),X3)
    | c_Numeral_Onumber__of(X2,X3) != c_uminus(X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    c_0_10147,
    [final] ).

cnf(c_0_13085,plain,
    ( X1 = c_0
    | c_divide(c_1,X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10148,
    [final] ).

cnf(c_0_13086,plain,
    ( X1 = c_0
    | c_divide(c_1,X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10149,
    [final] ).

cnf(c_0_13087,plain,
    ( c_times(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10150,
    [final] ).

cnf(c_0_13088,plain,
    ( c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10151,
    [final] ).

cnf(c_0_13089,plain,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),c_Numeral_OBit(X2,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,X2),c_Numeral_Obit_OB1),
    c_0_10152,
    [final] ).

cnf(c_0_13090,plain,
    ( c_List_Oupt(X1,X2) = c_List_Olist_ONil
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_10153,
    [final] ).

cnf(c_0_13091,plain,
    ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    c_0_10154,
    [final] ).

cnf(c_0_13092,plain,
    ( c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10155,
    [final] ).

cnf(c_0_13093,plain,
    ( c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10156,
    [final] ).

cnf(c_0_13094,plain,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_10157,
    [final] ).

cnf(c_0_13095,plain,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_10158,
    [final] ).

cnf(c_0_13096,plain,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_10159,
    [final] ).

cnf(c_0_13097,plain,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_10160,
    [final] ).

cnf(c_0_13098,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(X1,X2),tc_Message_Omsg),
    c_0_10161,
    [final] ).

cnf(c_0_13099,plain,
    c_plus(c_Nat_Osize(X1,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(X1),tc_Message_Omsg),
    c_0_10162,
    [final] ).

cnf(c_0_13100,plain,
    ( X1 = c_0
    | X2 = c_0
    | c_times(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_10163,
    [final] ).

cnf(c_0_13101,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    c_0_10164,
    [final] ).

cnf(c_0_13102,plain,
    c_Nat_Osize(c_List_Oupt(X1,X2),tc_List_Olist(tc_nat)) = c_minus(X2,X1,tc_nat),
    c_0_10165,
    [final] ).

cnf(c_0_13103,plain,
    ( X1 = X2
    | c_minus(X1,X2,X3) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_10166,
    [final] ).

cnf(c_0_13104,plain,
    ( X1 = c_emptyset
    | ~ c_lessequals(X1,c_emptyset,tc_set(X2)) ),
    c_0_10167,
    [final] ).

cnf(c_0_13105,plain,
    c_Relation_Oconverse(c_Relation_Odiag(X1,X2),X2,X2) = c_Relation_Odiag(X1,X2),
    c_0_10168,
    [final] ).

cnf(c_0_13106,plain,
    c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    c_0_10169,
    [final] ).

cnf(c_0_13107,plain,
    ( c_HOL_Oinverse(c_uminus(X1,X2),X2) = c_uminus(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10170,
    [final] ).

cnf(c_0_13108,plain,
    ( c_HOL_Oinverse(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10171,
    [final] ).

cnf(c_0_13109,plain,
    ( c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_Numeral_Onumber__of(X1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10172,
    [final] ).

cnf(c_0_13110,plain,
    ~ c_less(X1,c_emptyset,tc_set(X2)),
    c_0_10173,
    [final] ).

cnf(c_0_13111,plain,
    ( ~ c_less(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_10174,
    [final] ).

cnf(c_0_13112,plain,
    c_inter(X1,c_uminus(X1,tc_set(X2)),X2) = c_emptyset,
    c_0_10175,
    [final] ).

cnf(c_0_13113,plain,
    c_inter(c_uminus(X1,tc_set(X2)),X1,X2) = c_emptyset,
    c_0_10176,
    [final] ).

cnf(c_0_13114,plain,
    c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2) = c_insert(X1,c_emptyset,X2),
    c_0_10177,
    [final] ).

cnf(c_0_13115,plain,
    ( c_IntDef_Oint(c_IntDef_Onat(X1)) = X1
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    c_0_10178,
    [final] ).

cnf(c_0_13116,plain,
    ( X1 = c_0
    | ~ c_lessequals(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint) ),
    c_0_10179,
    [final] ).

cnf(c_0_13117,plain,
    ( X1 = c_Suc(c_0)
    | ~ c_Divides_Oop_Advd(X1,c_Suc(c_0),tc_nat) ),
    c_0_10180,
    [final] ).

cnf(c_0_13118,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    c_0_10181,
    [final] ).

cnf(c_0_13119,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    c_0_10182,
    [final] ).

cnf(c_0_13120,plain,
    ( X1 = c_List_Olist_ONil
    | c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    c_0_10183,
    [final] ).

cnf(c_0_13121,plain,
    ~ c_less(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint),
    c_0_10184,
    [final] ).

cnf(c_0_13122,plain,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) != X1 ),
    c_0_10185,
    [final] ).

cnf(c_0_13123,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_Suc(c_0),tc_nat) ),
    c_0_10186,
    [final] ).

cnf(c_0_13124,plain,
    ( c_times(X1,c_HOL_Oinverse(X1,X2),X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2) ),
    c_0_10187,
    [final] ).

cnf(c_0_13125,plain,
    ( c_times(c_HOL_Oinverse(X1,X2),X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2) ),
    c_0_10188,
    [final] ).

cnf(c_0_13126,plain,
    ( X1 = c_List_Olist_ONil
    | X2 = c_0
    | c_List_Otake(X2,X1,X3) != c_List_Olist_ONil ),
    c_0_10189,
    [final] ).

cnf(c_0_13127,plain,
    ( X1 = c_1
    | c_times(X2,X1,tc_nat) != c_Suc(c_0) ),
    c_0_10190,
    [final] ).

cnf(c_0_13128,plain,
    ( X1 = c_1
    | c_times(X1,X2,tc_nat) != c_Suc(c_0) ),
    c_0_10191,
    [final] ).

cnf(c_0_13129,plain,
    ( X1 = c_1
    | c_times(X2,X1,tc_nat) != c_Suc(c_0) ),
    c_0_10192,
    [final] ).

cnf(c_0_13130,plain,
    ( X1 = c_1
    | c_times(X1,X2,tc_nat) != c_Suc(c_0) ),
    c_0_10193,
    [final] ).

cnf(c_0_13131,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    c_0_10194,
    [final] ).

cnf(c_0_13132,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    c_0_10195,
    [final] ).

cnf(c_0_13133,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    c_0_10196,
    [final] ).

cnf(c_0_13134,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    c_0_10197,
    [final] ).

cnf(c_0_13135,plain,
    ~ c_in(X1,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    c_0_10198,
    [final] ).

cnf(c_0_13136,plain,
    ( ~ c_less(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10199,
    [final] ).

cnf(c_0_13137,plain,
    ( ~ c_lessequals(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10200,
    [final] ).

cnf(c_0_13138,plain,
    ( X1 = c_0
    | c_less(c_0,c_HOL_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10201,
    [final] ).

cnf(c_0_13139,plain,
    ( c_plus(X1,c_uminus(X1,X2),X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10202,
    [final] ).

cnf(c_0_13140,plain,
    ( c_plus(c_uminus(X1,X2),X1,X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10203,
    [final] ).

cnf(c_0_13141,plain,
    ( X1 = c_emptyset
    | c_union(X2,X1,X3) != c_emptyset ),
    c_0_10204,
    [final] ).

cnf(c_0_13142,plain,
    ( X1 = c_emptyset
    | c_union(X1,X2,X3) != c_emptyset ),
    c_0_10205,
    [final] ).

cnf(c_0_13143,plain,
    ( X1 = c_UNIV
    | c_inter(X2,X1,X3) != c_UNIV ),
    c_0_10206,
    [final] ).

cnf(c_0_13144,plain,
    ( X1 = c_UNIV
    | c_inter(X1,X2,X3) != c_UNIV ),
    c_0_10207,
    [final] ).

cnf(c_0_13145,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orotate(X2,X1,X3) != c_List_Olist_ONil ),
    c_0_10208,
    [final] ).

cnf(c_0_13146,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    c_0_10209,
    [final] ).

cnf(c_0_13147,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    c_0_10210,
    [final] ).

cnf(c_0_13148,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    c_0_10211,
    [final] ).

cnf(c_0_13149,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    c_0_10212,
    [final] ).

cnf(c_0_13150,plain,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    c_0_10213,
    [final] ).

cnf(c_0_13151,plain,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    c_0_10214,
    [final] ).

cnf(c_0_13152,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    c_0_10215,
    [final] ).

cnf(c_0_13153,plain,
    c_List_Olist_OCons(X2,X1,X3) != X1,
    c_0_10216,
    [final] ).

cnf(c_0_13154,plain,
    ( X1 = c_0
    | X2 = c_0
    | c_times(X1,X2,tc_nat) != c_0 ),
    c_0_10217,
    [final] ).

cnf(c_0_13155,plain,
    ( c_Message_OinvKey(X1) = X1
    | ~ c_in(X1,c_Message_OsymKeys,tc_nat) ),
    c_0_10218,
    [final] ).

cnf(c_0_13156,plain,
    ( c_lessequals(c_0,c_OrderedGroup_Opprt(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10219,
    [final] ).

cnf(c_0_13157,plain,
    ( c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    c_0_10220,
    [final] ).

cnf(c_0_13158,plain,
    ( c_lessequals(c_0,c_HOL_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10221,
    [final] ).

cnf(c_0_13159,plain,
    ( c_lessequals(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_10222,
    [final] ).

cnf(c_0_13160,plain,
    ( c_in(c_NatArith_Oof__nat(X1,X2),c_IntDef_ONats,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2) ),
    c_0_10223,
    [final] ).

cnf(c_0_13161,plain,
    c_insert(X1,X2,X3) != c_emptyset,
    c_0_10224,
    [final] ).

cnf(c_0_13162,plain,
    c_insert(X1,X2,X3) != c_emptyset,
    c_0_10225,
    [final] ).

cnf(c_0_13163,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    c_0_10226,
    [final] ).

cnf(c_0_13164,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    c_0_10227,
    [final] ).

cnf(c_0_13165,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_10228,
    [final] ).

cnf(c_0_13166,plain,
    c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),X2) = c_Message_OHPair(X1,X2),
    c_0_10229,
    [final] ).

cnf(c_0_13167,plain,
    c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),X2) = c_Message_OHPair(X1,X2),
    c_0_10230,
    [final] ).

cnf(c_0_13168,plain,
    ( c_IntDef_Onat(X1) = c_0
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint) ),
    c_0_10231,
    [final] ).

cnf(c_0_13169,plain,
    ( X1 = c_0
    | c_plus(X2,X1,tc_nat) != c_0 ),
    c_0_10232,
    [final] ).

cnf(c_0_13170,plain,
    ( X1 = c_0
    | c_plus(X1,X2,tc_nat) != c_0 ),
    c_0_10233,
    [final] ).

cnf(c_0_13171,plain,
    c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
    c_0_10234,
    [final] ).

cnf(c_0_13172,plain,
    c_in(c_List_Olist_ONil,c_List_Olists(X1,X2),tc_List_Olist(X2)),
    c_0_10235,
    [final] ).

cnf(c_0_13173,plain,
    c_in(c_List_Oset(X1,X2),c_Finite__Set_OFinites,tc_set(X2)),
    c_0_10236,
    [final] ).

cnf(c_0_13174,plain,
    ( c_IntDef_Oof__int(c_uminus(X1,tc_IntDef_Oint),X2) = c_uminus(c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    c_0_10237,
    [final] ).

cnf(c_0_13175,plain,
    ~ c_in(X1,c_emptyset,X2),
    c_0_10238,
    [final] ).

cnf(c_0_13176,plain,
    ~ c_List_Oop_Amem(X1,c_List_Olist_ONil,X2),
    c_0_10239,
    [final] ).

cnf(c_0_13177,plain,
    ~ c_less(X1,X1,tc_nat),
    c_0_10240,
    [final] ).

cnf(c_0_13178,plain,
    ( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10241,
    [final] ).

cnf(c_0_13179,plain,
    ( c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_1
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10242,
    [final] ).

cnf(c_0_13180,plain,
    ( c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_10243,
    [final] ).

cnf(c_0_13181,plain,
    ( c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_10244,
    [final] ).

cnf(c_0_13182,plain,
    ( c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_10245,
    [final] ).

cnf(c_0_13183,plain,
    ( c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10246,
    [final] ).

cnf(c_0_13184,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_1,tc_nat) ),
    c_0_10247,
    [final] ).

cnf(c_0_13185,plain,
    ( X1 = c_0
    | ~ c_lessequals(X1,c_0,tc_nat) ),
    c_0_10248,
    [final] ).

cnf(c_0_13186,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint) ),
    c_0_10249,
    [final] ).

cnf(c_0_13187,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat) ),
    c_0_10250,
    [final] ).

cnf(c_0_13188,plain,
    ( X1 = c_emptyset
    | c_in(c_Main_Oall__not__in__conv__1(X1,X2),X1,X2) ),
    c_0_10251,
    [final] ).

cnf(c_0_13189,plain,
    c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2) = X1,
    c_0_10252,
    [final] ).

cnf(c_0_13190,plain,
    c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2) = X1,
    c_0_10253,
    [final] ).

cnf(c_0_13191,plain,
    ( c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X1),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10254,
    [final] ).

cnf(c_0_13192,plain,
    ~ c_less(X1,c_0,tc_nat),
    c_0_10255,
    [final] ).

cnf(c_0_13193,plain,
    c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_UNIV,
    c_0_10256,
    [final] ).

cnf(c_0_13194,plain,
    c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_UNIV,
    c_0_10257,
    [final] ).

cnf(c_0_13195,plain,
    c_in(c_SetInterval_OlessThan(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_10258,
    [final] ).

cnf(c_0_13196,plain,
    c_in(c_SetInterval_OatMost(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_10259,
    [final] ).

cnf(c_0_13197,plain,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    c_0_10260,
    [final] ).

cnf(c_0_13198,plain,
    ~ c_less(c_0,c_0,tc_nat),
    c_0_10261,
    [final] ).

cnf(c_0_13199,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orev(X1,X2),X2) ),
    c_0_10262,
    [final] ).

cnf(c_0_13200,plain,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate1(X1,X2),X2) ),
    c_0_10263,
    [final] ).

cnf(c_0_13201,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oused(X2),tc_Message_Omsg),
    c_0_10264,
    [final] ).

cnf(c_0_13202,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_OinitState(X1),tc_Message_Omsg),
    c_0_10265,
    [final] ).

cnf(c_0_13203,plain,
    ( X1 = c_0
    | c_lessequals(X1,X2,tc_nat)
    | c_List_Oupt(X2,X1) != c_List_Olist_ONil ),
    c_0_10266,
    [final] ).

cnf(c_0_13204,plain,
    ( X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3))
    | c_Message_Omsg_OMPair(X1,X4) != c_Message_OHPair(X2,X3) ),
    c_0_10267,
    [final] ).

cnf(c_0_13205,plain,
    ( X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3))
    | c_Message_OHPair(X2,X3) != c_Message_Omsg_OMPair(X1,X4) ),
    c_0_10268,
    [final] ).

cnf(c_0_13206,plain,
    c_union(c_Message_Oparts(X1),c_Message_Osynth(X1),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(X1)),
    c_0_10269,
    [final] ).

cnf(c_0_13207,plain,
    c_union(c_Message_Oanalz(X1),c_Message_Osynth(X1),tc_Message_Omsg) = c_Message_Oanalz(c_Message_Osynth(X1)),
    c_0_10270,
    [final] ).

cnf(c_0_13208,plain,
    c_Numeral_Obin__mult(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2) = c_Numeral_OBit(c_Numeral_Obin__mult(X1,X2),c_Numeral_Obit_OB0),
    c_0_10271,
    [final] ).

cnf(c_0_13209,plain,
    ( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10272,
    [final] ).

cnf(c_0_13210,plain,
    ( c_minus(c_0,X1,X2) = c_uminus(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10273,
    [final] ).

cnf(c_0_13211,plain,
    ( c_List_Oupt(X1,c_Suc(X2)) = c_List_Olist_ONil
    | c_lessequals(X1,X2,tc_nat) ),
    c_0_10274,
    [final] ).

cnf(c_0_13212,plain,
    ( c_Finite__Set_Ocard(X1,X2) = c_0
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_10275,
    [final] ).

cnf(c_0_13213,plain,
    c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0,
    c_0_10276,
    [final] ).

cnf(c_0_13214,plain,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10277,
    [final] ).

cnf(c_0_13215,plain,
    c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_10278,
    [final] ).

cnf(c_0_13216,plain,
    c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
    c_0_10279,
    [final] ).

cnf(c_0_13217,plain,
    ( c_divide(X1,X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10280,
    [final] ).

cnf(c_0_13218,plain,
    ( c_divide(X1,X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10281,
    [final] ).

cnf(c_0_13219,plain,
    c_insert(c_emptyset,c_emptyset,tc_set(X1)) = c_Pow(c_emptyset,X1),
    c_0_10282,
    [final] ).

cnf(c_0_13220,plain,
    c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)) = c_List_Olistset(c_List_Olist_ONil,X1),
    c_0_10283,
    [final] ).

cnf(c_0_13221,plain,
    c_Public_OpublicKey(X1,X2) != c_Message_OinvKey(c_Public_OpublicKey(X3,X4)),
    c_0_10284,
    [final] ).

cnf(c_0_13222,plain,
    c_Message_OinvKey(c_Public_OpublicKey(X1,X2)) != c_Public_OpublicKey(X3,X4),
    c_0_10285,
    [final] ).

cnf(c_0_13223,plain,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10286,
    [final] ).

cnf(c_0_13224,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10287,
    [final] ).

cnf(c_0_13225,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10288,
    [final] ).

cnf(c_0_13226,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10289,
    [final] ).

cnf(c_0_13227,plain,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_10290,
    [final] ).

cnf(c_0_13228,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    c_0_10291,
    [final] ).

cnf(c_0_13229,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    c_0_10292,
    [final] ).

cnf(c_0_13230,plain,
    c_plus(c_1,c_IntDef_Oint(X1),tc_IntDef_Oint) = c_IntDef_Oint(c_Suc(X1)),
    c_0_10293,
    [final] ).

cnf(c_0_13231,plain,
    ( c_divide(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10294,
    [final] ).

cnf(c_0_13232,plain,
    ( c_divide(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10295,
    [final] ).

cnf(c_0_13233,plain,
    ( c_uminus(c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_SetInterval_OatLeast(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10296,
    [final] ).

cnf(c_0_13234,plain,
    ( c_uminus(c_SetInterval_OgreaterThan(X1,X2),tc_set(X2)) = c_SetInterval_OatMost(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10297,
    [final] ).

cnf(c_0_13235,plain,
    ( c_uminus(c_SetInterval_OatMost(X1,X2),tc_set(X2)) = c_SetInterval_OgreaterThan(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10298,
    [final] ).

cnf(c_0_13236,plain,
    ( c_uminus(c_SetInterval_OatLeast(X1,X2),tc_set(X2)) = c_SetInterval_OlessThan(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10299,
    [final] ).

cnf(c_0_13237,plain,
    ( c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    c_0_10300,
    [final] ).

cnf(c_0_13238,plain,
    ( c_Nat_Opower(c_0,c_Suc(X1),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    c_0_10301,
    [final] ).

cnf(c_0_13239,plain,
    c_Nat_Osize(c_List_Orotate1(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)),
    c_0_10302,
    [final] ).

cnf(c_0_13240,plain,
    c_Nat_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)),
    c_0_10303,
    [final] ).

cnf(c_0_13241,plain,
    ( c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_10304,
    [final] ).

cnf(c_0_13242,plain,
    ( c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_10305,
    [final] ).

cnf(c_0_13243,plain,
    ( c_divide(c_0,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_10306,
    [final] ).

cnf(c_0_13244,plain,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10307,
    [final] ).

cnf(c_0_13245,plain,
    ( X1 = X2
    | c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3)) ),
    c_0_10308,
    [final] ).

cnf(c_0_13246,plain,
    c_in(c_Message_Omsg_ONumber(X1),c_Message_Osynth(X2),tc_Message_Omsg),
    c_0_10309,
    [final] ).

cnf(c_0_13247,plain,
    c_in(c_Message_Omsg_OAgent(X1),c_Message_Osynth(X2),tc_Message_Omsg),
    c_0_10310,
    [final] ).

cnf(c_0_13248,plain,
    ( c_List_Odistinct(c_List_Orev(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    c_0_10311,
    [final] ).

cnf(c_0_13249,plain,
    ( c_List_Odistinct(c_List_Orotate1(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    c_0_10312,
    [final] ).

cnf(c_0_13250,plain,
    ( c_Orderings_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10313,
    [final] ).

cnf(c_0_13251,plain,
    ( c_Orderings_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_10314,
    [final] ).

cnf(c_0_13252,plain,
    ( c_LOrder_Omeet(X1,X1,X2) = X1
    | ~ class_LOrder_Omeet__semilorder(X2) ),
    c_0_10315,
    [final] ).

cnf(c_0_13253,plain,
    ( c_LOrder_Ojoin(X1,X1,X2) = X1
    | ~ class_LOrder_Ojoin__semilorder(X2) ),
    c_0_10316,
    [final] ).

cnf(c_0_13254,plain,
    ( c_IntDef_Oint(c_IntDef_Onat(X1)) = c_0
    | c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    c_0_10317,
    [final] ).

cnf(c_0_13255,plain,
    ( c_minus(X1,X1,X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10318,
    [final] ).

cnf(c_0_13256,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_10319,
    [final] ).

cnf(c_0_13257,plain,
    ( c_times(c_1,X1,X2) = X1
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_10320,
    [final] ).

cnf(c_0_13258,plain,
    ( c_times(X1,c_1,X2) = X1
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_10321,
    [final] ).

cnf(c_0_13259,plain,
    ( c_divide(X1,c_1,X2) = X1
    | ~ class_Ring__and__Field_Ofield(X2) ),
    c_0_10322,
    [final] ).

cnf(c_0_13260,plain,
    ( c_Nat_Opower(X1,c_1,X2) = X1
    | ~ class_Power_Orecpower(X2) ),
    c_0_10323,
    [final] ).

cnf(c_0_13261,plain,
    ( c_times(X1,c_1,X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    c_0_10324,
    [final] ).

cnf(c_0_13262,plain,
    ( c_times(c_1,X1,X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    c_0_10325,
    [final] ).

cnf(c_0_13263,plain,
    ( c_minus(X1,c_0,X2) = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10326,
    [final] ).

cnf(c_0_13264,plain,
    ( c_plus(c_0,X1,X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    c_0_10327,
    [final] ).

cnf(c_0_13265,plain,
    ( c_plus(X1,c_0,X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    c_0_10328,
    [final] ).

cnf(c_0_13266,plain,
    ( c_HOL_Oabs(c_uminus(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10329,
    [final] ).

cnf(c_0_13267,plain,
    ( c_HOL_Oabs(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10330,
    [final] ).

cnf(c_0_13268,plain,
    c_minus(X1,X1,tc_set(X2)) = c_emptyset,
    c_0_10331,
    [final] ).

cnf(c_0_13269,plain,
    c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatMost(c_0,tc_nat),
    c_0_10332,
    [final] ).

cnf(c_0_13270,plain,
    ( X1 = X2
    | c_HOL_Oinverse(X1,X3) != c_HOL_Oinverse(X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    c_0_10333,
    [final] ).

cnf(c_0_13271,plain,
    c_lessequals(X1,X1,tc_set(X2)),
    c_0_10334,
    [final] ).

cnf(c_0_13272,plain,
    ( c_times(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X2) ),
    c_0_10335,
    [final] ).

cnf(c_0_13273,plain,
    ( c_times(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X2) ),
    c_0_10336,
    [final] ).

cnf(c_0_13274,plain,
    ( c_times(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_10337,
    [final] ).

cnf(c_0_13275,plain,
    ( c_times(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_10338,
    [final] ).

cnf(c_0_13276,plain,
    ( c_Nat_Opower(X1,c_0,X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    c_0_10339,
    [final] ).

cnf(c_0_13277,plain,
    ( c_Nat_Opower(c_1,X1,X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    c_0_10340,
    [final] ).

cnf(c_0_13278,plain,
    c_minus(X1,c_emptyset,tc_set(X2)) = X1,
    c_0_10341,
    [final] ).

cnf(c_0_13279,plain,
    c_lessequals(X1,c_UNIV,tc_set(X2)),
    c_0_10342,
    [final] ).

cnf(c_0_13280,plain,
    c_minus(c_emptyset,X1,tc_set(X2)) = c_emptyset,
    c_0_10343,
    [final] ).

cnf(c_0_13281,plain,
    c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
    c_0_10344,
    [final] ).

cnf(c_0_13282,plain,
    c_minus(X1,c_UNIV,tc_set(X2)) = c_emptyset,
    c_0_10345,
    [final] ).

cnf(c_0_13283,plain,
    c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
    c_0_10346,
    [final] ).

cnf(c_0_13284,plain,
    c_lessequals(c_emptyset,X1,tc_set(X2)),
    c_0_10347,
    [final] ).

cnf(c_0_13285,plain,
    c_less(X1,c_Suc(X1),tc_nat),
    c_0_10348,
    [final] ).

cnf(c_0_13286,plain,
    ( c_lessequals(c_0,c_1,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10349,
    [final] ).

cnf(c_0_13287,plain,
    ( c_less(c_0,c_1,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10350,
    [final] ).

cnf(c_0_13288,plain,
    ( c_in(c_1,c_IntDef_ONats,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_10351,
    [final] ).

cnf(c_0_13289,plain,
    ( c_in(c_0,c_IntDef_ONats,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_10352,
    [final] ).

cnf(c_0_13290,plain,
    ( c_in(c_1,c_IntDef_OInts,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_10353,
    [final] ).

cnf(c_0_13291,plain,
    ( c_in(c_0,c_IntDef_OInts,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_10354,
    [final] ).

cnf(c_0_13292,plain,
    ( c_IntDef_Oof__int(c_NatArith_Oof__nat(X1,tc_IntDef_Oint),X2) = c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    c_0_10355,
    [final] ).

cnf(c_0_13293,plain,
    c_in(c_Public_OshrK(X1),c_Message_OsymKeys,tc_nat),
    c_0_10356,
    [final] ).

cnf(c_0_13294,plain,
    c_lessequals(c_emptyset,c_emptyset,tc_set(X1)),
    c_0_10357,
    [final] ).

cnf(c_0_13295,plain,
    c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X1)),c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)),
    c_0_10358,
    [final] ).

cnf(c_0_13296,plain,
    c_lessequals(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint),
    c_0_10359,
    [final] ).

cnf(c_0_13297,plain,
    c_less(c_0,c_Suc(X1),tc_nat),
    c_0_10360,
    [final] ).

cnf(c_0_13298,plain,
    c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    c_0_10361,
    [final] ).

cnf(c_0_13299,plain,
    c_div(X1,c_Suc(c_0),tc_nat) = X1,
    c_0_10362,
    [final] ).

cnf(c_0_13300,plain,
    c_Divides_Oop_Amod(X1,c_Suc(c_0),tc_nat) = c_0,
    c_0_10363,
    [final] ).

cnf(c_0_13301,plain,
    c_Divides_Oop_Advd(c_Suc(c_0),X1,tc_nat),
    c_0_10364,
    [final] ).

cnf(c_0_13302,plain,
    ( c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    c_0_10365,
    [final] ).

cnf(c_0_13303,plain,
    c_union(X1,X1,X2) = X1,
    c_0_10366,
    [final] ).

cnf(c_0_13304,plain,
    c_inter(X1,X1,X2) = X1,
    c_0_10367,
    [final] ).

cnf(c_0_13305,plain,
    ( c_HOL_Oinverse(c_HOL_Oinverse(X1,X2),X2) = X1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10368,
    [final] ).

cnf(c_0_13306,plain,
    c_less(c_0,c_Suc(c_0),tc_nat),
    c_0_10369,
    [final] ).

cnf(c_0_13307,plain,
    ( c_div(X1,X1,tc_IntDef_Oint) = c_1
    | X1 = c_0 ),
    c_0_10370,
    [final] ).

cnf(c_0_13308,plain,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    c_0_10371,
    [final] ).

cnf(c_0_13309,plain,
    ( X1 = c_IntDef_Onat(c_Numeral_Onumber__of(X2,tc_IntDef_Oint))
    | c_IntDef_Oint(X1) != c_Numeral_Onumber__of(X2,tc_IntDef_Oint) ),
    c_0_10372,
    [final] ).

cnf(c_0_13310,plain,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    c_0_10373,
    [final] ).

cnf(c_0_13311,plain,
    c_union(X1,c_emptyset,X2) = X1,
    c_0_10374,
    [final] ).

cnf(c_0_13312,plain,
    c_union(c_emptyset,X1,X2) = X1,
    c_0_10375,
    [final] ).

cnf(c_0_13313,plain,
    c_inter(X1,c_UNIV,X2) = X1,
    c_0_10376,
    [final] ).

cnf(c_0_13314,plain,
    c_inter(c_UNIV,X1,X2) = X1,
    c_0_10377,
    [final] ).

cnf(c_0_13315,plain,
    c_List_Oset(c_List_Orotate1(X1,X2),X2) = c_List_Oset(X1,X2),
    c_0_10378,
    [final] ).

cnf(c_0_13316,plain,
    c_List_Oset(c_List_Orev(X1,X2),X2) = c_List_Oset(X1,X2),
    c_0_10379,
    [final] ).

cnf(c_0_13317,plain,
    c_List_Oset(c_List_Oremdups(X1,X2),X2) = c_List_Oset(X1,X2),
    c_0_10380,
    [final] ).

cnf(c_0_13318,plain,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    c_0_10381,
    [final] ).

cnf(c_0_13319,plain,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    c_0_10382,
    [final] ).

cnf(c_0_13320,plain,
    c_List_Oitrev(c_List_Olist_ONil,X1,X2) = X1,
    c_0_10383,
    [final] ).

cnf(c_0_13321,plain,
    c_List_Odrop(c_0,X1,X2) = X1,
    c_0_10384,
    [final] ).

cnf(c_0_13322,plain,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    c_0_10385,
    [final] ).

cnf(c_0_13323,plain,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    c_0_10386,
    [final] ).

cnf(c_0_13324,plain,
    c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X2) = X1,
    c_0_10387,
    [final] ).

cnf(c_0_13325,plain,
    c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X2) = X1,
    c_0_10388,
    [final] ).

cnf(c_0_13326,plain,
    c_Message_OinvKey(c_Public_OpublicKey(X1,X2)) != c_Public_OshrK(X3),
    c_0_10389,
    [final] ).

cnf(c_0_13327,plain,
    c_Public_OshrK(X1) != c_Message_OinvKey(c_Public_OpublicKey(X2,X3)),
    c_0_10390,
    [final] ).

cnf(c_0_13328,plain,
    ( X1 = X2
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_10391,
    [final] ).

cnf(c_0_13329,plain,
    ( X1 = X2
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_10392,
    [final] ).

cnf(c_0_13330,plain,
    ( X1 = X2
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_10393,
    [final] ).

cnf(c_0_13331,plain,
    ( X1 = X2
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_10394,
    [final] ).

cnf(c_0_13332,plain,
    ( X1 = X2
    | c_uminus(X1,X3) != c_uminus(X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_10395,
    [final] ).

cnf(c_0_13333,plain,
    ( X1 = X2
    | c_NatArith_Oof__nat(X1,X3) != c_NatArith_Oof__nat(X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_10396,
    [final] ).

cnf(c_0_13334,plain,
    ( X1 = X2
    | c_IntDef_Oof__int(X1,X3) != c_IntDef_Oof__int(X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_10397,
    [final] ).

cnf(c_0_13335,plain,
    ( c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10398,
    [final] ).

cnf(c_0_13336,plain,
    c_union(X1,c_UNIV,X2) = c_UNIV,
    c_0_10399,
    [final] ).

cnf(c_0_13337,plain,
    c_union(c_UNIV,X1,X2) = c_UNIV,
    c_0_10400,
    [final] ).

cnf(c_0_13338,plain,
    c_inter(X1,c_emptyset,X2) = c_emptyset,
    c_0_10401,
    [final] ).

cnf(c_0_13339,plain,
    c_inter(c_emptyset,X1,X2) = c_emptyset,
    c_0_10402,
    [final] ).

cnf(c_0_13340,plain,
    c_Relation_Oconverse(c_Relation_OId,X1,X1) = c_Relation_OId,
    c_0_10403,
    [final] ).

cnf(c_0_13341,plain,
    c_Relation_ORange(c_emptyset,X1,X2) = c_emptyset,
    c_0_10404,
    [final] ).

cnf(c_0_13342,plain,
    c_Relation_ORange(c_Relation_OId,X1,X1) = c_UNIV,
    c_0_10405,
    [final] ).

cnf(c_0_13343,plain,
    c_Relation_ODomain(c_emptyset,X1,X2) = c_emptyset,
    c_0_10406,
    [final] ).

cnf(c_0_13344,plain,
    c_Relation_ODomain(c_Relation_OId,X1,X1) = c_UNIV,
    c_0_10407,
    [final] ).

cnf(c_0_13345,plain,
    ( X1 = c_0
    | c_less(c_0,X1,tc_nat) ),
    c_0_10408,
    [final] ).

cnf(c_0_13346,plain,
    c_minus(X1,X1,tc_nat) = c_0,
    c_0_10409,
    [final] ).

cnf(c_0_13347,plain,
    c_List_Otake(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    c_0_10410,
    [final] ).

cnf(c_0_13348,plain,
    c_List_Otake(c_0,X1,X2) = c_List_Olist_ONil,
    c_0_10411,
    [final] ).

cnf(c_0_13349,plain,
    c_List_Osublist(c_List_Olist_ONil,X1,X2) = c_List_Olist_ONil,
    c_0_10412,
    [final] ).

cnf(c_0_13350,plain,
    c_List_Osublist(X1,c_emptyset,X2) = c_List_Olist_ONil,
    c_0_10413,
    [final] ).

cnf(c_0_13351,plain,
    c_List_Orotate(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    c_0_10414,
    [final] ).

cnf(c_0_13352,plain,
    c_List_Oreplicate(c_0,X1,X2) = c_List_Olist_ONil,
    c_0_10415,
    [final] ).

cnf(c_0_13353,plain,
    c_List_Oremove1(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    c_0_10416,
    [final] ).

cnf(c_0_13354,plain,
    c_List_Olist__inter(c_List_Olist_ONil,X1,X2) = c_List_Olist_ONil,
    c_0_10417,
    [final] ).

cnf(c_0_13355,plain,
    c_List_Olexn(X1,c_0,X2) = c_emptyset,
    c_0_10418,
    [final] ).

cnf(c_0_13356,plain,
    c_List_Odrop(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    c_0_10419,
    [final] ).

cnf(c_0_13357,plain,
    c_Divides_Oop_Amod(X1,X1,tc_IntDef_Oint) = c_0,
    c_0_10420,
    [final] ).

cnf(c_0_13358,plain,
    c_Divides_Oop_Advd(X1,X1,tc_IntDef_Oint),
    c_0_10421,
    [final] ).

cnf(c_0_13359,plain,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    c_0_10422,
    [final] ).

cnf(c_0_13360,plain,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    c_0_10423,
    [final] ).

cnf(c_0_13361,plain,
    c_Divides_Oop_Amod(X1,X1,tc_nat) = c_0,
    c_0_10424,
    [final] ).

cnf(c_0_13362,plain,
    c_Divides_Oop_Advd(X1,X1,tc_nat),
    c_0_10425,
    [final] ).

cnf(c_0_13363,plain,
    c_in(X1,c_UNIV,X2),
    c_0_10426,
    [final] ).

cnf(c_0_13364,plain,
    c_minus(X1,c_0,tc_nat) = X1,
    c_0_10427,
    [final] ).

cnf(c_0_13365,plain,
    c_plus(c_0,X1,tc_nat) = X1,
    c_0_10428,
    [final] ).

cnf(c_0_13366,plain,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    c_0_10429,
    [final] ).

cnf(c_0_13367,plain,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    c_0_10430,
    [final] ).

cnf(c_0_13368,plain,
    c_Orderings_Omax(X1,c_0,tc_nat) = X1,
    c_0_10431,
    [final] ).

cnf(c_0_13369,plain,
    c_Orderings_Omax(c_0,X1,tc_nat) = X1,
    c_0_10432,
    [final] ).

cnf(c_0_13370,plain,
    c_plus(X1,c_0,tc_nat) = X1,
    c_0_10433,
    [final] ).

cnf(c_0_13371,plain,
    c_div(X1,c_1,tc_IntDef_Oint) = X1,
    c_0_10434,
    [final] ).

cnf(c_0_13372,plain,
    c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
    c_0_10435,
    [final] ).

cnf(c_0_13373,plain,
    c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1,
    c_0_10436,
    [final] ).

cnf(c_0_13374,plain,
    c_union(c_emptyset,c_emptyset,X1) = c_emptyset,
    c_0_10437,
    [final] ).

cnf(c_0_13375,plain,
    c_inter(c_UNIV,c_UNIV,X1) = c_UNIV,
    c_0_10438,
    [final] ).

cnf(c_0_13376,plain,
    c_Nat_Opower(X1,c_0,tc_nat) = c_1,
    c_0_10439,
    [final] ).

cnf(c_0_13377,plain,
    c_times(c_0,X1,tc_nat) = c_0,
    c_0_10440,
    [final] ).

cnf(c_0_13378,plain,
    c_times(X1,c_0,tc_nat) = c_0,
    c_0_10441,
    [final] ).

cnf(c_0_13379,plain,
    c_Orderings_Omin(X1,c_0,tc_nat) = c_0,
    c_0_10442,
    [final] ).

cnf(c_0_13380,plain,
    c_Orderings_Omin(c_0,X1,tc_nat) = c_0,
    c_0_10443,
    [final] ).

cnf(c_0_13381,plain,
    c_minus(c_0,X1,tc_nat) = c_0,
    c_0_10444,
    [final] ).

cnf(c_0_13382,plain,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10445,
    [final] ).

cnf(c_0_13383,plain,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10446,
    [final] ).

cnf(c_0_13384,plain,
    c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint) = c_0,
    c_0_10447,
    [final] ).

cnf(c_0_13385,plain,
    c_Divides_Oop_Amod(X1,c_1,tc_IntDef_Oint) = c_0,
    c_0_10448,
    [final] ).

cnf(c_0_13386,plain,
    c_div(c_0,X1,tc_IntDef_Oint) = c_0,
    c_0_10449,
    [final] ).

cnf(c_0_13387,plain,
    c_Nat_Opower(X1,c_0,tc_IntDef_Oint) = c_1,
    c_0_10450,
    [final] ).

cnf(c_0_13388,plain,
    c_Divides_Oop_Amod(c_0,X1,tc_nat) = c_0,
    c_0_10451,
    [final] ).

cnf(c_0_13389,plain,
    c_div(c_0,X1,tc_nat) = c_0,
    c_0_10452,
    [final] ).

cnf(c_0_13390,plain,
    c_div(X1,c_0,tc_nat) = c_0,
    c_0_10453,
    [final] ).

cnf(c_0_13391,plain,
    c_lessequals(c_0,X1,tc_nat),
    c_0_10454,
    [final] ).

cnf(c_0_13392,plain,
    c_Divides_Oop_Advd(c_1,X1,tc_IntDef_Oint),
    c_0_10455,
    [final] ).

cnf(c_0_13393,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_IntDef_Oint),
    c_0_10456,
    [final] ).

cnf(c_0_13394,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_nat),
    c_0_10457,
    [final] ).

cnf(c_0_13395,plain,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10458,
    [final] ).

cnf(c_0_13396,plain,
    ( c_uminus(c_uminus(c_1,X1),X1) = c_1
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    c_0_10459,
    [final] ).

cnf(c_0_13397,plain,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10460,
    [final] ).

cnf(c_0_13398,plain,
    ( X1 = c_uminus(c_1,X2)
    | c_uminus(X1,X2) != c_1
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    c_0_10461,
    [final] ).

cnf(c_0_13399,plain,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    c_0_10462,
    [final] ).

cnf(c_0_13400,plain,
    ( ~ c_Parity_Oeven(c_Suc(X1),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    c_0_10463,
    [final] ).

cnf(c_0_13401,plain,
    c_less(c_0,c_1,tc_nat),
    c_0_10464,
    [final] ).

cnf(c_0_13402,plain,
    c_lessequals(c_0,c_0,tc_nat),
    c_0_10465,
    [final] ).

cnf(c_0_13403,plain,
    c_plus(c_0,c_0,tc_nat) = c_0,
    c_0_10466,
    [final] ).

cnf(c_0_13404,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    c_0_10467,
    [final] ).

cnf(c_0_13405,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    c_0_10468,
    [final] ).

cnf(c_0_13406,plain,
    c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,X1)) != c_Public_OshrK(X2),
    c_0_10469,
    [final] ).

cnf(c_0_13407,plain,
    ( c_uminus(c_uminus(X1,X2),X2) = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10470,
    [final] ).

cnf(c_0_13408,plain,
    ( X1 = X2
    | c_Public_OpublicKey(X3,X1) != c_Public_OpublicKey(X4,X2) ),
    c_0_10471,
    [final] ).

cnf(c_0_13409,plain,
    ( X1 = X2
    | c_Public_OpublicKey(X1,X3) != c_Public_OpublicKey(X2,X4) ),
    c_0_10472,
    [final] ).

cnf(c_0_13410,plain,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X3,X1) != c_Message_OHPair(X4,X2) ),
    c_0_10473,
    [final] ).

cnf(c_0_13411,plain,
    ( X1 = X2
    | c_Message_OHPair(X3,X2) != c_Message_Omsg_OMPair(X4,X1) ),
    c_0_10474,
    [final] ).

cnf(c_0_13412,plain,
    ( X1 = X2
    | c_Message_OHPair(X3,X1) != c_Message_OHPair(X4,X2) ),
    c_0_10475,
    [final] ).

cnf(c_0_13413,plain,
    ( X1 = X2
    | c_Message_OHPair(X1,X3) != c_Message_OHPair(X2,X4) ),
    c_0_10476,
    [final] ).

cnf(c_0_13414,plain,
    ( X1 = X2
    | c_Event_Oevent_ONotes(X3,X1) != c_Event_Oevent_ONotes(X4,X2) ),
    c_0_10477,
    [final] ).

cnf(c_0_13415,plain,
    ( X1 = X2
    | c_Event_Oevent_ONotes(X1,X3) != c_Event_Oevent_ONotes(X2,X4) ),
    c_0_10478,
    [final] ).

cnf(c_0_13416,plain,
    ( X1 = X2
    | c_Event_Oevent_OGets(X3,X1) != c_Event_Oevent_OGets(X4,X2) ),
    c_0_10479,
    [final] ).

cnf(c_0_13417,plain,
    ( X1 = X2
    | c_Event_Oevent_OGets(X1,X3) != c_Event_Oevent_OGets(X2,X4) ),
    c_0_10480,
    [final] ).

cnf(c_0_13418,plain,
    ( X1 = X2
    | c_Message_Omsg_OCrypt(X3,X1) != c_Message_Omsg_OCrypt(X4,X2) ),
    c_0_10481,
    [final] ).

cnf(c_0_13419,plain,
    ( X1 = X2
    | c_Message_Omsg_OCrypt(X1,X3) != c_Message_Omsg_OCrypt(X2,X4) ),
    c_0_10482,
    [final] ).

cnf(c_0_13420,plain,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X3,X1) != c_Message_Omsg_OMPair(X4,X2) ),
    c_0_10483,
    [final] ).

cnf(c_0_13421,plain,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X1,X3) != c_Message_Omsg_OMPair(X2,X4) ),
    c_0_10484,
    [final] ).

cnf(c_0_13422,plain,
    ( X1 = X2
    | c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
    c_0_10485,
    [final] ).

cnf(c_0_13423,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2) ),
    c_0_10486,
    [final] ).

cnf(c_0_13424,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4) ),
    c_0_10487,
    [final] ).

cnf(c_0_13425,plain,
    ( X1 = X2
    | c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3) ),
    c_0_10488,
    [final] ).

cnf(c_0_13426,plain,
    c_Nat_Osize(c_Datatype_Ooption_OSome(X1,X2),tc_Datatype_Ooption(X2)) = c_0,
    c_0_10489,
    [final] ).

cnf(c_0_13427,plain,
    c_Numeral_Obin__succ(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X1),c_Numeral_Obit_OB0),
    c_0_10490,
    [final] ).

cnf(c_0_13428,plain,
    c_Numeral_Obin__pred(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X1),c_Numeral_Obit_OB1),
    c_0_10491,
    [final] ).

cnf(c_0_13429,plain,
    c_Numeral_Obin__minus(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X1),c_Numeral_Obit_OB0),
    c_0_10492,
    [final] ).

cnf(c_0_13430,plain,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    c_0_10493,
    [final] ).

cnf(c_0_13431,plain,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    c_0_10494,
    [final] ).

cnf(c_0_13432,plain,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    c_0_10495,
    [final] ).

cnf(c_0_13433,plain,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10496,
    [final] ).

cnf(c_0_13434,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OCrypt(X3,X4),
    c_0_10497,
    [final] ).

cnf(c_0_13435,plain,
    c_Message_Omsg_OCrypt(X1,X2) != c_Message_OHPair(X3,X4),
    c_0_10498,
    [final] ).

cnf(c_0_13436,plain,
    c_Event_Oevent_ONotes(X1,X2) != c_Event_Oevent_OGets(X3,X4),
    c_0_10499,
    [final] ).

cnf(c_0_13437,plain,
    c_Event_Oevent_OGets(X1,X2) != c_Event_Oevent_ONotes(X3,X4),
    c_0_10500,
    [final] ).

cnf(c_0_13438,plain,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    c_0_10501,
    [final] ).

cnf(c_0_13439,plain,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    c_0_10502,
    [final] ).

cnf(c_0_13440,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) = c_1
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10503,
    [final] ).

cnf(c_0_13441,plain,
    ( c_IntDef_Oof__int(c_IntDef_Oint(X1),X2) = c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    c_0_10504,
    [final] ).

cnf(c_0_13442,plain,
    c_Union(c_Pow(X1,X2),X2) = X1,
    c_0_10505,
    [final] ).

cnf(c_0_13443,plain,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    c_0_10506,
    [final] ).

cnf(c_0_13444,plain,
    c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X2),X2) = X1,
    c_0_10507,
    [final] ).

cnf(c_0_13445,plain,
    c_List_Odistinct(c_List_Oremdups(X1,X2),X2),
    c_0_10508,
    [final] ).

cnf(c_0_13446,plain,
    c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat) = c_Suc(X1),
    c_0_10509,
    [final] ).

cnf(c_0_13447,plain,
    c_Numeral_Obin__succ(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(X1,c_Numeral_Obit_OB1),
    c_0_10510,
    [final] ).

cnf(c_0_13448,plain,
    c_Numeral_Obin__pred(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(X1,c_Numeral_Obit_OB0),
    c_0_10511,
    [final] ).

cnf(c_0_13449,plain,
    c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X1,tc_nat),
    c_0_10512,
    [final] ).

cnf(c_0_13450,plain,
    c_IntDef_Onat(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint)) = c_0,
    c_0_10513,
    [final] ).

cnf(c_0_13451,plain,
    c_Nat_Osize(c_Event_Oevent_ONotes(X1,X2),tc_Event_Oevent) = c_0,
    c_0_10514,
    [final] ).

cnf(c_0_13452,plain,
    c_Nat_Osize(c_Event_Oevent_OGets(X1,X2),tc_Event_Oevent) = c_0,
    c_0_10515,
    [final] ).

cnf(c_0_13453,plain,
    c_List_Odistinct(c_List_Oupt(X1,X2),tc_nat),
    c_0_10516,
    [final] ).

cnf(c_0_13454,plain,
    c_Nat_Osize(c_List_Ochar_OChar(X1,X2),tc_List_Ochar) = c_0,
    c_0_10517,
    [final] ).

cnf(c_0_13455,plain,
    ( X1 = c_0
    | c_HOL_Oinverse(X1,X2) != c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10518,
    [final] ).

cnf(c_0_13456,plain,
    ( X1 = c_1
    | c_HOL_Oinverse(X1,X2) != c_1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    c_0_10519,
    [final] ).

cnf(c_0_13457,plain,
    ( X1 = c_0
    | c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) != c_IntDef_Oint(X1) ),
    c_0_10520,
    [final] ).

cnf(c_0_13458,plain,
    ( X1 = c_0
    | c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint) != c_IntDef_Oint(X2) ),
    c_0_10521,
    [final] ).

cnf(c_0_13459,plain,
    ( c_Union(X1,X2) = c_emptyset
    | c_Main_Oempty__Union__conv__1(X1,X2) != c_emptyset ),
    c_0_10522,
    [final] ).

cnf(c_0_13460,plain,
    ( c_Union(X1,X2) = c_emptyset
    | c_Main_OUnion__empty__conv__1(X1,X2) != c_emptyset ),
    c_0_10523,
    [final] ).

cnf(c_0_13461,plain,
    ( c_Inter(X1,X2) = c_UNIV
    | c_Main_OInter__UNIV__conv__2__1(X1,X2) != c_UNIV ),
    c_0_10524,
    [final] ).

cnf(c_0_13462,plain,
    ( c_Inter(X1,X2) = c_UNIV
    | c_Main_OInter__UNIV__conv__1__1(X1,X2) != c_UNIV ),
    c_0_10525,
    [final] ).

cnf(c_0_13463,plain,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_Main_Oconcat__eq__Nil__conv__1(X1,X2) != c_List_Olist_ONil ),
    c_0_10526,
    [final] ).

cnf(c_0_13464,plain,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_Main_ONil__eq__concat__conv__1(X1,X2) != c_List_Olist_ONil ),
    c_0_10527,
    [final] ).

cnf(c_0_13465,plain,
    c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
    c_0_10528,
    [final] ).

cnf(c_0_13466,plain,
    ( X1 = c_List_Olist_ONil
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0 ),
    c_0_10529,
    [final] ).

cnf(c_0_13467,plain,
    c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1,
    c_0_10530,
    [final] ).

cnf(c_0_13468,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10531,
    [final] ).

cnf(c_0_13469,plain,
    ( c_Parity_Oeven(c_Suc(X1),tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    c_0_10532,
    [final] ).

cnf(c_0_13470,plain,
    ( X1 = c_0
    | c_uminus(X1,X2) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10533,
    [final] ).

cnf(c_0_13471,plain,
    ( c_0 = X1
    | c_uminus(X1,X2) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_10534,
    [final] ).

cnf(c_0_13472,plain,
    ( X1 = c_0
    | c_HOL_Oabs(X1,X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10535,
    [final] ).

cnf(c_0_13473,plain,
    ( X1 = c_0
    | c_HOL_Oabs(X1,X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    c_0_10536,
    [final] ).

cnf(c_0_13474,plain,
    ( X1 = c_0
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_10537,
    [final] ).

cnf(c_0_13475,plain,
    ( c_0 = X1
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_10538,
    [final] ).

cnf(c_0_13476,plain,
    ( X1 = c_0
    | c_IntDef_Oof__int(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_10539,
    [final] ).

cnf(c_0_13477,plain,
    ( c_0 = X1
    | c_IntDef_Oof__int(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_10540,
    [final] ).

cnf(c_0_13478,plain,
    class_Nat_Opower(tc_fun(X1,X2)),
    c_0_10541,
    [final] ).

cnf(c_0_13479,plain,
    ~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
    c_0_10542,
    [final] ).

cnf(c_0_13480,plain,
    c_Public_OpublicKey(X1,X2) != c_Public_OshrK(X3),
    c_0_10543,
    [final] ).

cnf(c_0_13481,plain,
    c_Public_OshrK(X1) != c_Public_OpublicKey(X2,X3),
    c_0_10544,
    [final] ).

cnf(c_0_13482,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_ONumber(X3),
    c_0_10545,
    [final] ).

cnf(c_0_13483,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_ONonce(X3),
    c_0_10546,
    [final] ).

cnf(c_0_13484,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OKey(X3),
    c_0_10547,
    [final] ).

cnf(c_0_13485,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OHash(X3),
    c_0_10548,
    [final] ).

cnf(c_0_13486,plain,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OAgent(X3),
    c_0_10549,
    [final] ).

cnf(c_0_13487,plain,
    c_Message_Omsg_OHash(X1) != c_Message_OHPair(X2,X3),
    c_0_10550,
    [final] ).

cnf(c_0_13488,plain,
    c_Message_Omsg_OKey(X1) != c_Message_OHPair(X2,X3),
    c_0_10551,
    [final] ).

cnf(c_0_13489,plain,
    c_Message_Omsg_ONumber(X1) != c_Message_OHPair(X2,X3),
    c_0_10552,
    [final] ).

cnf(c_0_13490,plain,
    c_Message_Omsg_ONonce(X1) != c_Message_OHPair(X2,X3),
    c_0_10553,
    [final] ).

cnf(c_0_13491,plain,
    c_Message_Omsg_OAgent(X1) != c_Message_OHPair(X2,X3),
    c_0_10554,
    [final] ).

cnf(c_0_13492,plain,
    ( ~ c_IntDef_Oneg(c_1,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10555,
    [final] ).

cnf(c_0_13493,plain,
    ( ~ c_IntDef_Oneg(c_0,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10556,
    [final] ).

cnf(c_0_13494,plain,
    ( ~ c_IntDef_Oiszero(c_1,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_10557,
    [final] ).

cnf(c_0_13495,plain,
    ( c_HOL_Oinverse(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_10558,
    [final] ).

cnf(c_0_13496,plain,
    ( c_HOL_Oinverse(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_10559,
    [final] ).

cnf(c_0_13497,plain,
    c_Binomial_Obinomial(c_Suc(X1),X1) = c_Suc(X1),
    c_0_10560,
    [final] ).

cnf(c_0_13498,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    c_0_10561,
    [final] ).

cnf(c_0_13499,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    c_0_10562,
    [final] ).

cnf(c_0_13500,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orotate1(X1,X2) != c_List_Olist_ONil ),
    c_0_10563,
    [final] ).

cnf(c_0_13501,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    c_0_10564,
    [final] ).

cnf(c_0_13502,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil ),
    c_0_10565,
    [final] ).

cnf(c_0_13503,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil ),
    c_0_10566,
    [final] ).

cnf(c_0_13504,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    c_0_10567,
    [final] ).

cnf(c_0_13505,plain,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Oo2s(X1,X2) != c_emptyset ),
    c_0_10568,
    [final] ).

cnf(c_0_13506,plain,
    c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X1))) = c_emptyset,
    c_0_10569,
    [final] ).

cnf(c_0_13507,plain,
    c_HOL_Oabs(c_IntDef_Oint(X1),tc_IntDef_Oint) = c_IntDef_Oint(X1),
    c_0_10570,
    [final] ).

cnf(c_0_13508,plain,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    c_0_10571,
    [final] ).

cnf(c_0_13509,plain,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    c_0_10572,
    [final] ).

cnf(c_0_13510,plain,
    ( c_HOL_Oabs(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10573,
    [final] ).

cnf(c_0_13511,plain,
    ( c_OrderedGroup_Opprt(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_10574,
    [final] ).

cnf(c_0_13512,plain,
    ( c_OrderedGroup_Onprt(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_10575,
    [final] ).

cnf(c_0_13513,plain,
    ( c_uminus(c_0,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_10576,
    [final] ).

cnf(c_0_13514,plain,
    ( c_uminus(c_0,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_10577,
    [final] ).

cnf(c_0_13515,plain,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_10578,
    [final] ).

cnf(c_0_13516,plain,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_10579,
    [final] ).

cnf(c_0_13517,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OPls,X1) = c_0
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_10580,
    [final] ).

cnf(c_0_13518,plain,
    ( c_NatArith_Oof__nat(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10581,
    [final] ).

cnf(c_0_13519,plain,
    ( c_NatArith_Oof__nat(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_10582,
    [final] ).

cnf(c_0_13520,plain,
    ( c_NatArith_Oof__nat(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10583,
    [final] ).

cnf(c_0_13521,plain,
    ( c_IntDef_Oof__int(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10584,
    [final] ).

cnf(c_0_13522,plain,
    ( c_IntDef_Oof__int(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_10585,
    [final] ).

cnf(c_0_13523,plain,
    ( c_IntDef_Oof__int(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10586,
    [final] ).

cnf(c_0_13524,plain,
    c_Nat_Osize(c_Message_Omsg_OKey(X1),tc_Message_Omsg) = c_0,
    c_0_10587,
    [final] ).

cnf(c_0_13525,plain,
    c_Nat_Osize(c_Message_Omsg_ONonce(X1),tc_Message_Omsg) = c_0,
    c_0_10588,
    [final] ).

cnf(c_0_13526,plain,
    c_Nat_Osize(c_Message_Omsg_ONumber(X1),tc_Message_Omsg) = c_0,
    c_0_10589,
    [final] ).

cnf(c_0_13527,plain,
    c_Nat_Osize(c_Message_Omsg_OAgent(X1),tc_Message_Omsg) = c_0,
    c_0_10590,
    [final] ).

cnf(c_0_13528,plain,
    c_Nat_Osize(c_Message_Oagent_OFriend(X1),tc_Message_Oagent) = c_0,
    c_0_10591,
    [final] ).

cnf(c_0_13529,plain,
    c_uminus(c_emptyset,tc_set(X1)) = c_UNIV,
    c_0_10592,
    [final] ).

cnf(c_0_13530,plain,
    c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
    c_0_10593,
    [final] ).

cnf(c_0_13531,plain,
    c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) = c_0,
    c_0_10594,
    [final] ).

cnf(c_0_13532,plain,
    c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) = c_0,
    c_0_10595,
    [final] ).

cnf(c_0_13533,plain,
    c_Binomial_Obinomial(c_0,c_Suc(X1)) = c_0,
    c_0_10596,
    [final] ).

cnf(c_0_13534,plain,
    c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
    c_0_10597,
    [final] ).

cnf(c_0_13535,plain,
    c_Binomial_Obinomial(X1,c_Suc(c_0)) = X1,
    c_0_10598,
    [final] ).

cnf(c_0_13536,plain,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    c_0_10599,
    [final] ).

cnf(c_0_13537,plain,
    ( class_Finite__Set_Ofinite(tc_set(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    c_0_10600,
    [final] ).

cnf(c_0_13538,plain,
    ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    c_0_10601,
    [final] ).

cnf(c_0_13539,plain,
    c_Event_Oknows(X1,c_List_Olist_ONil) = c_Event_OinitState(X1),
    c_0_10602,
    [final] ).

cnf(c_0_13540,plain,
    c_Numeral_Obin__mult(c_Numeral_OMin,X1) = c_Numeral_Obin__minus(X1),
    c_0_10603,
    [final] ).

cnf(c_0_13541,plain,
    c_Numeral_Obin__add(X1,c_Numeral_OMin) = c_Numeral_Obin__pred(X1),
    c_0_10604,
    [final] ).

cnf(c_0_13542,plain,
    c_Numeral_Obin__add(c_Numeral_OMin,X1) = c_Numeral_Obin__pred(X1),
    c_0_10605,
    [final] ).

cnf(c_0_13543,plain,
    ( X1 = X2
    | c_Public_OshrK(X1) != c_Public_OshrK(X2) ),
    c_0_10606,
    [final] ).

cnf(c_0_13544,plain,
    ( X1 = X2
    | c_Message_Omsg_OHash(X1) != c_Message_Omsg_OHash(X2) ),
    c_0_10607,
    [final] ).

cnf(c_0_13545,plain,
    ( X1 = X2
    | c_Message_Omsg_OKey(X1) != c_Message_Omsg_OKey(X2) ),
    c_0_10608,
    [final] ).

cnf(c_0_13546,plain,
    ( X1 = X2
    | c_Message_Omsg_ONonce(X1) != c_Message_Omsg_ONonce(X2) ),
    c_0_10609,
    [final] ).

cnf(c_0_13547,plain,
    ( X1 = X2
    | c_Message_Omsg_ONumber(X1) != c_Message_Omsg_ONumber(X2) ),
    c_0_10610,
    [final] ).

cnf(c_0_13548,plain,
    ( X1 = X2
    | c_Message_Omsg_OAgent(X1) != c_Message_Omsg_OAgent(X2) ),
    c_0_10611,
    [final] ).

cnf(c_0_13549,plain,
    ( X1 = X2
    | c_Message_OinvKey(X1) != c_Message_OinvKey(X2) ),
    c_0_10612,
    [final] ).

cnf(c_0_13550,plain,
    ( X1 = X2
    | c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OFriend(X2) ),
    c_0_10613,
    [final] ).

cnf(c_0_13551,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_10614,
    [final] ).

cnf(c_0_13552,plain,
    ( X1 = X2
    | c_IntDef_Oint(X1) != c_IntDef_Oint(X2) ),
    c_0_10615,
    [final] ).

cnf(c_0_13553,plain,
    c_Fun_Oid(X1,X2) = X1,
    c_0_10616,
    [final] ).

cnf(c_0_13554,plain,
    c_Message_OinvKey(c_Public_OshrK(X1)) = c_Public_OshrK(X1),
    c_0_10617,
    [final] ).

cnf(c_0_13555,plain,
    c_Message_Oparts(c_Message_Oparts(X1)) = c_Message_Oparts(X1),
    c_0_10618,
    [final] ).

cnf(c_0_13556,plain,
    c_Message_Oparts(c_Message_Oanalz(X1)) = c_Message_Oparts(X1),
    c_0_10619,
    [final] ).

cnf(c_0_13557,plain,
    c_Message_Oanalz(c_Message_Oparts(X1)) = c_Message_Oparts(X1),
    c_0_10620,
    [final] ).

cnf(c_0_13558,plain,
    c_Message_Oanalz(c_Message_Oanalz(X1)) = c_Message_Oanalz(X1),
    c_0_10621,
    [final] ).

cnf(c_0_13559,plain,
    c_Binomial_Obinomial(X1,X1) = c_1,
    c_0_10622,
    [final] ).

cnf(c_0_13560,plain,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
    c_0_10623,
    [final] ).

cnf(c_0_13561,plain,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OMin),
    c_0_10624,
    [final] ).

cnf(c_0_13562,plain,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
    c_0_10625,
    [final] ).

cnf(c_0_13563,plain,
    c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1,
    c_0_10626,
    [final] ).

cnf(c_0_13564,plain,
    c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1,
    c_0_10627,
    [final] ).

cnf(c_0_13565,plain,
    c_NatArith_Oof__nat(X1,tc_nat) = X1,
    c_0_10628,
    [final] ).

cnf(c_0_13566,plain,
    c_Transitive__Closure_Otrancl(c_emptyset,X1) = c_emptyset,
    c_0_10629,
    [final] ).

cnf(c_0_13567,plain,
    c_Transitive__Closure_Ortrancl(c_emptyset,X1) = c_Relation_OId,
    c_0_10630,
    [final] ).

cnf(c_0_13568,plain,
    c_Union(c_emptyset,X1) = c_emptyset,
    c_0_10631,
    [final] ).

cnf(c_0_13569,plain,
    c_Union(c_UNIV,X1) = c_UNIV,
    c_0_10632,
    [final] ).

cnf(c_0_13570,plain,
    c_Pow(c_UNIV,X1) = c_UNIV,
    c_0_10633,
    [final] ).

cnf(c_0_13571,plain,
    c_Inter(c_emptyset,X1) = c_UNIV,
    c_0_10634,
    [final] ).

cnf(c_0_13572,plain,
    c_Inter(c_UNIV,X1) = c_emptyset,
    c_0_10635,
    [final] ).

cnf(c_0_13573,plain,
    c_Relation_Odiag(c_emptyset,X1) = c_emptyset,
    c_0_10636,
    [final] ).

cnf(c_0_13574,plain,
    c_Numeral_Obin__mult(c_Numeral_OPls,X1) = c_Numeral_OPls,
    c_0_10637,
    [final] ).

cnf(c_0_13575,plain,
    c_List_Oupt(X1,c_0) = c_List_Olist_ONil,
    c_0_10638,
    [final] ).

cnf(c_0_13576,plain,
    c_List_Otl(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10639,
    [final] ).

cnf(c_0_13577,plain,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    c_0_10640,
    [final] ).

cnf(c_0_13578,plain,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    c_0_10641,
    [final] ).

cnf(c_0_13579,plain,
    c_List_Orotate1(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10642,
    [final] ).

cnf(c_0_13580,plain,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10643,
    [final] ).

cnf(c_0_13581,plain,
    c_List_Oremdups(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10644,
    [final] ).

cnf(c_0_13582,plain,
    c_List_Oremdups(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10645,
    [final] ).

cnf(c_0_13583,plain,
    c_List_Onull(c_List_Olist_ONil,X1),
    c_0_10646,
    [final] ).

cnf(c_0_13584,plain,
    c_List_Olists(c_UNIV,X1) = c_UNIV,
    c_0_10647,
    [final] ).

cnf(c_0_13585,plain,
    c_List_Odistinct(c_List_Olist_ONil,X1),
    c_0_10648,
    [final] ).

cnf(c_0_13586,plain,
    c_List_Oconcat(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10649,
    [final] ).

cnf(c_0_13587,plain,
    c_List_Obutlast(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10650,
    [final] ).

cnf(c_0_13588,plain,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_10651,
    [final] ).

cnf(c_0_13589,plain,
    c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
    c_0_10652,
    [final] ).

cnf(c_0_13590,plain,
    c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) = c_emptyset,
    c_0_10653,
    [final] ).

cnf(c_0_13591,plain,
    c_Binomial_Obinomial(X1,c_0) = c_1,
    c_0_10654,
    [final] ).

cnf(c_0_13592,plain,
    c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    c_0_10655,
    [final] ).

cnf(c_0_13593,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_10656,
    [final] ).

cnf(c_0_13594,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_10657,
    [final] ).

cnf(c_0_13595,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_10658,
    [final] ).

cnf(c_0_13596,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_10659,
    [final] ).

cnf(c_0_13597,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_10660,
    [final] ).

cnf(c_0_13598,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_10661,
    [final] ).

cnf(c_0_13599,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10662,
    [final] ).

cnf(c_0_13600,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10663,
    [final] ).

cnf(c_0_13601,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10664,
    [final] ).

cnf(c_0_13602,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10665,
    [final] ).

cnf(c_0_13603,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10666,
    [final] ).

cnf(c_0_13604,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10667,
    [final] ).

cnf(c_0_13605,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10668,
    [final] ).

cnf(c_0_13606,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10669,
    [final] ).

cnf(c_0_13607,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10670,
    [final] ).

cnf(c_0_13608,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10671,
    [final] ).

cnf(c_0_13609,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10672,
    [final] ).

cnf(c_0_13610,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10673,
    [final] ).

cnf(c_0_13611,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10674,
    [final] ).

cnf(c_0_13612,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10675,
    [final] ).

cnf(c_0_13613,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10676,
    [final] ).

cnf(c_0_13614,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_10677,
    [final] ).

cnf(c_0_13615,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10678,
    [final] ).

cnf(c_0_13616,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10679,
    [final] ).

cnf(c_0_13617,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10680,
    [final] ).

cnf(c_0_13618,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10681,
    [final] ).

cnf(c_0_13619,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10682,
    [final] ).

cnf(c_0_13620,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10683,
    [final] ).

cnf(c_0_13621,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10684,
    [final] ).

cnf(c_0_13622,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10685,
    [final] ).

cnf(c_0_13623,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10686,
    [final] ).

cnf(c_0_13624,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10687,
    [final] ).

cnf(c_0_13625,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10688,
    [final] ).

cnf(c_0_13626,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_10689,
    [final] ).

cnf(c_0_13627,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10690,
    [final] ).

cnf(c_0_13628,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10691,
    [final] ).

cnf(c_0_13629,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10692,
    [final] ).

cnf(c_0_13630,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10693,
    [final] ).

cnf(c_0_13631,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10694,
    [final] ).

cnf(c_0_13632,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10695,
    [final] ).

cnf(c_0_13633,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10696,
    [final] ).

cnf(c_0_13634,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10697,
    [final] ).

cnf(c_0_13635,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10698,
    [final] ).

cnf(c_0_13636,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10699,
    [final] ).

cnf(c_0_13637,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_10700,
    [final] ).

cnf(c_0_13638,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10701,
    [final] ).

cnf(c_0_13639,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10702,
    [final] ).

cnf(c_0_13640,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10703,
    [final] ).

cnf(c_0_13641,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10704,
    [final] ).

cnf(c_0_13642,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10705,
    [final] ).

cnf(c_0_13643,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10706,
    [final] ).

cnf(c_0_13644,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10707,
    [final] ).

cnf(c_0_13645,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_10708,
    [final] ).

cnf(c_0_13646,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_10709,
    [final] ).

cnf(c_0_13647,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_10710,
    [final] ).

cnf(c_0_13648,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_10711,
    [final] ).

cnf(c_0_13649,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_10712,
    [final] ).

cnf(c_0_13650,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_10713,
    [final] ).

cnf(c_0_13651,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10714,
    [final] ).

cnf(c_0_13652,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10715,
    [final] ).

cnf(c_0_13653,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10716,
    [final] ).

cnf(c_0_13654,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10717,
    [final] ).

cnf(c_0_13655,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10718,
    [final] ).

cnf(c_0_13656,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10719,
    [final] ).

cnf(c_0_13657,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10720,
    [final] ).

cnf(c_0_13658,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10721,
    [final] ).

cnf(c_0_13659,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10722,
    [final] ).

cnf(c_0_13660,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10723,
    [final] ).

cnf(c_0_13661,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10724,
    [final] ).

cnf(c_0_13662,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10725,
    [final] ).

cnf(c_0_13663,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10726,
    [final] ).

cnf(c_0_13664,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10727,
    [final] ).

cnf(c_0_13665,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10728,
    [final] ).

cnf(c_0_13666,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10729,
    [final] ).

cnf(c_0_13667,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10730,
    [final] ).

cnf(c_0_13668,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10731,
    [final] ).

cnf(c_0_13669,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10732,
    [final] ).

cnf(c_0_13670,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_10733,
    [final] ).

cnf(c_0_13671,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10734,
    [final] ).

cnf(c_0_13672,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10735,
    [final] ).

cnf(c_0_13673,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10736,
    [final] ).

cnf(c_0_13674,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10737,
    [final] ).

cnf(c_0_13675,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10738,
    [final] ).

cnf(c_0_13676,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10739,
    [final] ).

cnf(c_0_13677,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10740,
    [final] ).

cnf(c_0_13678,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10741,
    [final] ).

cnf(c_0_13679,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10742,
    [final] ).

cnf(c_0_13680,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10743,
    [final] ).

cnf(c_0_13681,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10744,
    [final] ).

cnf(c_0_13682,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10745,
    [final] ).

cnf(c_0_13683,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10746,
    [final] ).

cnf(c_0_13684,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_10747,
    [final] ).

cnf(c_0_13685,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10748,
    [final] ).

cnf(c_0_13686,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10749,
    [final] ).

cnf(c_0_13687,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10750,
    [final] ).

cnf(c_0_13688,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10751,
    [final] ).

cnf(c_0_13689,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10752,
    [final] ).

cnf(c_0_13690,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10753,
    [final] ).

cnf(c_0_13691,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10754,
    [final] ).

cnf(c_0_13692,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10755,
    [final] ).

cnf(c_0_13693,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10756,
    [final] ).

cnf(c_0_13694,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10757,
    [final] ).

cnf(c_0_13695,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10758,
    [final] ).

cnf(c_0_13696,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_10759,
    [final] ).

cnf(c_0_13697,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10760,
    [final] ).

cnf(c_0_13698,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10761,
    [final] ).

cnf(c_0_13699,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10762,
    [final] ).

cnf(c_0_13700,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10763,
    [final] ).

cnf(c_0_13701,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10764,
    [final] ).

cnf(c_0_13702,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10765,
    [final] ).

cnf(c_0_13703,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10766,
    [final] ).

cnf(c_0_13704,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10767,
    [final] ).

cnf(c_0_13705,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10768,
    [final] ).

cnf(c_0_13706,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10769,
    [final] ).

cnf(c_0_13707,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10770,
    [final] ).

cnf(c_0_13708,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10771,
    [final] ).

cnf(c_0_13709,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10772,
    [final] ).

cnf(c_0_13710,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10773,
    [final] ).

cnf(c_0_13711,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10774,
    [final] ).

cnf(c_0_13712,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10775,
    [final] ).

cnf(c_0_13713,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10776,
    [final] ).

cnf(c_0_13714,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10777,
    [final] ).

cnf(c_0_13715,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10778,
    [final] ).

cnf(c_0_13716,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10779,
    [final] ).

cnf(c_0_13717,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10780,
    [final] ).

cnf(c_0_13718,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10781,
    [final] ).

cnf(c_0_13719,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_10782,
    [final] ).

cnf(c_0_13720,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10783,
    [final] ).

cnf(c_0_13721,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10784,
    [final] ).

cnf(c_0_13722,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10785,
    [final] ).

cnf(c_0_13723,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10786,
    [final] ).

cnf(c_0_13724,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10787,
    [final] ).

cnf(c_0_13725,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10788,
    [final] ).

cnf(c_0_13726,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10789,
    [final] ).

cnf(c_0_13727,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10790,
    [final] ).

cnf(c_0_13728,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10791,
    [final] ).

cnf(c_0_13729,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10792,
    [final] ).

cnf(c_0_13730,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10793,
    [final] ).

cnf(c_0_13731,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10794,
    [final] ).

cnf(c_0_13732,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10795,
    [final] ).

cnf(c_0_13733,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10796,
    [final] ).

cnf(c_0_13734,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10797,
    [final] ).

cnf(c_0_13735,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_10798,
    [final] ).

cnf(c_0_13736,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10799,
    [final] ).

cnf(c_0_13737,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10800,
    [final] ).

cnf(c_0_13738,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10801,
    [final] ).

cnf(c_0_13739,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10802,
    [final] ).

cnf(c_0_13740,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10803,
    [final] ).

cnf(c_0_13741,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10804,
    [final] ).

cnf(c_0_13742,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10805,
    [final] ).

cnf(c_0_13743,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10806,
    [final] ).

cnf(c_0_13744,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10807,
    [final] ).

cnf(c_0_13745,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10808,
    [final] ).

cnf(c_0_13746,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10809,
    [final] ).

cnf(c_0_13747,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10810,
    [final] ).

cnf(c_0_13748,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10811,
    [final] ).

cnf(c_0_13749,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10812,
    [final] ).

cnf(c_0_13750,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10813,
    [final] ).

cnf(c_0_13751,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10814,
    [final] ).

cnf(c_0_13752,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10815,
    [final] ).

cnf(c_0_13753,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10816,
    [final] ).

cnf(c_0_13754,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10817,
    [final] ).

cnf(c_0_13755,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10818,
    [final] ).

cnf(c_0_13756,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10819,
    [final] ).

cnf(c_0_13757,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10820,
    [final] ).

cnf(c_0_13758,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10821,
    [final] ).

cnf(c_0_13759,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10822,
    [final] ).

cnf(c_0_13760,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_10823,
    [final] ).

cnf(c_0_13761,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10824,
    [final] ).

cnf(c_0_13762,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10825,
    [final] ).

cnf(c_0_13763,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10826,
    [final] ).

cnf(c_0_13764,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10827,
    [final] ).

cnf(c_0_13765,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10828,
    [final] ).

cnf(c_0_13766,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10829,
    [final] ).

cnf(c_0_13767,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10830,
    [final] ).

cnf(c_0_13768,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10831,
    [final] ).

cnf(c_0_13769,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10832,
    [final] ).

cnf(c_0_13770,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10833,
    [final] ).

cnf(c_0_13771,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10834,
    [final] ).

cnf(c_0_13772,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10835,
    [final] ).

cnf(c_0_13773,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10836,
    [final] ).

cnf(c_0_13774,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10837,
    [final] ).

cnf(c_0_13775,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10838,
    [final] ).

cnf(c_0_13776,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_10839,
    [final] ).

cnf(c_0_13777,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10840,
    [final] ).

cnf(c_0_13778,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10841,
    [final] ).

cnf(c_0_13779,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10842,
    [final] ).

cnf(c_0_13780,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10843,
    [final] ).

cnf(c_0_13781,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10844,
    [final] ).

cnf(c_0_13782,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10845,
    [final] ).

cnf(c_0_13783,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10846,
    [final] ).

cnf(c_0_13784,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10847,
    [final] ).

cnf(c_0_13785,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10848,
    [final] ).

cnf(c_0_13786,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10849,
    [final] ).

cnf(c_0_13787,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10850,
    [final] ).

cnf(c_0_13788,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10851,
    [final] ).

cnf(c_0_13789,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10852,
    [final] ).

cnf(c_0_13790,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10853,
    [final] ).

cnf(c_0_13791,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10854,
    [final] ).

cnf(c_0_13792,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10855,
    [final] ).

cnf(c_0_13793,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10856,
    [final] ).

cnf(c_0_13794,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10857,
    [final] ).

cnf(c_0_13795,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10858,
    [final] ).

cnf(c_0_13796,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10859,
    [final] ).

cnf(c_0_13797,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_10860,
    [final] ).

cnf(c_0_13798,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10861,
    [final] ).

cnf(c_0_13799,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10862,
    [final] ).

cnf(c_0_13800,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10863,
    [final] ).

cnf(c_0_13801,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10864,
    [final] ).

cnf(c_0_13802,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10865,
    [final] ).

cnf(c_0_13803,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10866,
    [final] ).

cnf(c_0_13804,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10867,
    [final] ).

cnf(c_0_13805,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10868,
    [final] ).

cnf(c_0_13806,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10869,
    [final] ).

cnf(c_0_13807,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10870,
    [final] ).

cnf(c_0_13808,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10871,
    [final] ).

cnf(c_0_13809,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10872,
    [final] ).

cnf(c_0_13810,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10873,
    [final] ).

cnf(c_0_13811,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10874,
    [final] ).

cnf(c_0_13812,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10875,
    [final] ).

cnf(c_0_13813,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10876,
    [final] ).

cnf(c_0_13814,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10877,
    [final] ).

cnf(c_0_13815,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10878,
    [final] ).

cnf(c_0_13816,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10879,
    [final] ).

cnf(c_0_13817,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10880,
    [final] ).

cnf(c_0_13818,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10881,
    [final] ).

cnf(c_0_13819,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10882,
    [final] ).

cnf(c_0_13820,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10883,
    [final] ).

cnf(c_0_13821,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_10884,
    [final] ).

cnf(c_0_13822,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10885,
    [final] ).

cnf(c_0_13823,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10886,
    [final] ).

cnf(c_0_13824,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10887,
    [final] ).

cnf(c_0_13825,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10888,
    [final] ).

cnf(c_0_13826,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10889,
    [final] ).

cnf(c_0_13827,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10890,
    [final] ).

cnf(c_0_13828,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10891,
    [final] ).

cnf(c_0_13829,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10892,
    [final] ).

cnf(c_0_13830,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10893,
    [final] ).

cnf(c_0_13831,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10894,
    [final] ).

cnf(c_0_13832,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10895,
    [final] ).

cnf(c_0_13833,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10896,
    [final] ).

cnf(c_0_13834,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10897,
    [final] ).

cnf(c_0_13835,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10898,
    [final] ).

cnf(c_0_13836,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10899,
    [final] ).

cnf(c_0_13837,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10900,
    [final] ).

cnf(c_0_13838,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10901,
    [final] ).

cnf(c_0_13839,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10902,
    [final] ).

cnf(c_0_13840,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10903,
    [final] ).

cnf(c_0_13841,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10904,
    [final] ).

cnf(c_0_13842,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10905,
    [final] ).

cnf(c_0_13843,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10906,
    [final] ).

cnf(c_0_13844,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10907,
    [final] ).

cnf(c_0_13845,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10908,
    [final] ).

cnf(c_0_13846,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10909,
    [final] ).

cnf(c_0_13847,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10910,
    [final] ).

cnf(c_0_13848,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10911,
    [final] ).

cnf(c_0_13849,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10912,
    [final] ).

cnf(c_0_13850,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10913,
    [final] ).

cnf(c_0_13851,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10914,
    [final] ).

cnf(c_0_13852,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10915,
    [final] ).

cnf(c_0_13853,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10916,
    [final] ).

cnf(c_0_13854,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10917,
    [final] ).

cnf(c_0_13855,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10918,
    [final] ).

cnf(c_0_13856,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10919,
    [final] ).

cnf(c_0_13857,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10920,
    [final] ).

cnf(c_0_13858,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10921,
    [final] ).

cnf(c_0_13859,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10922,
    [final] ).

cnf(c_0_13860,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10923,
    [final] ).

cnf(c_0_13861,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_10924,
    [final] ).

cnf(c_0_13862,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10925,
    [final] ).

cnf(c_0_13863,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10926,
    [final] ).

cnf(c_0_13864,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10927,
    [final] ).

cnf(c_0_13865,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10928,
    [final] ).

cnf(c_0_13866,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10929,
    [final] ).

cnf(c_0_13867,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10930,
    [final] ).

cnf(c_0_13868,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10931,
    [final] ).

cnf(c_0_13869,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10932,
    [final] ).

cnf(c_0_13870,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10933,
    [final] ).

cnf(c_0_13871,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10934,
    [final] ).

cnf(c_0_13872,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10935,
    [final] ).

cnf(c_0_13873,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10936,
    [final] ).

cnf(c_0_13874,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10937,
    [final] ).

cnf(c_0_13875,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10938,
    [final] ).

cnf(c_0_13876,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10939,
    [final] ).

cnf(c_0_13877,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10940,
    [final] ).

cnf(c_0_13878,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10941,
    [final] ).

cnf(c_0_13879,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10942,
    [final] ).

cnf(c_0_13880,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10943,
    [final] ).

cnf(c_0_13881,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10944,
    [final] ).

cnf(c_0_13882,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10945,
    [final] ).

cnf(c_0_13883,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10946,
    [final] ).

cnf(c_0_13884,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10947,
    [final] ).

cnf(c_0_13885,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10948,
    [final] ).

cnf(c_0_13886,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10949,
    [final] ).

cnf(c_0_13887,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10950,
    [final] ).

cnf(c_0_13888,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10951,
    [final] ).

cnf(c_0_13889,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10952,
    [final] ).

cnf(c_0_13890,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10953,
    [final] ).

cnf(c_0_13891,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10954,
    [final] ).

cnf(c_0_13892,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10955,
    [final] ).

cnf(c_0_13893,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10956,
    [final] ).

cnf(c_0_13894,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10957,
    [final] ).

cnf(c_0_13895,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10958,
    [final] ).

cnf(c_0_13896,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10959,
    [final] ).

cnf(c_0_13897,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10960,
    [final] ).

cnf(c_0_13898,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_10961,
    [final] ).

cnf(c_0_13899,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10962,
    [final] ).

cnf(c_0_13900,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10963,
    [final] ).

cnf(c_0_13901,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10964,
    [final] ).

cnf(c_0_13902,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10965,
    [final] ).

cnf(c_0_13903,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10966,
    [final] ).

cnf(c_0_13904,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10967,
    [final] ).

cnf(c_0_13905,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10968,
    [final] ).

cnf(c_0_13906,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10969,
    [final] ).

cnf(c_0_13907,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10970,
    [final] ).

cnf(c_0_13908,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10971,
    [final] ).

cnf(c_0_13909,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10972,
    [final] ).

cnf(c_0_13910,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10973,
    [final] ).

cnf(c_0_13911,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10974,
    [final] ).

cnf(c_0_13912,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10975,
    [final] ).

cnf(c_0_13913,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10976,
    [final] ).

cnf(c_0_13914,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10977,
    [final] ).

cnf(c_0_13915,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10978,
    [final] ).

cnf(c_0_13916,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10979,
    [final] ).

cnf(c_0_13917,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10980,
    [final] ).

cnf(c_0_13918,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10981,
    [final] ).

cnf(c_0_13919,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10982,
    [final] ).

cnf(c_0_13920,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10983,
    [final] ).

cnf(c_0_13921,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10984,
    [final] ).

cnf(c_0_13922,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10985,
    [final] ).

cnf(c_0_13923,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10986,
    [final] ).

cnf(c_0_13924,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10987,
    [final] ).

cnf(c_0_13925,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10988,
    [final] ).

cnf(c_0_13926,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10989,
    [final] ).

cnf(c_0_13927,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10990,
    [final] ).

cnf(c_0_13928,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10991,
    [final] ).

cnf(c_0_13929,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10992,
    [final] ).

cnf(c_0_13930,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10993,
    [final] ).

cnf(c_0_13931,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10994,
    [final] ).

cnf(c_0_13932,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10995,
    [final] ).

cnf(c_0_13933,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10996,
    [final] ).

cnf(c_0_13934,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10997,
    [final] ).

cnf(c_0_13935,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10998,
    [final] ).

cnf(c_0_13936,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_10999,
    [final] ).

cnf(c_0_13937,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11000,
    [final] ).

cnf(c_0_13938,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11001,
    [final] ).

cnf(c_0_13939,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11002,
    [final] ).

cnf(c_0_13940,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11003,
    [final] ).

cnf(c_0_13941,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11004,
    [final] ).

cnf(c_0_13942,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11005,
    [final] ).

cnf(c_0_13943,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11006,
    [final] ).

cnf(c_0_13944,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11007,
    [final] ).

cnf(c_0_13945,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11008,
    [final] ).

cnf(c_0_13946,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11009,
    [final] ).

cnf(c_0_13947,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11010,
    [final] ).

cnf(c_0_13948,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11011,
    [final] ).

cnf(c_0_13949,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11012,
    [final] ).

cnf(c_0_13950,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11013,
    [final] ).

cnf(c_0_13951,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11014,
    [final] ).

cnf(c_0_13952,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11015,
    [final] ).

cnf(c_0_13953,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11016,
    [final] ).

cnf(c_0_13954,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11017,
    [final] ).

cnf(c_0_13955,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11018,
    [final] ).

cnf(c_0_13956,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_11019,
    [final] ).

cnf(c_0_13957,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11020,
    [final] ).

cnf(c_0_13958,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11021,
    [final] ).

cnf(c_0_13959,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11022,
    [final] ).

cnf(c_0_13960,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11023,
    [final] ).

cnf(c_0_13961,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11024,
    [final] ).

cnf(c_0_13962,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11025,
    [final] ).

cnf(c_0_13963,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11026,
    [final] ).

cnf(c_0_13964,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11027,
    [final] ).

cnf(c_0_13965,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11028,
    [final] ).

cnf(c_0_13966,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11029,
    [final] ).

cnf(c_0_13967,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11030,
    [final] ).

cnf(c_0_13968,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11031,
    [final] ).

cnf(c_0_13969,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11032,
    [final] ).

cnf(c_0_13970,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11033,
    [final] ).

cnf(c_0_13971,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11034,
    [final] ).

cnf(c_0_13972,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11035,
    [final] ).

cnf(c_0_13973,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11036,
    [final] ).

cnf(c_0_13974,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11037,
    [final] ).

cnf(c_0_13975,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11038,
    [final] ).

cnf(c_0_13976,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11039,
    [final] ).

cnf(c_0_13977,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11040,
    [final] ).

cnf(c_0_13978,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11041,
    [final] ).

cnf(c_0_13979,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11042,
    [final] ).

cnf(c_0_13980,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11043,
    [final] ).

cnf(c_0_13981,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11044,
    [final] ).

cnf(c_0_13982,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11045,
    [final] ).

cnf(c_0_13983,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11046,
    [final] ).

cnf(c_0_13984,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11047,
    [final] ).

cnf(c_0_13985,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11048,
    [final] ).

cnf(c_0_13986,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11049,
    [final] ).

cnf(c_0_13987,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11050,
    [final] ).

cnf(c_0_13988,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11051,
    [final] ).

cnf(c_0_13989,plain,
    ( class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11052,
    [final] ).

cnf(c_0_13990,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11053,
    [final] ).

cnf(c_0_13991,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11054,
    [final] ).

cnf(c_0_13992,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11055,
    [final] ).

cnf(c_0_13993,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11056,
    [final] ).

cnf(c_0_13994,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11057,
    [final] ).

cnf(c_0_13995,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11058,
    [final] ).

cnf(c_0_13996,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11059,
    [final] ).

cnf(c_0_13997,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11060,
    [final] ).

cnf(c_0_13998,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11061,
    [final] ).

cnf(c_0_13999,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11062,
    [final] ).

cnf(c_0_14000,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11063,
    [final] ).

cnf(c_0_14001,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11064,
    [final] ).

cnf(c_0_14002,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11065,
    [final] ).

cnf(c_0_14003,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11066,
    [final] ).

cnf(c_0_14004,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11067,
    [final] ).

cnf(c_0_14005,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11068,
    [final] ).

cnf(c_0_14006,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11069,
    [final] ).

cnf(c_0_14007,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11070,
    [final] ).

cnf(c_0_14008,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11071,
    [final] ).

cnf(c_0_14009,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11072,
    [final] ).

cnf(c_0_14010,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11073,
    [final] ).

cnf(c_0_14011,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11074,
    [final] ).

cnf(c_0_14012,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11075,
    [final] ).

cnf(c_0_14013,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11076,
    [final] ).

cnf(c_0_14014,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11077,
    [final] ).

cnf(c_0_14015,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11078,
    [final] ).

cnf(c_0_14016,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11079,
    [final] ).

cnf(c_0_14017,plain,
    ( class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_11080,
    [final] ).

cnf(c_0_14018,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11081,
    [final] ).

cnf(c_0_14019,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11082,
    [final] ).

cnf(c_0_14020,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11083,
    [final] ).

cnf(c_0_14021,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11084,
    [final] ).

cnf(c_0_14022,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11085,
    [final] ).

cnf(c_0_14023,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11086,
    [final] ).

cnf(c_0_14024,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11087,
    [final] ).

cnf(c_0_14025,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11088,
    [final] ).

cnf(c_0_14026,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11089,
    [final] ).

cnf(c_0_14027,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11090,
    [final] ).

cnf(c_0_14028,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11091,
    [final] ).

cnf(c_0_14029,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11092,
    [final] ).

cnf(c_0_14030,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11093,
    [final] ).

cnf(c_0_14031,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11094,
    [final] ).

cnf(c_0_14032,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11095,
    [final] ).

cnf(c_0_14033,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11096,
    [final] ).

cnf(c_0_14034,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11097,
    [final] ).

cnf(c_0_14035,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11098,
    [final] ).

cnf(c_0_14036,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11099,
    [final] ).

cnf(c_0_14037,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11100,
    [final] ).

cnf(c_0_14038,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11101,
    [final] ).

cnf(c_0_14039,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11102,
    [final] ).

cnf(c_0_14040,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11103,
    [final] ).

cnf(c_0_14041,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11104,
    [final] ).

cnf(c_0_14042,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11105,
    [final] ).

cnf(c_0_14043,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11106,
    [final] ).

cnf(c_0_14044,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11107,
    [final] ).

cnf(c_0_14045,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11108,
    [final] ).

cnf(c_0_14046,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11109,
    [final] ).

cnf(c_0_14047,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_11110,
    [final] ).

cnf(c_0_14048,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11111,
    [final] ).

cnf(c_0_14049,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11112,
    [final] ).

cnf(c_0_14050,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11113,
    [final] ).

cnf(c_0_14051,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11114,
    [final] ).

cnf(c_0_14052,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11115,
    [final] ).

cnf(c_0_14053,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11116,
    [final] ).

cnf(c_0_14054,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11117,
    [final] ).

cnf(c_0_14055,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11118,
    [final] ).

cnf(c_0_14056,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11119,
    [final] ).

cnf(c_0_14057,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11120,
    [final] ).

cnf(c_0_14058,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11121,
    [final] ).

cnf(c_0_14059,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11122,
    [final] ).

cnf(c_0_14060,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11123,
    [final] ).

cnf(c_0_14061,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11124,
    [final] ).

cnf(c_0_14062,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11125,
    [final] ).

cnf(c_0_14063,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11126,
    [final] ).

cnf(c_0_14064,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11127,
    [final] ).

cnf(c_0_14065,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11128,
    [final] ).

cnf(c_0_14066,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11129,
    [final] ).

cnf(c_0_14067,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11130,
    [final] ).

cnf(c_0_14068,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11131,
    [final] ).

cnf(c_0_14069,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11132,
    [final] ).

cnf(c_0_14070,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11133,
    [final] ).

cnf(c_0_14071,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11134,
    [final] ).

cnf(c_0_14072,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11135,
    [final] ).

cnf(c_0_14073,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11136,
    [final] ).

cnf(c_0_14074,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11137,
    [final] ).

cnf(c_0_14075,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11138,
    [final] ).

cnf(c_0_14076,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11139,
    [final] ).

cnf(c_0_14077,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11140,
    [final] ).

cnf(c_0_14078,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_11141,
    [final] ).

cnf(c_0_14079,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11142,
    [final] ).

cnf(c_0_14080,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11143,
    [final] ).

cnf(c_0_14081,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11144,
    [final] ).

cnf(c_0_14082,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11145,
    [final] ).

cnf(c_0_14083,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11146,
    [final] ).

cnf(c_0_14084,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11147,
    [final] ).

cnf(c_0_14085,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11148,
    [final] ).

cnf(c_0_14086,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11149,
    [final] ).

cnf(c_0_14087,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11150,
    [final] ).

cnf(c_0_14088,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11151,
    [final] ).

cnf(c_0_14089,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11152,
    [final] ).

cnf(c_0_14090,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11153,
    [final] ).

cnf(c_0_14091,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11154,
    [final] ).

cnf(c_0_14092,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11155,
    [final] ).

cnf(c_0_14093,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11156,
    [final] ).

cnf(c_0_14094,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11157,
    [final] ).

cnf(c_0_14095,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11158,
    [final] ).

cnf(c_0_14096,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11159,
    [final] ).

cnf(c_0_14097,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11160,
    [final] ).

cnf(c_0_14098,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11161,
    [final] ).

cnf(c_0_14099,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11162,
    [final] ).

cnf(c_0_14100,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11163,
    [final] ).

cnf(c_0_14101,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11164,
    [final] ).

cnf(c_0_14102,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11165,
    [final] ).

cnf(c_0_14103,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11166,
    [final] ).

cnf(c_0_14104,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11167,
    [final] ).

cnf(c_0_14105,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11168,
    [final] ).

cnf(c_0_14106,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11169,
    [final] ).

cnf(c_0_14107,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11170,
    [final] ).

cnf(c_0_14108,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11171,
    [final] ).

cnf(c_0_14109,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_11172,
    [final] ).

cnf(c_0_14110,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11173,
    [final] ).

cnf(c_0_14111,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11174,
    [final] ).

cnf(c_0_14112,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11175,
    [final] ).

cnf(c_0_14113,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11176,
    [final] ).

cnf(c_0_14114,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11177,
    [final] ).

cnf(c_0_14115,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11178,
    [final] ).

cnf(c_0_14116,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11179,
    [final] ).

cnf(c_0_14117,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11180,
    [final] ).

cnf(c_0_14118,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11181,
    [final] ).

cnf(c_0_14119,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11182,
    [final] ).

cnf(c_0_14120,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11183,
    [final] ).

cnf(c_0_14121,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11184,
    [final] ).

cnf(c_0_14122,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11185,
    [final] ).

cnf(c_0_14123,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11186,
    [final] ).

cnf(c_0_14124,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11187,
    [final] ).

cnf(c_0_14125,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11188,
    [final] ).

cnf(c_0_14126,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11189,
    [final] ).

cnf(c_0_14127,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11190,
    [final] ).

cnf(c_0_14128,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11191,
    [final] ).

cnf(c_0_14129,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11192,
    [final] ).

cnf(c_0_14130,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11193,
    [final] ).

cnf(c_0_14131,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11194,
    [final] ).

cnf(c_0_14132,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11195,
    [final] ).

cnf(c_0_14133,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11196,
    [final] ).

cnf(c_0_14134,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11197,
    [final] ).

cnf(c_0_14135,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11198,
    [final] ).

cnf(c_0_14136,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11199,
    [final] ).

cnf(c_0_14137,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11200,
    [final] ).

cnf(c_0_14138,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11201,
    [final] ).

cnf(c_0_14139,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11202,
    [final] ).

cnf(c_0_14140,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11203,
    [final] ).

cnf(c_0_14141,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11204,
    [final] ).

cnf(c_0_14142,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_11205,
    [final] ).

cnf(c_0_14143,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_11206,
    [final] ).

cnf(c_0_14144,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_11207,
    [final] ).

cnf(c_0_14145,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11208,
    [final] ).

cnf(c_0_14146,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11209,
    [final] ).

cnf(c_0_14147,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11210,
    [final] ).

cnf(c_0_14148,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11211,
    [final] ).

cnf(c_0_14149,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11212,
    [final] ).

cnf(c_0_14150,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11213,
    [final] ).

cnf(c_0_14151,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11214,
    [final] ).

cnf(c_0_14152,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11215,
    [final] ).

cnf(c_0_14153,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11216,
    [final] ).

cnf(c_0_14154,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11217,
    [final] ).

cnf(c_0_14155,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11218,
    [final] ).

cnf(c_0_14156,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11219,
    [final] ).

cnf(c_0_14157,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11220,
    [final] ).

cnf(c_0_14158,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11221,
    [final] ).

cnf(c_0_14159,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11222,
    [final] ).

cnf(c_0_14160,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11223,
    [final] ).

cnf(c_0_14161,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11224,
    [final] ).

cnf(c_0_14162,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11225,
    [final] ).

cnf(c_0_14163,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11226,
    [final] ).

cnf(c_0_14164,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11227,
    [final] ).

cnf(c_0_14165,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11228,
    [final] ).

cnf(c_0_14166,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11229,
    [final] ).

cnf(c_0_14167,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_11230,
    [final] ).

cnf(c_0_14168,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11231,
    [final] ).

cnf(c_0_14169,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11232,
    [final] ).

cnf(c_0_14170,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11233,
    [final] ).

cnf(c_0_14171,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11234,
    [final] ).

cnf(c_0_14172,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11235,
    [final] ).

cnf(c_0_14173,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11236,
    [final] ).

cnf(c_0_14174,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11237,
    [final] ).

cnf(c_0_14175,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11238,
    [final] ).

cnf(c_0_14176,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11239,
    [final] ).

cnf(c_0_14177,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11240,
    [final] ).

cnf(c_0_14178,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11241,
    [final] ).

cnf(c_0_14179,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11242,
    [final] ).

cnf(c_0_14180,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11243,
    [final] ).

cnf(c_0_14181,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11244,
    [final] ).

cnf(c_0_14182,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11245,
    [final] ).

cnf(c_0_14183,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11246,
    [final] ).

cnf(c_0_14184,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_11247,
    [final] ).

cnf(c_0_14185,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11248,
    [final] ).

cnf(c_0_14186,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11249,
    [final] ).

cnf(c_0_14187,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11250,
    [final] ).

cnf(c_0_14188,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11251,
    [final] ).

cnf(c_0_14189,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11252,
    [final] ).

cnf(c_0_14190,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11253,
    [final] ).

cnf(c_0_14191,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11254,
    [final] ).

cnf(c_0_14192,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11255,
    [final] ).

cnf(c_0_14193,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11256,
    [final] ).

cnf(c_0_14194,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11257,
    [final] ).

cnf(c_0_14195,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11258,
    [final] ).

cnf(c_0_14196,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11259,
    [final] ).

cnf(c_0_14197,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11260,
    [final] ).

cnf(c_0_14198,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11261,
    [final] ).

cnf(c_0_14199,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_11262,
    [final] ).

cnf(c_0_14200,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11263,
    [final] ).

cnf(c_0_14201,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11264,
    [final] ).

cnf(c_0_14202,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11265,
    [final] ).

cnf(c_0_14203,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11266,
    [final] ).

cnf(c_0_14204,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11267,
    [final] ).

cnf(c_0_14205,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11268,
    [final] ).

cnf(c_0_14206,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11269,
    [final] ).

cnf(c_0_14207,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11270,
    [final] ).

cnf(c_0_14208,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11271,
    [final] ).

cnf(c_0_14209,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11272,
    [final] ).

cnf(c_0_14210,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_11273,
    [final] ).

cnf(c_0_14211,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11274,
    [final] ).

cnf(c_0_14212,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11275,
    [final] ).

cnf(c_0_14213,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11276,
    [final] ).

cnf(c_0_14214,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11277,
    [final] ).

cnf(c_0_14215,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11278,
    [final] ).

cnf(c_0_14216,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11279,
    [final] ).

cnf(c_0_14217,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_11280,
    [final] ).

cnf(c_0_14218,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11281,
    [final] ).

cnf(c_0_14219,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11282,
    [final] ).

cnf(c_0_14220,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11283,
    [final] ).

cnf(c_0_14221,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11284,
    [final] ).

cnf(c_0_14222,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11285,
    [final] ).

cnf(c_0_14223,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11286,
    [final] ).

cnf(c_0_14224,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11287,
    [final] ).

cnf(c_0_14225,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11288,
    [final] ).

cnf(c_0_14226,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11289,
    [final] ).

cnf(c_0_14227,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11290,
    [final] ).

cnf(c_0_14228,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11291,
    [final] ).

cnf(c_0_14229,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11292,
    [final] ).

cnf(c_0_14230,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11293,
    [final] ).

cnf(c_0_14231,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11294,
    [final] ).

cnf(c_0_14232,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11295,
    [final] ).

cnf(c_0_14233,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11296,
    [final] ).

cnf(c_0_14234,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11297,
    [final] ).

cnf(c_0_14235,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11298,
    [final] ).

cnf(c_0_14236,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11299,
    [final] ).

cnf(c_0_14237,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11300,
    [final] ).

cnf(c_0_14238,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11301,
    [final] ).

cnf(c_0_14239,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11302,
    [final] ).

cnf(c_0_14240,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11303,
    [final] ).

cnf(c_0_14241,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11304,
    [final] ).

cnf(c_0_14242,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11305,
    [final] ).

cnf(c_0_14243,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11306,
    [final] ).

cnf(c_0_14244,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11307,
    [final] ).

cnf(c_0_14245,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11308,
    [final] ).

cnf(c_0_14246,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_11309,
    [final] ).

cnf(c_0_14247,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11310,
    [final] ).

cnf(c_0_14248,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11311,
    [final] ).

cnf(c_0_14249,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11312,
    [final] ).

cnf(c_0_14250,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11313,
    [final] ).

cnf(c_0_14251,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11314,
    [final] ).

cnf(c_0_14252,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11315,
    [final] ).

cnf(c_0_14253,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11316,
    [final] ).

cnf(c_0_14254,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11317,
    [final] ).

cnf(c_0_14255,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11318,
    [final] ).

cnf(c_0_14256,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11319,
    [final] ).

cnf(c_0_14257,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11320,
    [final] ).

cnf(c_0_14258,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11321,
    [final] ).

cnf(c_0_14259,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11322,
    [final] ).

cnf(c_0_14260,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11323,
    [final] ).

cnf(c_0_14261,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11324,
    [final] ).

cnf(c_0_14262,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11325,
    [final] ).

cnf(c_0_14263,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11326,
    [final] ).

cnf(c_0_14264,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11327,
    [final] ).

cnf(c_0_14265,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_11328,
    [final] ).

cnf(c_0_14266,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    c_0_11329,
    [final] ).

cnf(c_0_14267,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    c_0_11330,
    [final] ).

cnf(c_0_14268,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    c_0_11331,
    [final] ).

cnf(c_0_14269,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    c_0_11332,
    [final] ).

cnf(c_0_14270,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    c_0_11333,
    [final] ).

cnf(c_0_14271,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    c_0_11334,
    [final] ).

cnf(c_0_14272,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    c_0_11335,
    [final] ).

cnf(c_0_14273,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11336,
    [final] ).

cnf(c_0_14274,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11337,
    [final] ).

cnf(c_0_14275,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11338,
    [final] ).

cnf(c_0_14276,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11339,
    [final] ).

cnf(c_0_14277,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11340,
    [final] ).

cnf(c_0_14278,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11341,
    [final] ).

cnf(c_0_14279,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11342,
    [final] ).

cnf(c_0_14280,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11343,
    [final] ).

cnf(c_0_14281,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11344,
    [final] ).

cnf(c_0_14282,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11345,
    [final] ).

cnf(c_0_14283,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11346,
    [final] ).

cnf(c_0_14284,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11347,
    [final] ).

cnf(c_0_14285,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11348,
    [final] ).

cnf(c_0_14286,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11349,
    [final] ).

cnf(c_0_14287,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11350,
    [final] ).

cnf(c_0_14288,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11351,
    [final] ).

cnf(c_0_14289,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11352,
    [final] ).

cnf(c_0_14290,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11353,
    [final] ).

cnf(c_0_14291,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11354,
    [final] ).

cnf(c_0_14292,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11355,
    [final] ).

cnf(c_0_14293,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11356,
    [final] ).

cnf(c_0_14294,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11357,
    [final] ).

cnf(c_0_14295,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11358,
    [final] ).

cnf(c_0_14296,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11359,
    [final] ).

cnf(c_0_14297,plain,
    ( class_Nat_Opower(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_11360,
    [final] ).

cnf(c_0_14298,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Oorder(X1) ),
    c_0_11361,
    [final] ).

cnf(c_0_14299,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_11362,
    [final] ).

cnf(c_0_14300,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_11363,
    [final] ).

cnf(c_0_14301,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_11364,
    [final] ).

cnf(c_0_14302,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_11365,
    [final] ).

cnf(c_0_14303,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_11366,
    [final] ).

cnf(c_0_14304,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Osemigroup__mult(X1) ),
    c_0_11367,
    [final] ).

cnf(c_0_14305,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    c_0_11368,
    [final] ).

cnf(c_0_14306,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11369,
    [final] ).

cnf(c_0_14307,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11370,
    [final] ).

cnf(c_0_14308,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11371,
    [final] ).

cnf(c_0_14309,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11372,
    [final] ).

cnf(c_0_14310,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11373,
    [final] ).

cnf(c_0_14311,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11374,
    [final] ).

cnf(c_0_14312,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11375,
    [final] ).

cnf(c_0_14313,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_11376,
    [final] ).

cnf(c_0_14314,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11377,
    [final] ).

cnf(c_0_14315,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11378,
    [final] ).

cnf(c_0_14316,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11379,
    [final] ).

cnf(c_0_14317,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11380,
    [final] ).

cnf(c_0_14318,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11381,
    [final] ).

cnf(c_0_14319,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11382,
    [final] ).

cnf(c_0_14320,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11383,
    [final] ).

cnf(c_0_14321,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11384,
    [final] ).

cnf(c_0_14322,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_11385,
    [final] ).

cnf(c_0_14323,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_11386,
    [final] ).

cnf(c_0_14324,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_11387,
    [final] ).

cnf(c_0_14325,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_11388,
    [final] ).

cnf(c_0_14326,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_11389,
    [final] ).

cnf(c_0_14327,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_11390,
    [final] ).

cnf(c_0_14328,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11391,
    [final] ).

cnf(c_0_14329,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11392,
    [final] ).

cnf(c_0_14330,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11393,
    [final] ).

cnf(c_0_14331,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11394,
    [final] ).

cnf(c_0_14332,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11395,
    [final] ).

cnf(c_0_14333,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11396,
    [final] ).

cnf(c_0_14334,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11397,
    [final] ).

cnf(c_0_14335,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11398,
    [final] ).

cnf(c_0_14336,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11399,
    [final] ).

cnf(c_0_14337,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11400,
    [final] ).

cnf(c_0_14338,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11401,
    [final] ).

cnf(c_0_14339,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11402,
    [final] ).

cnf(c_0_14340,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11403,
    [final] ).

cnf(c_0_14341,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_11404,
    [final] ).

cnf(c_0_14342,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11405,
    [final] ).

cnf(c_0_14343,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11406,
    [final] ).

cnf(c_0_14344,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11407,
    [final] ).

cnf(c_0_14345,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11408,
    [final] ).

cnf(c_0_14346,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11409,
    [final] ).

cnf(c_0_14347,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11410,
    [final] ).

cnf(c_0_14348,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11411,
    [final] ).

cnf(c_0_14349,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11412,
    [final] ).

cnf(c_0_14350,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11413,
    [final] ).

cnf(c_0_14351,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11414,
    [final] ).

cnf(c_0_14352,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11415,
    [final] ).

cnf(c_0_14353,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11416,
    [final] ).

cnf(c_0_14354,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11417,
    [final] ).

cnf(c_0_14355,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_11418,
    [final] ).

cnf(c_0_14356,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_11419,
    [final] ).

cnf(c_0_14357,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_11420,
    [final] ).

cnf(c_0_14358,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_11421,
    [final] ).

cnf(c_0_14359,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11422,
    [final] ).

cnf(c_0_14360,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11423,
    [final] ).

cnf(c_0_14361,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11424,
    [final] ).

cnf(c_0_14362,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11425,
    [final] ).

cnf(c_0_14363,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11426,
    [final] ).

cnf(c_0_14364,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11427,
    [final] ).

cnf(c_0_14365,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11428,
    [final] ).

cnf(c_0_14366,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11429,
    [final] ).

cnf(c_0_14367,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11430,
    [final] ).

cnf(c_0_14368,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11431,
    [final] ).

cnf(c_0_14369,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11432,
    [final] ).

cnf(c_0_14370,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11433,
    [final] ).

cnf(c_0_14371,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11434,
    [final] ).

cnf(c_0_14372,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11435,
    [final] ).

cnf(c_0_14373,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11436,
    [final] ).

cnf(c_0_14374,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11437,
    [final] ).

cnf(c_0_14375,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11438,
    [final] ).

cnf(c_0_14376,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11439,
    [final] ).

cnf(c_0_14377,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_11440,
    [final] ).

cnf(c_0_14378,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11441,
    [final] ).

cnf(c_0_14379,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11442,
    [final] ).

cnf(c_0_14380,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11443,
    [final] ).

cnf(c_0_14381,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11444,
    [final] ).

cnf(c_0_14382,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11445,
    [final] ).

cnf(c_0_14383,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11446,
    [final] ).

cnf(c_0_14384,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11447,
    [final] ).

cnf(c_0_14385,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11448,
    [final] ).

cnf(c_0_14386,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11449,
    [final] ).

cnf(c_0_14387,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11450,
    [final] ).

cnf(c_0_14388,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11451,
    [final] ).

cnf(c_0_14389,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11452,
    [final] ).

cnf(c_0_14390,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11453,
    [final] ).

cnf(c_0_14391,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11454,
    [final] ).

cnf(c_0_14392,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11455,
    [final] ).

cnf(c_0_14393,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11456,
    [final] ).

cnf(c_0_14394,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11457,
    [final] ).

cnf(c_0_14395,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11458,
    [final] ).

cnf(c_0_14396,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_11459,
    [final] ).

cnf(c_0_14397,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11460,
    [final] ).

cnf(c_0_14398,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11461,
    [final] ).

cnf(c_0_14399,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11462,
    [final] ).

cnf(c_0_14400,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11463,
    [final] ).

cnf(c_0_14401,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11464,
    [final] ).

cnf(c_0_14402,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11465,
    [final] ).

cnf(c_0_14403,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11466,
    [final] ).

cnf(c_0_14404,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11467,
    [final] ).

cnf(c_0_14405,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11468,
    [final] ).

cnf(c_0_14406,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11469,
    [final] ).

cnf(c_0_14407,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11470,
    [final] ).

cnf(c_0_14408,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11471,
    [final] ).

cnf(c_0_14409,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11472,
    [final] ).

cnf(c_0_14410,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11473,
    [final] ).

cnf(c_0_14411,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11474,
    [final] ).

cnf(c_0_14412,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11475,
    [final] ).

cnf(c_0_14413,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11476,
    [final] ).

cnf(c_0_14414,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11477,
    [final] ).

cnf(c_0_14415,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_11478,
    [final] ).

cnf(c_0_14416,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11479,
    [final] ).

cnf(c_0_14417,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11480,
    [final] ).

cnf(c_0_14418,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11481,
    [final] ).

cnf(c_0_14419,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11482,
    [final] ).

cnf(c_0_14420,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11483,
    [final] ).

cnf(c_0_14421,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11484,
    [final] ).

cnf(c_0_14422,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11485,
    [final] ).

cnf(c_0_14423,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11486,
    [final] ).

cnf(c_0_14424,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11487,
    [final] ).

cnf(c_0_14425,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11488,
    [final] ).

cnf(c_0_14426,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11489,
    [final] ).

cnf(c_0_14427,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11490,
    [final] ).

cnf(c_0_14428,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11491,
    [final] ).

cnf(c_0_14429,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11492,
    [final] ).

cnf(c_0_14430,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11493,
    [final] ).

cnf(c_0_14431,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11494,
    [final] ).

cnf(c_0_14432,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11495,
    [final] ).

cnf(c_0_14433,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_11496,
    [final] ).

cnf(c_0_14434,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_11497,
    [final] ).

cnf(c_0_14435,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_11498,
    [final] ).

cnf(c_0_14436,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_11499,
    [final] ).

cnf(c_0_14437,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_11500,
    [final] ).

cnf(c_0_14438,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_11501,
    [final] ).

cnf(c_0_14439,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_11502,
    [final] ).

cnf(c_0_14440,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_11503,
    [final] ).

cnf(c_0_14441,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_11504,
    [final] ).

cnf(c_0_14442,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_11505,
    [final] ).

cnf(c_0_14443,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    c_0_11506,
    [final] ).

cnf(c_0_14444,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    c_0_11507,
    [final] ).

cnf(c_0_14445,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_11508,
    [final] ).

cnf(c_0_14446,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_11509,
    [final] ).

cnf(c_0_14447,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_11510,
    [final] ).

cnf(c_0_14448,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_11511,
    [final] ).

cnf(c_0_14449,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    c_0_11512,
    [final] ).

cnf(c_0_14450,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    c_0_11513,
    [final] ).

cnf(c_0_14451,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    c_0_11514,
    [final] ).

cnf(c_0_14452,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    c_0_11515,
    [final] ).

cnf(c_0_14453,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11516,
    [final] ).

cnf(c_0_14454,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11517,
    [final] ).

cnf(c_0_14455,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11518,
    [final] ).

cnf(c_0_14456,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11519,
    [final] ).

cnf(c_0_14457,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11520,
    [final] ).

cnf(c_0_14458,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11521,
    [final] ).

cnf(c_0_14459,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11522,
    [final] ).

cnf(c_0_14460,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_11523,
    [final] ).

cnf(c_0_14461,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11524,
    [final] ).

cnf(c_0_14462,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11525,
    [final] ).

cnf(c_0_14463,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11526,
    [final] ).

cnf(c_0_14464,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11527,
    [final] ).

cnf(c_0_14465,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11528,
    [final] ).

cnf(c_0_14466,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11529,
    [final] ).

cnf(c_0_14467,plain,
    ( class_Numeral_Onumber(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11530,
    [final] ).

cnf(c_0_14468,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11531,
    [final] ).

cnf(c_0_14469,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11532,
    [final] ).

cnf(c_0_14470,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11533,
    [final] ).

cnf(c_0_14471,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11534,
    [final] ).

cnf(c_0_14472,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11535,
    [final] ).

cnf(c_0_14473,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11536,
    [final] ).

cnf(c_0_14474,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11537,
    [final] ).

cnf(c_0_14475,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11538,
    [final] ).

cnf(c_0_14476,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11539,
    [final] ).

cnf(c_0_14477,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11540,
    [final] ).

cnf(c_0_14478,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11541,
    [final] ).

cnf(c_0_14479,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11542,
    [final] ).

cnf(c_0_14480,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11543,
    [final] ).

cnf(c_0_14481,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11544,
    [final] ).

cnf(c_0_14482,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11545,
    [final] ).

cnf(c_0_14483,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11546,
    [final] ).

cnf(c_0_14484,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11547,
    [final] ).

cnf(c_0_14485,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11548,
    [final] ).

cnf(c_0_14486,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11549,
    [final] ).

cnf(c_0_14487,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11550,
    [final] ).

cnf(c_0_14488,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11551,
    [final] ).

cnf(c_0_14489,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11552,
    [final] ).

cnf(c_0_14490,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11553,
    [final] ).

cnf(c_0_14491,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_11554,
    [final] ).

cnf(c_0_14492,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    c_0_11555,
    [final] ).

cnf(c_0_14493,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    c_0_11556,
    [final] ).

cnf(c_0_14494,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_11557,
    [final] ).

cnf(c_0_14495,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_11558,
    [final] ).

cnf(c_0_14496,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_11559,
    [final] ).

cnf(c_0_14497,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_11560,
    [final] ).

cnf(c_0_14498,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    c_0_11561,
    [final] ).

cnf(c_0_14499,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    c_0_11562,
    [final] ).

cnf(c_0_14500,plain,
    c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
    c_0_11563,
    [final] ).

cnf(c_0_14501,plain,
    c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
    c_0_11564,
    [final] ).

cnf(c_0_14502,plain,
    c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
    c_0_11565,
    [final] ).

cnf(c_0_14503,plain,
    c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
    c_0_11566,
    [final] ).

cnf(c_0_14504,plain,
    c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
    c_0_11567,
    [final] ).

cnf(c_0_14505,plain,
    c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
    c_0_11568,
    [final] ).

cnf(c_0_14506,plain,
    c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
    c_0_11569,
    [final] ).

cnf(c_0_14507,plain,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    c_0_11570,
    [final] ).

cnf(c_0_14508,plain,
    c_Parity_Oeven(c_0,tc_nat),
    c_0_11571,
    [final] ).

cnf(c_0_14509,plain,
    c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
    c_0_11572,
    [final] ).

cnf(c_0_14510,plain,
    c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
    c_0_11573,
    [final] ).

cnf(c_0_14511,plain,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
    c_0_11574,
    [final] ).

cnf(c_0_14512,plain,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
    c_0_11575,
    [final] ).

cnf(c_0_14513,plain,
    c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
    c_0_11576,
    [final] ).

cnf(c_0_14514,plain,
    c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
    c_0_11577,
    [final] ).

cnf(c_0_14515,plain,
    c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
    c_0_11578,
    [final] ).

cnf(c_0_14516,plain,
    c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
    c_0_11579,
    [final] ).

cnf(c_0_14517,plain,
    c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
    c_0_11580,
    [final] ).

cnf(c_0_14518,plain,
    c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
    c_0_11581,
    [final] ).

cnf(c_0_14519,plain,
    c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
    c_0_11582,
    [final] ).

cnf(c_0_14520,plain,
    c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
    c_0_11583,
    [final] ).

cnf(c_0_14521,plain,
    c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
    c_0_11584,
    [final] ).

cnf(c_0_14522,plain,
    c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
    c_0_11585,
    [final] ).

cnf(c_0_14523,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
    c_0_11586,
    [final] ).

cnf(c_0_14524,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
    c_0_11587,
    [final] ).

cnf(c_0_14525,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
    c_0_11588,
    [final] ).

cnf(c_0_14526,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
    c_0_11589,
    [final] ).

cnf(c_0_14527,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
    c_0_11590,
    [final] ).

cnf(c_0_14528,plain,
    c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
    c_0_11591,
    [final] ).

cnf(c_0_14529,plain,
    c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
    c_0_11592,
    [final] ).

cnf(c_0_14530,plain,
    c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
    c_0_11593,
    [final] ).

cnf(c_0_14531,plain,
    c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
    c_0_11594,
    [final] ).

cnf(c_0_14532,plain,
    c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
    c_0_11595,
    [final] ).

cnf(c_0_14533,plain,
    c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
    c_0_11596,
    [final] ).

cnf(c_0_14534,plain,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_11597,
    [final] ).

cnf(c_0_14535,plain,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_11598,
    [final] ).

cnf(c_0_14536,plain,
    class_Nat_Opower(tc_set(X1)),
    c_0_11599,
    [final] ).

cnf(c_0_14537,plain,
    class_Orderings_Oorder(tc_set(X1)),
    c_0_11600,
    [final] ).

cnf(c_0_14538,plain,
    class_Orderings_Oord(tc_set(X1)),
    c_0_11601,
    [final] ).

cnf(c_0_14539,plain,
    class_HOL_Ominus(tc_set(X1)),
    c_0_11602,
    [final] ).

cnf(c_0_14540,plain,
    ( X1 = c_0
    | c_IntDef_Oint(X1) != c_0 ),
    c_0_11603,
    [final] ).

cnf(c_0_14541,plain,
    ( c_1 != c_0
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    c_0_11604,
    [final] ).

cnf(c_0_14542,plain,
    ( c_1 != c_0
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    c_0_11605,
    [final] ).

cnf(c_0_14543,plain,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OSpy,
    c_0_11606,
    [final] ).

cnf(c_0_14544,plain,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OSpy,
    c_0_11607,
    [final] ).

cnf(c_0_14545,plain,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OServer,
    c_0_11608,
    [final] ).

cnf(c_0_14546,plain,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OServer,
    c_0_11609,
    [final] ).

cnf(c_0_14547,plain,
    c_Suc(X1) != c_0,
    c_0_11610,
    [final] ).

cnf(c_0_14548,plain,
    c_Suc(X1) != c_0,
    c_0_11611,
    [final] ).

cnf(c_0_14549,plain,
    c_IntDef_Onat(c_1) = c_Suc(c_0),
    c_0_11612,
    [final] ).

cnf(c_0_14550,plain,
    c_Message_Oanalz(c_emptyset) = c_emptyset,
    c_0_11613,
    [final] ).

cnf(c_0_14551,plain,
    c_Message_Oparts(c_emptyset) = c_emptyset,
    c_0_11614,
    [final] ).

cnf(c_0_14552,plain,
    c_Message_OkeysFor(c_emptyset) = c_emptyset,
    c_0_11615,
    [final] ).

cnf(c_0_14553,plain,
    c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
    c_0_11616,
    [final] ).

cnf(c_0_14554,plain,
    c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
    c_0_11617,
    [final] ).

cnf(c_0_14555,plain,
    c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
    c_0_11618,
    [final] ).

cnf(c_0_14556,plain,
    c_Suc(c_0) = c_1,
    c_0_11619,
    [final] ).

cnf(c_0_14557,plain,
    c_IntDef_Onat(c_0) = c_0,
    c_0_11620,
    [final] ).

cnf(c_0_14558,plain,
    c_IntDef_Oint(c_0) = c_0,
    c_0_11621,
    [final] ).

cnf(c_0_14559,plain,
    c_IntDef_Oint(c_1) = c_1,
    c_0_11622,
    [final] ).

cnf(c_0_14560,plain,
    class_HOL_Ominus(tc_nat),
    c_0_11623,
    [final] ).

cnf(c_0_14561,plain,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    c_0_11624,
    [final] ).

cnf(c_0_14562,plain,
    class_Orderings_Olinorder(tc_nat),
    c_0_11625,
    [final] ).

cnf(c_0_14563,plain,
    class_LOrder_Olorder(tc_nat),
    c_0_11626,
    [final] ).

cnf(c_0_14564,plain,
    class_LOrder_Ojoin__semilorder(tc_nat),
    c_0_11627,
    [final] ).

cnf(c_0_14565,plain,
    class_Parity_Oeven__odd(tc_nat),
    c_0_11628,
    [final] ).

cnf(c_0_14566,plain,
    class_Numeral_Onumber(tc_nat),
    c_0_11629,
    [final] ).

cnf(c_0_14567,plain,
    class_Power_Orecpower(tc_nat),
    c_0_11630,
    [final] ).

cnf(c_0_14568,plain,
    class_Divides_Odiv(tc_nat),
    c_0_11631,
    [final] ).

cnf(c_0_14569,plain,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_11632,
    [final] ).

cnf(c_0_14570,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_11633,
    [final] ).

cnf(c_0_14571,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    c_0_11634,
    [final] ).

cnf(c_0_14572,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    c_0_11635,
    [final] ).

cnf(c_0_14573,plain,
    class_LOrder_Omeet__semilorder(tc_nat),
    c_0_11636,
    [final] ).

cnf(c_0_14574,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_11637,
    [final] ).

cnf(c_0_14575,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_11638,
    [final] ).

cnf(c_0_14576,plain,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_11639,
    [final] ).

cnf(c_0_14577,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    c_0_11640,
    [final] ).

cnf(c_0_14578,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_11641,
    [final] ).

cnf(c_0_14579,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_11642,
    [final] ).

cnf(c_0_14580,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_11643,
    [final] ).

cnf(c_0_14581,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    c_0_11644,
    [final] ).

cnf(c_0_14582,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    c_0_11645,
    [final] ).

cnf(c_0_14583,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    c_0_11646,
    [final] ).

cnf(c_0_14584,plain,
    class_Orderings_Oorder(tc_nat),
    c_0_11647,
    [final] ).

cnf(c_0_14585,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    c_0_11648,
    [final] ).

cnf(c_0_14586,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_11649,
    [final] ).

cnf(c_0_14587,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_11650,
    [final] ).

cnf(c_0_14588,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_11651,
    [final] ).

cnf(c_0_14589,plain,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_11652,
    [final] ).

cnf(c_0_14590,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    c_0_11653,
    [final] ).

cnf(c_0_14591,plain,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    c_0_11654,
    [final] ).

cnf(c_0_14592,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    c_0_11655,
    [final] ).

cnf(c_0_14593,plain,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    c_0_11656,
    [final] ).

cnf(c_0_14594,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_11657,
    [final] ).

cnf(c_0_14595,plain,
    class_Orderings_Oord(tc_nat),
    c_0_11658,
    [final] ).

cnf(c_0_14596,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_11659,
    [final] ).

cnf(c_0_14597,plain,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_11660,
    [final] ).

cnf(c_0_14598,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_11661,
    [final] ).

cnf(c_0_14599,plain,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    c_0_11662,
    [final] ).

cnf(c_0_14600,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_11663,
    [final] ).

cnf(c_0_14601,plain,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    c_0_11664,
    [final] ).

cnf(c_0_14602,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    c_0_11665,
    [final] ).

cnf(c_0_14603,plain,
    class_Nat_Opower(tc_nat),
    c_0_11666,
    [final] ).

cnf(c_0_14604,plain,
    class_HOL_Otimes(tc_nat),
    c_0_11667,
    [final] ).

cnf(c_0_14605,plain,
    class_HOL_Oplus(tc_nat),
    c_0_11668,
    [final] ).

cnf(c_0_14606,plain,
    class_HOL_Ozero(tc_nat),
    c_0_11669,
    [final] ).

cnf(c_0_14607,plain,
    class_HOL_Oone(tc_nat),
    c_0_11670,
    [final] ).

cnf(c_0_14608,plain,
    class_Finite__Set_Ofinite(tc_bool),
    c_0_11671,
    [final] ).

cnf(c_0_14609,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    c_0_11672,
    [final] ).

cnf(c_0_14610,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    c_0_11673,
    [final] ).

cnf(c_0_14611,plain,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    c_0_11674,
    [final] ).

cnf(c_0_14612,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    c_0_11675,
    [final] ).

cnf(c_0_14613,plain,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    c_0_11676,
    [final] ).

cnf(c_0_14614,plain,
    class_Power_Orecpower(tc_IntDef_Oint),
    c_0_11677,
    [final] ).

cnf(c_0_14615,plain,
    class_Nat_Opower(tc_IntDef_Oint),
    c_0_11678,
    [final] ).

cnf(c_0_14616,plain,
    class_Divides_Odiv(tc_IntDef_Oint),
    c_0_11679,
    [final] ).

cnf(c_0_14617,plain,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    c_0_11680,
    [final] ).

cnf(c_0_14618,plain,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    c_0_11681,
    [final] ).

cnf(c_0_14619,plain,
    class_Numeral_Onumber(tc_IntDef_Oint),
    c_0_11682,
    [final] ).

cnf(c_0_14620,plain,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    c_0_11683,
    [final] ).

cnf(c_0_14621,plain,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    c_0_11684,
    [final] ).

cnf(c_0_14622,plain,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    c_0_11685,
    [final] ).

cnf(c_0_14623,plain,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    c_0_11686,
    [final] ).

cnf(c_0_14624,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    c_0_11687,
    [final] ).

cnf(c_0_14625,plain,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    c_0_11688,
    [final] ).

cnf(c_0_14626,plain,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    c_0_11689,
    [final] ).

cnf(c_0_14627,plain,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    c_0_11690,
    [final] ).

cnf(c_0_14628,plain,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    c_0_11691,
    [final] ).

cnf(c_0_14629,plain,
    class_Orderings_Oord(tc_IntDef_Oint),
    c_0_11692,
    [final] ).

cnf(c_0_14630,plain,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    c_0_11693,
    [final] ).

cnf(c_0_14631,plain,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    c_0_11694,
    [final] ).

cnf(c_0_14632,plain,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    c_0_11695,
    [final] ).

cnf(c_0_14633,plain,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    c_0_11696,
    [final] ).

cnf(c_0_14634,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    c_0_11697,
    [final] ).

cnf(c_0_14635,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    c_0_11698,
    [final] ).

cnf(c_0_14636,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    c_0_11699,
    [final] ).

cnf(c_0_14637,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    c_0_11700,
    [final] ).

cnf(c_0_14638,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    c_0_11701,
    [final] ).

cnf(c_0_14639,plain,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    c_0_11702,
    [final] ).

cnf(c_0_14640,plain,
    class_HOL_Ozero(tc_IntDef_Oint),
    c_0_11703,
    [final] ).

cnf(c_0_14641,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_11704,
    [final] ).

cnf(c_0_14642,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    c_0_11705,
    [final] ).

cnf(c_0_14643,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_11706,
    [final] ).

cnf(c_0_14644,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    c_0_11707,
    [final] ).

cnf(c_0_14645,plain,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    c_0_11708,
    [final] ).

cnf(c_0_14646,plain,
    class_LOrder_Olorder(tc_IntDef_Oint),
    c_0_11709,
    [final] ).

cnf(c_0_14647,plain,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    c_0_11710,
    [final] ).

cnf(c_0_14648,plain,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    c_0_11711,
    [final] ).

cnf(c_0_14649,plain,
    class_Orderings_Oorder(tc_IntDef_Oint),
    c_0_11712,
    [final] ).

cnf(c_0_14650,plain,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    c_0_11713,
    [final] ).

cnf(c_0_14651,plain,
    class_HOL_Otimes(tc_IntDef_Oint),
    c_0_11714,
    [final] ).

cnf(c_0_14652,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    c_0_11715,
    [final] ).

cnf(c_0_14653,plain,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    c_0_11716,
    [final] ).

cnf(c_0_14654,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    c_0_11717,
    [final] ).

cnf(c_0_14655,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    c_0_11718,
    [final] ).

cnf(c_0_14656,plain,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    c_0_11719,
    [final] ).

cnf(c_0_14657,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    c_0_11720,
    [final] ).

cnf(c_0_14658,plain,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    c_0_11721,
    [final] ).

cnf(c_0_14659,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    c_0_11722,
    [final] ).

cnf(c_0_14660,plain,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    c_0_11723,
    [final] ).

cnf(c_0_14661,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    c_0_11724,
    [final] ).

cnf(c_0_14662,plain,
    class_HOL_Oplus(tc_IntDef_Oint),
    c_0_11725,
    [final] ).

cnf(c_0_14663,plain,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    c_0_11726,
    [final] ).

cnf(c_0_14664,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    c_0_11727,
    [final] ).

cnf(c_0_14665,plain,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    c_0_11728,
    [final] ).

cnf(c_0_14666,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_11729,
    [final] ).

cnf(c_0_14667,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    c_0_11730,
    [final] ).

cnf(c_0_14668,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    c_0_11731,
    [final] ).

cnf(c_0_14669,plain,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    c_0_11732,
    [final] ).

cnf(c_0_14670,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    c_0_11733,
    [final] ).

cnf(c_0_14671,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    c_0_11734,
    [final] ).

cnf(c_0_14672,plain,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    c_0_11735,
    [final] ).

cnf(c_0_14673,plain,
    class_HOL_Oone(tc_IntDef_Oint),
    c_0_11736,
    [final] ).

cnf(c_0_14674,plain,
    class_HOL_Ominus(tc_IntDef_Oint),
    c_0_11737,
    [final] ).

cnf(c_0_14675,plain,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    c_0_11738,
    [final] ).

cnf(c_0_14676,plain,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    c_0_11739,
    [final] ).

cnf(c_0_14677,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    c_0_11740,
    [final] ).

cnf(c_0_14678,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    c_0_11741,
    [final] ).

cnf(c_0_14679,plain,
    c_UNIV != c_emptyset,
    c_0_11742,
    [final] ).

cnf(c_0_14680,plain,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    c_0_11743,
    [final] ).

cnf(c_0_14681,plain,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    c_0_11744,
    [final] ).

cnf(c_0_14682,plain,
    c_1 != c_0,
    c_0_11745,
    [final] ).

cnf(c_0_14683,plain,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_11746,
    [final] ).

cnf(c_0_14684,plain,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_11747,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_11780_0,axiom,
    ( c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11780]) ).

cnf(c_0_11780_1,axiom,
    ( ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5))
    | c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11780]) ).

cnf(c_0_11781_0,axiom,
    ( c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11781]) ).

cnf(c_0_11781_1,axiom,
    ( ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5))
    | c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11781]) ).

cnf(c_0_11782_0,axiom,
    ( c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5) = X1
    | ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11782]) ).

cnf(c_0_11782_1,axiom,
    ( ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5))
    | c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11782]) ).

cnf(c_0_11783_0,axiom,
    ( c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11783]) ).

cnf(c_0_11783_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11783]) ).

cnf(c_0_11784_0,axiom,
    ( c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11784]) ).

cnf(c_0_11784_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11784]) ).

cnf(c_0_11785_0,axiom,
    ( c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11785]) ).

cnf(c_0_11785_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11785]) ).

cnf(c_0_11786_0,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11786]) ).

cnf(c_0_11786_1,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11786]) ).

cnf(c_0_11786_2,axiom,
    ( ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11786]) ).

cnf(c_0_11787_0,axiom,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11787]) ).

cnf(c_0_11787_1,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11787]) ).

cnf(c_0_11787_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11787]) ).

cnf(c_0_11788_0,axiom,
    ( c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11788]) ).

cnf(c_0_11788_1,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11788]) ).

cnf(c_0_11788_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11788]) ).

cnf(c_0_11789_0,axiom,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11789]) ).

cnf(c_0_11789_1,axiom,
    ( ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11789]) ).

cnf(c_0_11790_0,axiom,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11790]) ).

cnf(c_0_11790_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11790]) ).

cnf(c_0_11791_0,axiom,
    ( c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11791]) ).

cnf(c_0_11791_1,axiom,
    ( ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11791]) ).

cnf(c_0_11791_2,axiom,
    ( ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11791]) ).

cnf(c_0_11792_0,axiom,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11792]) ).

cnf(c_0_11792_1,axiom,
    ( ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11792]) ).

cnf(c_0_11793_0,axiom,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11793]) ).

cnf(c_0_11793_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11793]) ).

cnf(c_0_11794_0,axiom,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11794]) ).

cnf(c_0_11794_1,axiom,
    ( c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11794]) ).

cnf(c_0_11794_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11794]) ).

cnf(c_0_11795_0,axiom,
    ( c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11795]) ).

cnf(c_0_11795_1,axiom,
    ( ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5)
    | c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11795]) ).

cnf(c_0_11796_0,axiom,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11796]) ).

cnf(c_0_11796_1,axiom,
    ( ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11796]) ).

cnf(c_0_11797_0,axiom,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11797]) ).

cnf(c_0_11797_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11797]) ).

cnf(c_0_11798_0,axiom,
    ( c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11798]) ).

cnf(c_0_11798_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11798]) ).

cnf(c_0_11799_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11799]) ).

cnf(c_0_11799_1,axiom,
    ( ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11799]) ).

cnf(c_0_11799_2,axiom,
    ( ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11799]) ).

cnf(c_0_11800_0,axiom,
    ( c_plus(X1,X2,tc_nat) = c_plus(X3,X4,tc_nat)
    | ~ c_in(c_Pair(c_Pair(X1,X4,tc_nat,tc_nat),c_Pair(X3,X2,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_11800]) ).

cnf(c_0_11800_1,axiom,
    ( ~ c_in(c_Pair(c_Pair(X1,X4,tc_nat,tc_nat),c_Pair(X3,X2,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_plus(X1,X2,tc_nat) = c_plus(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11800]) ).

cnf(c_0_11801_0,axiom,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11801]) ).

cnf(c_0_11801_1,axiom,
    ( c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11801]) ).

cnf(c_0_11801_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_11801]) ).

cnf(c_0_11802_0,axiom,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11802]) ).

cnf(c_0_11802_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11802]) ).

cnf(c_0_11802_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_11802]) ).

cnf(c_0_11803_0,axiom,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11803]) ).

cnf(c_0_11803_1,axiom,
    ( c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11803]) ).

cnf(c_0_11803_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_11803]) ).

cnf(c_0_11804_0,axiom,
    ( c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11804]) ).

cnf(c_0_11804_1,axiom,
    ( ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11804]) ).

cnf(c_0_11805_0,axiom,
    ( c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11805]) ).

cnf(c_0_11805_1,axiom,
    ( ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_11805]) ).

cnf(c_0_11806_0,axiom,
    ( c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11806]) ).

cnf(c_0_11806_1,axiom,
    ( c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11806]) ).

cnf(c_0_11806_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_Oadjust(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) = c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_11806]) ).

cnf(c_0_11807_0,axiom,
    ( c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11807]) ).

cnf(c_0_11807_1,axiom,
    ( ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11807]) ).

cnf(c_0_11808_0,axiom,
    ( c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11808]) ).

cnf(c_0_11808_1,axiom,
    ( ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_11808]) ).

cnf(c_0_11809_0,axiom,
    ( c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11809]) ).

cnf(c_0_11809_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11809]) ).

cnf(c_0_11809_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11809]) ).

cnf(c_0_11810_0,axiom,
    ( c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11810]) ).

cnf(c_0_11810_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11810]) ).

cnf(c_0_11810_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11810]) ).

cnf(c_0_11811_0,axiom,
    ( c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11811]) ).

cnf(c_0_11811_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11811]) ).

cnf(c_0_11811_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11811]) ).

cnf(c_0_11812_0,axiom,
    ( c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11812]) ).

cnf(c_0_11812_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11812]) ).

cnf(c_0_11812_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11812]) ).

cnf(c_0_11813_0,axiom,
    ( c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11813]) ).

cnf(c_0_11813_1,axiom,
    ( ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5)
    | c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11813]) ).

cnf(c_0_11814_0,axiom,
    ( c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11814]) ).

cnf(c_0_11814_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11814]) ).

cnf(c_0_11815_0,axiom,
    ( c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11815]) ).

cnf(c_0_11815_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11815]) ).

cnf(c_0_11816_0,axiom,
    ( c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11816]) ).

cnf(c_0_11816_1,axiom,
    ( c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11816]) ).

cnf(c_0_11816_2,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11816]) ).

cnf(c_0_11817_0,axiom,
    ( c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11817]) ).

cnf(c_0_11817_1,axiom,
    ( c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11817]) ).

cnf(c_0_11817_2,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X3),c_List_Olist_OCons(X6,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X5,X6,X3,X3),X4,tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11817]) ).

cnf(c_0_11819_0,axiom,
    ( c_in(c_Pair(c_Pair(X1,X2,tc_nat,tc_nat),c_Pair(X3,X4,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_plus(X1,X4,tc_nat) != c_plus(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11819]) ).

cnf(c_0_11819_1,axiom,
    ( c_plus(X1,X4,tc_nat) != c_plus(X3,X2,tc_nat)
    | c_in(c_Pair(c_Pair(X1,X2,tc_nat,tc_nat),c_Pair(X3,X4,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_11819]) ).

cnf(c_0_11820_0,axiom,
    ( c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11820]) ).

cnf(c_0_11820_1,axiom,
    ( ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3))
    | c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11820]) ).

cnf(c_0_11821_0,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11821]) ).

cnf(c_0_11821_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11821]) ).

cnf(c_0_11822_0,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11822]) ).

cnf(c_0_11822_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11822]) ).

cnf(c_0_11823_0,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | c_in(c_Pair(X1,X3,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X2),c_List_Olist_OCons(X6,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11823]) ).

cnf(c_0_11823_1,axiom,
    ( c_in(c_Pair(X1,X3,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X2),c_List_Olist_OCons(X6,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11823]) ).

cnf(c_0_11823_2,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X5,X1,X2),c_List_Olist_OCons(X6,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | c_in(c_Pair(X1,X3,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X4,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_11823]) ).

cnf(c_0_11824_0,axiom,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11824]) ).

cnf(c_0_11824_1,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | X1 = X2
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11824]) ).

cnf(c_0_11824_2,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11824]) ).

cnf(c_0_11825_0,axiom,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11825]) ).

cnf(c_0_11825_1,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | X1 = X2
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11825]) ).

cnf(c_0_11825_2,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X2,X6,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11825]) ).

cnf(c_0_11826_0,axiom,
    ( c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11826]) ).

cnf(c_0_11826_1,axiom,
    ( c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11826]) ).

cnf(c_0_11826_2,axiom,
    ( ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11826]) ).

cnf(c_0_11827_0,axiom,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11827]) ).

cnf(c_0_11827_1,axiom,
    ( c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11827]) ).

cnf(c_0_11827_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11827]) ).

cnf(c_0_11828_0,axiom,
    ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11828]) ).

cnf(c_0_11828_1,axiom,
    ( c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11828]) ).

cnf(c_0_11828_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11828]) ).

cnf(c_0_11829_0,axiom,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11829]) ).

cnf(c_0_11829_1,axiom,
    ( ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11829]) ).

cnf(c_0_11830_0,axiom,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11830]) ).

cnf(c_0_11830_1,axiom,
    ( ~ c_in(c_Pair(X2,X4,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X5,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11830]) ).

cnf(c_0_11831_0,axiom,
    ( c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_11831]) ).

cnf(c_0_11831_1,axiom,
    ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_11831]) ).

cnf(c_0_11832_0,axiom,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11832]) ).

cnf(c_0_11832_1,axiom,
    ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11832]) ).

cnf(c_0_11832_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11832]) ).

cnf(c_0_11833_0,axiom,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X3))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11833]) ).

cnf(c_0_11833_1,axiom,
    ( c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X3))
    | c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11833]) ).

cnf(c_0_11833_2,axiom,
    ( ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X3))
    | c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11833]) ).

cnf(c_0_11834_0,axiom,
    ( c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_11834]) ).

cnf(c_0_11834_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
    | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X2,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_11834]) ).

cnf(c_0_11835_0,axiom,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11835]) ).

cnf(c_0_11835_1,axiom,
    ( c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11835]) ).

cnf(c_0_11835_2,axiom,
    ( ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3))
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11835]) ).

cnf(c_0_11836_0,axiom,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11836]) ).

cnf(c_0_11836_1,axiom,
    ( c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11836]) ).

cnf(c_0_11836_2,axiom,
    ( ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3))
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11836]) ).

cnf(c_0_11837_0,axiom,
    ( c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11837]) ).

cnf(c_0_11837_1,axiom,
    ( c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11837]) ).

cnf(c_0_11837_2,axiom,
    ( ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4))
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11837]) ).

cnf(c_0_11838_0,axiom,
    ( c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11838]) ).

cnf(c_0_11838_1,axiom,
    ( c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11838]) ).

cnf(c_0_11838_2,axiom,
    ( ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3))
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11838]) ).

cnf(c_0_11840_0,axiom,
    ( c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
    | ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11840]) ).

cnf(c_0_11840_1,axiom,
    ( ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3))
    | c_in(c_Pair(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X6,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11840]) ).

cnf(c_0_11841_0,axiom,
    ( c_Wellfounded__Recursion_Owf(X1,X2)
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11841]) ).

cnf(c_0_11841_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2)
    | c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11841]) ).

cnf(c_0_11842_0,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11842]) ).

cnf(c_0_11842_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2)
    | c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11842]) ).

cnf(c_0_11843_0,axiom,
    ( c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
    | ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11843]) ).

cnf(c_0_11843_1,axiom,
    ( ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3)
    | c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11843]) ).

cnf(c_0_11844_0,axiom,
    ( c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
    | ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11844]) ).

cnf(c_0_11844_1,axiom,
    ( ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11844]) ).

cnf(c_0_11845_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11845]) ).

cnf(c_0_11845_1,axiom,
    ( c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11845]) ).

cnf(c_0_11845_2,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X4,X3)
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11845]) ).

cnf(c_0_11846_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11846]) ).

cnf(c_0_11846_1,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11846]) ).

cnf(c_0_11846_2,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(X4,X3)
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11846]) ).

cnf(c_0_11847_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11847]) ).

cnf(c_0_11847_1,axiom,
    ( ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4)
    | c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11847]) ).

cnf(c_0_11848_0,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | X4 = X5
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X2),c_List_Olist_OCons(X5,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X6,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11848]) ).

cnf(c_0_11848_1,axiom,
    ( X4 = X5
    | c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X2),c_List_Olist_OCons(X5,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X6,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11848]) ).

cnf(c_0_11848_2,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X2),c_List_Olist_OCons(X5,X3,X2),tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X6,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | X4 = X5
    | c_Nat_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize(X3,tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_11848]) ).

cnf(c_0_11849_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11849]) ).

cnf(c_0_11849_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat)
    | c_Divides_Oop_Advd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11849]) ).

cnf(c_0_11850_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11850]) ).

cnf(c_0_11850_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | c_Divides_Oop_Advd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11850]) ).

cnf(c_0_11851_0,axiom,
    ( c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5)
    | ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_11851]) ).

cnf(c_0_11851_1,axiom,
    ( ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5))
    | c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11851]) ).

cnf(c_0_11852_0,axiom,
    ( c_append(c_List_Ozip(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_append(X1,X2,X3),c_append(X4,X5,X6),X3,X6)
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X4,tc_List_Olist(X6))
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_11852]) ).

cnf(c_0_11852_1,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X4,tc_List_Olist(X6))
    | c_append(c_List_Ozip(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_append(X1,X2,X3),c_append(X4,X5,X6),X3,X6)
    | c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_11852]) ).

cnf(c_0_11852_2,axiom,
    ( c_Nat_Osize(X2,tc_List_Olist(X3)) != c_Nat_Osize(X5,tc_List_Olist(X6))
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X4,tc_List_Olist(X6))
    | c_append(c_List_Ozip(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_append(X1,X2,X3),c_append(X4,X5,X6),X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_11852]) ).

cnf(c_0_11853_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11853]) ).

cnf(c_0_11853_1,axiom,
    ( ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
    | c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11853]) ).

cnf(c_0_11856_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11856]) ).

cnf(c_0_11856_1,axiom,
    ( ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
    | c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11856]) ).

cnf(c_0_11857_0,axiom,
    ( c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11857]) ).

cnf(c_0_11857_1,axiom,
    ( ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11857]) ).

cnf(c_0_11857_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_11857]) ).

cnf(c_0_11858_0,axiom,
    ( c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11858]) ).

cnf(c_0_11858_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11858]) ).

cnf(c_0_11858_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11858]) ).

cnf(c_0_11859_0,axiom,
    ( c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11859]) ).

cnf(c_0_11859_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11859]) ).

cnf(c_0_11859_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11859]) ).

cnf(c_0_11860_0,axiom,
    ( c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11860]) ).

cnf(c_0_11860_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11860]) ).

cnf(c_0_11860_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11860]) ).

cnf(c_0_11861_0,axiom,
    ( c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11861]) ).

cnf(c_0_11861_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11861]) ).

cnf(c_0_11861_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11861]) ).

cnf(c_0_11863_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11863]) ).

cnf(c_0_11863_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11863]) ).

cnf(c_0_11864_0,axiom,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11864]) ).

cnf(c_0_11864_1,axiom,
    ( ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(X6,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11864]) ).

cnf(c_0_11864_2,axiom,
    ( ~ c_in(X6,X3,X4)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11864]) ).

cnf(c_0_11865_0,axiom,
    ( c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3) = X1
    | ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11865]) ).

cnf(c_0_11865_1,axiom,
    ( ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3))
    | c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11865]) ).

cnf(c_0_11867_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11867]) ).

cnf(c_0_11867_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11867]) ).

cnf(c_0_11868_0,axiom,
    ( c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11868]) ).

cnf(c_0_11868_1,axiom,
    ( ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11868]) ).

cnf(c_0_11868_2,axiom,
    ( ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_11868]) ).

cnf(c_0_11869_0,axiom,
    ( c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11869]) ).

cnf(c_0_11869_1,axiom,
    ( ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11869]) ).

cnf(c_0_11869_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_11869]) ).

cnf(c_0_11870_0,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) != c_Nat_Osize(X3,tc_List_Olist(X4))
    | c_Map_Omap__of(c_List_Ozip(X1,X3,X2,X4),X5,X2,X4) != c_Datatype_Ooption_ONone
    | ~ c_in(X5,c_List_Oset(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11870]) ).

cnf(c_0_11870_1,axiom,
    ( c_Map_Omap__of(c_List_Ozip(X1,X3,X2,X4),X5,X2,X4) != c_Datatype_Ooption_ONone
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_Nat_Osize(X3,tc_List_Olist(X4))
    | ~ c_in(X5,c_List_Oset(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11870]) ).

cnf(c_0_11870_2,axiom,
    ( ~ c_in(X5,c_List_Oset(X1,X2),X2)
    | c_Map_Omap__of(c_List_Ozip(X1,X3,X2,X4),X5,X2,X4) != c_Datatype_Ooption_ONone
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_Nat_Osize(X3,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11870]) ).

cnf(c_0_11871_0,axiom,
    ( c_Pair(c_List_Onth(X1,X5,X3),c_List_Onth(X2,X5,X4),X3,X4) = c_List_Onth(c_List_Ozip(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_less(X5,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_less(X5,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11871]) ).

cnf(c_0_11871_1,axiom,
    ( ~ c_less(X5,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | c_Pair(c_List_Onth(X1,X5,X3),c_List_Onth(X2,X5,X4),X3,X4) = c_List_Onth(c_List_Ozip(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_less(X5,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11871]) ).

cnf(c_0_11871_2,axiom,
    ( ~ c_less(X5,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat)
    | ~ c_less(X5,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | c_Pair(c_List_Onth(X1,X5,X3),c_List_Onth(X2,X5,X4),X3,X4) = c_List_Onth(c_List_Ozip(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11871]) ).

cnf(c_0_11872_0,axiom,
    ( c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11872]) ).

cnf(c_0_11872_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11872]) ).

cnf(c_0_11873_0,axiom,
    ( c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11873]) ).

cnf(c_0_11873_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) = c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11873]) ).

cnf(c_0_11877_0,axiom,
    ( c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11877]) ).

cnf(c_0_11877_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11877]) ).

cnf(c_0_11877_2,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X3,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11877]) ).

cnf(c_0_11882_0,axiom,
    ( c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4) = c_List_Olist__update(X1,X2,X5,X4)
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11882]) ).

cnf(c_0_11882_1,axiom,
    ( ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat)
    | c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4) = c_List_Olist__update(X1,X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11882]) ).

cnf(c_0_11883_0,axiom,
    ( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X2),c_Main_Olexord__Nil__left__2(X1,X2),X2) = X1
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11883]) ).

cnf(c_0_11883_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X2),c_Main_Olexord__Nil__left__2(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11883]) ).

cnf(c_0_11884_0,axiom,
    ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11884]) ).

cnf(c_0_11884_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11884]) ).

cnf(c_0_11884_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11884]) ).

cnf(c_0_11885_0,axiom,
    ( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
    | ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11885]) ).

cnf(c_0_11885_1,axiom,
    ( ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4))
    | c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11885]) ).

cnf(c_0_11886_0,axiom,
    ( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11886]) ).

cnf(c_0_11886_1,axiom,
    ( ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4))
    | c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11886]) ).

cnf(c_0_11889_0,axiom,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11889_1,axiom,
    ( ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11889_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11889_3,axiom,
    ( ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11889_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11889_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11889_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11889]) ).

cnf(c_0_11890_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11890_1,axiom,
    ( ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11890_2,axiom,
    ( ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11890_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11890_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11890_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11890_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11890]) ).

cnf(c_0_11891_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11891_1,axiom,
    ( ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11891_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11891_3,axiom,
    ( ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11891_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11891_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11891_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11891]) ).

cnf(c_0_11892_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11892_1,axiom,
    ( ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11892_2,axiom,
    ( ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11892_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11892_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11892_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11892_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11892]) ).

cnf(c_0_11893_0,axiom,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11893]) ).

cnf(c_0_11893_1,axiom,
    ( ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_11893]) ).

cnf(c_0_11894_0,axiom,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_11894]) ).

cnf(c_0_11894_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_11894]) ).

cnf(c_0_11898_0,axiom,
    ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11898]) ).

cnf(c_0_11898_1,axiom,
    ( ~ c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11898]) ).

cnf(c_0_11898_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_11898]) ).

cnf(c_0_11899_0,axiom,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11899_1,axiom,
    ( ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11899_2,axiom,
    ( ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11899_3,axiom,
    ( ~ c_less(X1,c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11899_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(X1,c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11899_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(X1,c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11899_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(X1,c_0,X4)
    | ~ c_less(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11899]) ).

cnf(c_0_11900_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11900_1,axiom,
    ( ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11900_2,axiom,
    ( ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11900_3,axiom,
    ( ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11900_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11900_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11900_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11900]) ).

cnf(c_0_11901_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11901_1,axiom,
    ( ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11901_2,axiom,
    ( ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11901_3,axiom,
    ( ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11901_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11901_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11901_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11901]) ).

cnf(c_0_11902_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11902_1,axiom,
    ( ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11902_2,axiom,
    ( ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11902_3,axiom,
    ( ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11902_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11902_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11902_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11902]) ).

cnf(c_0_11903_0,axiom,
    ( c_Nat_Opower(c_uminus(X1,X2),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2) = c_Nat_Opower(X1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11903]) ).

cnf(c_0_11903_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_Nat_Opower(c_uminus(X1,X2),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2) = c_Nat_Opower(X1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11903]) ).

cnf(c_0_11903_2,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_Nat_Opower(c_uminus(X1,X2),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2) = c_Nat_Opower(X1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3,tc_nat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11903]) ).

cnf(c_0_11904_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_11904]) ).

cnf(c_0_11904_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11904]) ).

cnf(c_0_11907_0,axiom,
    ( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
    | ~ c_Wellfounded__Recursion_Owf(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11907]) ).

cnf(c_0_11907_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X3,X2)
    | ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_11907]) ).

cnf(c_0_11908_0,axiom,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1
    | ~ c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11908]) ).

cnf(c_0_11908_1,axiom,
    ( ~ c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_11908]) ).

cnf(c_0_11909_0,axiom,
    ( X1 = X2
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11909]) ).

cnf(c_0_11909_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11909]) ).

cnf(c_0_11911_0,axiom,
    ( c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11911]) ).

cnf(c_0_11911_1,axiom,
    ( ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11911]) ).

cnf(c_0_11912_0,axiom,
    ( c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11912]) ).

cnf(c_0_11912_1,axiom,
    ( ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_11912]) ).

cnf(c_0_11915_0,axiom,
    ( c_Map_Omap__of(c_List_Ozip(X1,X2,X3,X4),X5,X3,X4) = c_Datatype_Ooption_ONone
    | c_in(X5,c_List_Oset(X1,X3),X3)
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11915]) ).

cnf(c_0_11915_1,axiom,
    ( c_in(X5,c_List_Oset(X1,X3),X3)
    | c_Map_Omap__of(c_List_Ozip(X1,X2,X3,X4),X5,X3,X4) = c_Datatype_Ooption_ONone
    | c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11915]) ).

cnf(c_0_11915_2,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X3)) != c_Nat_Osize(X2,tc_List_Olist(X4))
    | c_in(X5,c_List_Oset(X1,X3),X3)
    | c_Map_Omap__of(c_List_Ozip(X1,X2,X3,X4),X5,X3,X4) = c_Datatype_Ooption_ONone ),
    inference(literals_permutation,[status(thm)],[c_0_11915]) ).

cnf(c_0_11919_0,axiom,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11919]) ).

cnf(c_0_11919_1,axiom,
    ( ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11919]) ).

cnf(c_0_11922_0,axiom,
    ( X1 = X2
    | c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11922]) ).

cnf(c_0_11922_1,axiom,
    ( c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11922]) ).

cnf(c_0_11923_0,axiom,
    ( X1 = X2
    | c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11923]) ).

cnf(c_0_11923_1,axiom,
    ( c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11923]) ).

cnf(c_0_11924_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11924]) ).

cnf(c_0_11924_1,axiom,
    ( c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11924]) ).

cnf(c_0_11925_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_11925]) ).

cnf(c_0_11925_1,axiom,
    ( c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_11925]) ).

cnf(c_0_11926_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11926]) ).

cnf(c_0_11926_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11926]) ).

cnf(c_0_11926_2,axiom,
    ( ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11926]) ).

cnf(c_0_11926_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11926]) ).

cnf(c_0_11926_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11926]) ).

cnf(c_0_11927_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11927]) ).

cnf(c_0_11927_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11927]) ).

cnf(c_0_11927_2,axiom,
    ( ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11927]) ).

cnf(c_0_11927_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11927]) ).

cnf(c_0_11927_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11927]) ).

cnf(c_0_11928_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11928]) ).

cnf(c_0_11928_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11928]) ).

cnf(c_0_11928_2,axiom,
    ( ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11928]) ).

cnf(c_0_11928_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11928]) ).

cnf(c_0_11928_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11928]) ).

cnf(c_0_11929_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11929]) ).

cnf(c_0_11929_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11929]) ).

cnf(c_0_11929_2,axiom,
    ( ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11929]) ).

cnf(c_0_11929_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11929]) ).

cnf(c_0_11929_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11929]) ).

cnf(c_0_11930_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11930]) ).

cnf(c_0_11930_1,axiom,
    ( ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11930]) ).

cnf(c_0_11930_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11930]) ).

cnf(c_0_11930_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11930]) ).

cnf(c_0_11930_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11930]) ).

cnf(c_0_11931_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11931]) ).

cnf(c_0_11931_1,axiom,
    ( ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11931]) ).

cnf(c_0_11931_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11931]) ).

cnf(c_0_11931_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11931]) ).

cnf(c_0_11931_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11931]) ).

cnf(c_0_11932_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11932]) ).

cnf(c_0_11932_1,axiom,
    ( ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11932]) ).

cnf(c_0_11932_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11932]) ).

cnf(c_0_11932_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11932]) ).

cnf(c_0_11932_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_Numeral_Onumber__of(X4,X3),c_0,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11932]) ).

cnf(c_0_11933_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11933]) ).

cnf(c_0_11933_1,axiom,
    ( ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11933]) ).

cnf(c_0_11933_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11933]) ).

cnf(c_0_11933_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11933]) ).

cnf(c_0_11933_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X4,X3),X3)
    | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X4,X3),X1,X3),c_times(c_Numeral_Onumber__of(X4,X3),X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11933]) ).

cnf(c_0_11934_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11934_1,axiom,
    ( c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11934_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11934_3,axiom,
    ( ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11934_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11934_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11934_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11934]) ).

cnf(c_0_11935_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11935_1,axiom,
    ( c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11935_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11935_3,axiom,
    ( ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11935_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11935_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11935_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X4,c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11935]) ).

cnf(c_0_11936_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11936_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11936_2,axiom,
    ( ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11936_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11936_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11936_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11936_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11936]) ).

cnf(c_0_11937_0,axiom,
    ( c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11937_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11937_2,axiom,
    ( ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11937_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11937_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11937_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11937_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(X2,c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11937]) ).

cnf(c_0_11938_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11938_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11938_2,axiom,
    ( ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11938_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11938_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11938_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11938_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11938]) ).

cnf(c_0_11939_0,axiom,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11939_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11939_2,axiom,
    ( ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11939_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11939_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11939_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11939_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11939]) ).

cnf(c_0_11940_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11940_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11940_2,axiom,
    ( ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11940_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11940_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11940_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11940_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11940]) ).

cnf(c_0_11941_0,axiom,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11941_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11941_2,axiom,
    ( ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11941_3,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11941_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11941_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11941_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11941]) ).

cnf(c_0_11942_0,axiom,
    ( c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_11942]) ).

cnf(c_0_11942_1,axiom,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) != c_1
    | c_less(c_0,c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11942]) ).

cnf(c_0_11944_0,axiom,
    ( c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2))
    | ~ c_in(X1,X5,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11944]) ).

cnf(c_0_11944_1,axiom,
    ( ~ c_in(X1,X5,X2)
    | c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_11944]) ).

cnf(c_0_11945_0,axiom,
    ( c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3))
    | ~ c_in(X1,X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11945]) ).

cnf(c_0_11945_1,axiom,
    ( ~ c_in(X1,X4,X2)
    | c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11945]) ).

cnf(c_0_11947_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11947_1,axiom,
    ( c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11947_2,axiom,
    ( ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11947_3,axiom,
    ( ~ c_less(X3,c_0,X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11947_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11947_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11947_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X4,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11947]) ).

cnf(c_0_11948_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11948_1,axiom,
    ( c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11948_2,axiom,
    ( ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11948_3,axiom,
    ( ~ c_less(X3,c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11948_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11948_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11948_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X4,c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11948]) ).

cnf(c_0_11949_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11949_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11949_2,axiom,
    ( ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11949_3,axiom,
    ( ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11949_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11949_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11949_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11949]) ).

cnf(c_0_11950_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11950_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11950_2,axiom,
    ( ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11950_3,axiom,
    ( ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11950_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11950_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11950_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ c_lessequals(X2,c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11950]) ).

cnf(c_0_11951_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11951_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11951_2,axiom,
    ( ~ c_less(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11951_3,axiom,
    ( ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11951_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11951_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11951_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11951]) ).

cnf(c_0_11952_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11952_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11952_2,axiom,
    ( ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11952_3,axiom,
    ( ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11952_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11952_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11952_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X4,X3)
    | ~ c_less(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11952]) ).

cnf(c_0_11953_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11953_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11953_2,axiom,
    ( ~ c_lessequals(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11953_3,axiom,
    ( ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11953_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11953_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11953_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11953]) ).

cnf(c_0_11954_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11954_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11954_2,axiom,
    ( ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11954_3,axiom,
    ( ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11954_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11954_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11954_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ c_lessequals(c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11954]) ).

cnf(c_0_11957_0,axiom,
    ( c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11957]) ).

cnf(c_0_11957_1,axiom,
    ( ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11957]) ).

cnf(c_0_11957_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11957]) ).

cnf(c_0_11957_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11957]) ).

cnf(c_0_11957_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11957]) ).

cnf(c_0_11957_5,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11957]) ).

cnf(c_0_11958_0,axiom,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11958]) ).

cnf(c_0_11958_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11958]) ).

cnf(c_0_11958_2,axiom,
    ( ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11958]) ).

cnf(c_0_11958_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11958]) ).

cnf(c_0_11958_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11958]) ).

cnf(c_0_11958_5,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11958]) ).

cnf(c_0_11959_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11959]) ).

cnf(c_0_11959_1,axiom,
    ( ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11959]) ).

cnf(c_0_11959_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11959]) ).

cnf(c_0_11959_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11959]) ).

cnf(c_0_11959_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11959]) ).

cnf(c_0_11959_5,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_times(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11959]) ).

cnf(c_0_11960_0,axiom,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11960]) ).

cnf(c_0_11960_1,axiom,
    ( ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11960]) ).

cnf(c_0_11960_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11960]) ).

cnf(c_0_11960_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11960]) ).

cnf(c_0_11960_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11960]) ).

cnf(c_0_11960_5,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11960]) ).

cnf(c_0_11961_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11961]) ).

cnf(c_0_11961_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11961]) ).

cnf(c_0_11961_2,axiom,
    ( ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11961]) ).

cnf(c_0_11961_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11961]) ).

cnf(c_0_11961_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11961]) ).

cnf(c_0_11961_5,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11961]) ).

cnf(c_0_11962_0,axiom,
    ( c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11962]) ).

cnf(c_0_11962_1,axiom,
    ( ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11962]) ).

cnf(c_0_11962_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11962]) ).

cnf(c_0_11962_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11962]) ).

cnf(c_0_11962_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11962]) ).

cnf(c_0_11962_5,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_less(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_less(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11962]) ).

cnf(c_0_11963_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11963]) ).

cnf(c_0_11963_1,axiom,
    ( ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11963]) ).

cnf(c_0_11963_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11963]) ).

cnf(c_0_11963_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11963]) ).

cnf(c_0_11963_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11963]) ).

cnf(c_0_11963_5,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X1,c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11963]) ).

cnf(c_0_11964_0,axiom,
    ( c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11964]) ).

cnf(c_0_11964_1,axiom,
    ( ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11964]) ).

cnf(c_0_11964_2,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11964]) ).

cnf(c_0_11964_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11964]) ).

cnf(c_0_11964_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11964]) ).

cnf(c_0_11964_5,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_times(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11964]) ).

cnf(c_0_11966_0,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X2,X4) = X3
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11966]) ).

cnf(c_0_11966_1,axiom,
    ( ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X4)),tc_nat)
    | c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X2,X4) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_11966]) ).

cnf(c_0_11967_0,axiom,
    ( c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2))
    | ~ c_in(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11967]) ).

cnf(c_0_11967_1,axiom,
    ( ~ c_in(X1,X3,X2)
    | c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_11967]) ).

cnf(c_0_11968_0,axiom,
    ( c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11968]) ).

cnf(c_0_11968_1,axiom,
    ( ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11968]) ).

cnf(c_0_11969_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Olist_OCons(X2,c_List_Otake(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4),X4) = c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11969]) ).

cnf(c_0_11969_1,axiom,
    ( c_List_Olist_OCons(X2,c_List_Otake(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4),X4) = c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_11969]) ).

cnf(c_0_11970_0,axiom,
    ( c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11970]) ).

cnf(c_0_11970_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_11970]) ).

cnf(c_0_11971_0,axiom,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_11971]) ).

cnf(c_0_11971_1,axiom,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_11971]) ).

cnf(c_0_11972_0,axiom,
    ( c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3) = X1
    | ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_11972]) ).

cnf(c_0_11972_1,axiom,
    ( ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3))
    | c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_11972]) ).

cnf(c_0_11973_0,axiom,
    ( c_List_Onth(c_List_Odrop(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_plus(X1,X4,tc_nat),X3)
    | ~ c_lessequals(c_plus(X1,X4,tc_nat),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11973]) ).

cnf(c_0_11973_1,axiom,
    ( ~ c_lessequals(c_plus(X1,X4,tc_nat),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat)
    | c_List_Onth(c_List_Odrop(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_plus(X1,X4,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11973]) ).

cnf(c_0_11975_0,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_11975]) ).

cnf(c_0_11975_1,axiom,
    ( X2 = X5
    | c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11975]) ).

cnf(c_0_11976_0,axiom,
    ( c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_plus(X3,c_div(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11976]) ).

cnf(c_0_11976_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_plus(X3,c_div(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11976]) ).

cnf(c_0_11977_0,axiom,
    ( c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_plus(X2,c_div(X1,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11977]) ).

cnf(c_0_11977_1,axiom,
    ( ~ c_less(c_0,X3,tc_nat)
    | c_div(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_plus(X2,c_div(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11977]) ).

cnf(c_0_11982_0,axiom,
    ( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11982]) ).

cnf(c_0_11982_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11982]) ).

cnf(c_0_11982_2,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X2,X4)
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11982]) ).

cnf(c_0_11983_0,axiom,
    ( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X1,X3)
    | ~ c_Relation_Otrans(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11983]) ).

cnf(c_0_11983_1,axiom,
    ( ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11983]) ).

cnf(c_0_11983_2,axiom,
    ( ~ c_Relation_Otrans(X2,X4)
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_11983]) ).

cnf(c_0_11984_0,axiom,
    ( c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg))
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_11984]) ).

cnf(c_0_11984_1,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_11984]) ).

cnf(c_0_11985_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11985]) ).

cnf(c_0_11985_1,axiom,
    ( ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_less(X1,X2,tc_nat)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11985]) ).

cnf(c_0_11985_2,axiom,
    ( ~ c_less(c_1,X3,X4)
    | ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_less(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11985]) ).

cnf(c_0_11985_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ c_less(c_1,X3,X4)
    | ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_less(X1,X2,tc_nat)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11985]) ).

cnf(c_0_11985_4,axiom,
    ( ~ class_Power_Orecpower(X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ c_less(c_1,X3,X4)
    | ~ c_less(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11985]) ).

cnf(c_0_11986_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11986]) ).

cnf(c_0_11986_1,axiom,
    ( ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11986]) ).

cnf(c_0_11986_2,axiom,
    ( ~ c_less(c_1,X3,X4)
    | ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11986]) ).

cnf(c_0_11986_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ c_less(c_1,X3,X4)
    | ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_lessequals(X1,X2,tc_nat)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_11986]) ).

cnf(c_0_11986_4,axiom,
    ( ~ class_Power_Orecpower(X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ c_less(c_1,X3,X4)
    | ~ c_lessequals(c_Nat_Opower(X3,X1,X4),c_Nat_Opower(X3,X2,X4),X4)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_11986]) ).

cnf(c_0_11987_0,axiom,
    ( c_plus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_plus(X3,X4,X2),X2)
    | ~ class_Ring__and__Field_Osemiring(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11987]) ).

cnf(c_0_11987_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X2)
    | c_plus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_plus(X3,X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11987]) ).

cnf(c_0_11987_2,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Osemiring(X2)
    | c_plus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_plus(X3,X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11987]) ).

cnf(c_0_11988_0,axiom,
    ( c_minus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_minus(X3,X4,X2),X2)
    | ~ class_Ring__and__Field_Oring(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11988]) ).

cnf(c_0_11988_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X2)
    | c_minus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_minus(X3,X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11988]) ).

cnf(c_0_11988_2,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oring(X2)
    | c_minus(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_minus(X3,X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11988]) ).

cnf(c_0_11989_0,axiom,
    ( c_plus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_plus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Osemiring(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11989]) ).

cnf(c_0_11989_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X3)
    | c_plus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_plus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11989]) ).

cnf(c_0_11989_2,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Osemiring(X3)
    | c_plus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_plus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11989]) ).

cnf(c_0_11990_0,axiom,
    ( c_minus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_minus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Ring__and__Field_Oring(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11990]) ).

cnf(c_0_11990_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X3)
    | c_minus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_minus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11990]) ).

cnf(c_0_11990_2,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oring(X3)
    | c_minus(c_times(X1,c_Numeral_Onumber__of(X4,X3),X3),c_times(X2,c_Numeral_Onumber__of(X4,X3),X3),X3) = c_times(c_minus(X1,X2,X3),c_Numeral_Onumber__of(X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11990]) ).

cnf(c_0_11992_0,axiom,
    ( ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11992]) ).

cnf(c_0_11992_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11992]) ).

cnf(c_0_11992_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11992]) ).

cnf(c_0_11992_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11992]) ).

cnf(c_0_11993_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11993_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11993_2,axiom,
    ( c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11993_3,axiom,
    ( ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11993_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11993_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11993_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11993]) ).

cnf(c_0_11994_0,axiom,
    ( c_lessequals(X1,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11994_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11994_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11994_3,axiom,
    ( ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11994_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11994_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11994_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11994]) ).

cnf(c_0_11995_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11995_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11995_2,axiom,
    ( c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11995_3,axiom,
    ( ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11995_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11995_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11995_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11995]) ).

cnf(c_0_11996_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11996_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11996_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11996_3,axiom,
    ( ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11996_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11996_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11996_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(X4,c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X2),X2)
    | c_less(c_Numeral_Onumber__of(X3,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11996]) ).

cnf(c_0_11997_0,axiom,
    ( c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11997]) ).

cnf(c_0_11997_1,axiom,
    ( ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11997]) ).

cnf(c_0_11997_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11997]) ).

cnf(c_0_11997_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11997]) ).

cnf(c_0_11997_4,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X2),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11997]) ).

cnf(c_0_11998_0,axiom,
    ( c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(X1,X4,X3)
    | ~ c_less(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11998]) ).

cnf(c_0_11998_1,axiom,
    ( ~ c_less(X1,X4,X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11998]) ).

cnf(c_0_11998_2,axiom,
    ( ~ c_less(X4,X1,X3)
    | ~ c_less(X1,X4,X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11998]) ).

cnf(c_0_11998_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(X4,X1,X3)
    | ~ c_less(X1,X4,X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11998]) ).

cnf(c_0_11998_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_less(X4,X1,X3)
    | ~ c_less(X1,X4,X3)
    | c_less(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_11998]) ).

cnf(c_0_11999_0,axiom,
    ( c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11999]) ).

cnf(c_0_11999_1,axiom,
    ( ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11999]) ).

cnf(c_0_11999_2,axiom,
    ( ~ c_less(X4,X3,X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11999]) ).

cnf(c_0_11999_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X4,X3,X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11999]) ).

cnf(c_0_11999_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X4,X3,X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_11999]) ).

cnf(c_0_12000_0,axiom,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12000]) ).

cnf(c_0_12000_1,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12000]) ).

cnf(c_0_12000_2,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12000]) ).

cnf(c_0_12000_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12000]) ).

cnf(c_0_12000_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12000]) ).

cnf(c_0_12001_0,axiom,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12001]) ).

cnf(c_0_12001_1,axiom,
    ( ~ c_lessequals(X3,X4,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12001]) ).

cnf(c_0_12001_2,axiom,
    ( ~ c_lessequals(X4,X3,X2)
    | ~ c_lessequals(X3,X4,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12001]) ).

cnf(c_0_12001_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ c_lessequals(X3,X4,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12001]) ).

cnf(c_0_12001_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ c_lessequals(X3,X4,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12001]) ).

cnf(c_0_12002_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12002]) ).

cnf(c_0_12002_1,axiom,
    ( c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12002]) ).

cnf(c_0_12002_2,axiom,
    ( ~ c_less(X3,X4,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12002]) ).

cnf(c_0_12002_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12002]) ).

cnf(c_0_12002_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12002]) ).

cnf(c_0_12003_0,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12003]) ).

cnf(c_0_12003_1,axiom,
    ( c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12003]) ).

cnf(c_0_12003_2,axiom,
    ( ~ c_less(X4,X3,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12003]) ).

cnf(c_0_12003_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X4,X3,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12003]) ).

cnf(c_0_12003_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X4,X3,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12003]) ).

cnf(c_0_12004_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12004]) ).

cnf(c_0_12004_1,axiom,
    ( c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12004]) ).

cnf(c_0_12004_2,axiom,
    ( ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12004]) ).

cnf(c_0_12004_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12004]) ).

cnf(c_0_12004_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X3,X4,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12004]) ).

cnf(c_0_12005_0,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12005]) ).

cnf(c_0_12005_1,axiom,
    ( c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12005]) ).

cnf(c_0_12005_2,axiom,
    ( ~ c_less(X4,X3,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12005]) ).

cnf(c_0_12005_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X4,X3,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12005]) ).

cnf(c_0_12005_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_less(X4,X3,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12005]) ).

cnf(c_0_12006_0,axiom,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12006]) ).

cnf(c_0_12006_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12006]) ).

cnf(c_0_12006_2,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12006]) ).

cnf(c_0_12006_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12006]) ).

cnf(c_0_12006_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12006]) ).

cnf(c_0_12007_0,axiom,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12007]) ).

cnf(c_0_12007_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12007]) ).

cnf(c_0_12007_2,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12007]) ).

cnf(c_0_12007_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(X4,X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12007]) ).

cnf(c_0_12007_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(X4,X1,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12007]) ).

cnf(c_0_12008_0,axiom,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12008]) ).

cnf(c_0_12008_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12008]) ).

cnf(c_0_12008_2,axiom,
    ( ~ c_lessequals(X3,X4,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12008]) ).

cnf(c_0_12008_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X3,X4,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12008]) ).

cnf(c_0_12008_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X3,X4,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12008]) ).

cnf(c_0_12009_0,axiom,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12009]) ).

cnf(c_0_12009_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ c_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12009]) ).

cnf(c_0_12009_2,axiom,
    ( ~ c_lessequals(X4,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12009]) ).

cnf(c_0_12009_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X4,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12009]) ).

cnf(c_0_12009_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X4,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12009]) ).

cnf(c_0_12010_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X5,X4,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12010]) ).

cnf(c_0_12010_1,axiom,
    ( c_lessequals(X1,X4,X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X5,X4,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12010]) ).

cnf(c_0_12010_2,axiom,
    ( ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X5,X4,X3),tc_set(X3))
    | c_lessequals(X1,X4,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12010]) ).

cnf(c_0_12010_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X5,X4,X3),tc_set(X3))
    | c_lessequals(X1,X4,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12010]) ).

cnf(c_0_12011_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12011]) ).

cnf(c_0_12011_1,axiom,
    ( c_lessequals(X4,X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12011]) ).

cnf(c_0_12011_2,axiom,
    ( ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | c_lessequals(X4,X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12011]) ).

cnf(c_0_12011_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X2,X1,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | c_lessequals(X4,X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12011]) ).

cnf(c_0_12016_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12016]) ).

cnf(c_0_12016_1,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12016]) ).

cnf(c_0_12016_2,axiom,
    ( c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12016]) ).

cnf(c_0_12016_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12016]) ).

cnf(c_0_12016_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_less(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_times(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12016]) ).

cnf(c_0_12017_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12017]) ).

cnf(c_0_12017_1,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12017]) ).

cnf(c_0_12017_2,axiom,
    ( c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12017]) ).

cnf(c_0_12017_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12017]) ).

cnf(c_0_12017_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_less(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12017]) ).

cnf(c_0_12018_0,axiom,
    ( c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12018]) ).

cnf(c_0_12018_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12018]) ).

cnf(c_0_12018_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12018]) ).

cnf(c_0_12018_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12018]) ).

cnf(c_0_12018_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_times(X4,c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12018]) ).

cnf(c_0_12019_0,axiom,
    ( c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12019]) ).

cnf(c_0_12019_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12019]) ).

cnf(c_0_12019_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12019]) ).

cnf(c_0_12019_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12019]) ).

cnf(c_0_12019_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_times(c_Numeral_Onumber__of(X1,X2),X3,X2),c_times(c_Numeral_Onumber__of(X1,X2),X4,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12019]) ).

cnf(c_0_12020_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12020]) ).

cnf(c_0_12020_1,axiom,
    ( ~ c_lessequals(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12020]) ).

cnf(c_0_12020_2,axiom,
    ( ~ c_less(c_0,X3,tc_nat)
    | ~ c_lessequals(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12020]) ).

cnf(c_0_12021_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12021]) ).

cnf(c_0_12021_1,axiom,
    ( ~ c_lessequals(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_less(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12021]) ).

cnf(c_0_12021_2,axiom,
    ( ~ c_less(c_0,X3,tc_nat)
    | ~ c_lessequals(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12021]) ).

cnf(c_0_12022_0,axiom,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(c_List_Osublist(X2,X4,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12022]) ).

cnf(c_0_12022_1,axiom,
    ( ~ c_in(X1,c_List_Oset(c_List_Osublist(X2,X4,X3),X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12022]) ).

cnf(c_0_12023_0,axiom,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(c_List_Oremove1(X4,X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12023]) ).

cnf(c_0_12023_1,axiom,
    ( ~ c_in(X1,c_List_Oset(c_List_Oremove1(X4,X2,X3),X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12023]) ).

cnf(c_0_12024_0,axiom,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12024]) ).

cnf(c_0_12024_1,axiom,
    ( c_in(X1,c_Message_Oparts(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12024]) ).

cnf(c_0_12024_2,axiom,
    ( ~ c_in(X1,c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg)),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12024]) ).

cnf(c_0_12027_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12027]) ).

cnf(c_0_12027_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12027]) ).

cnf(c_0_12027_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12027]) ).

cnf(c_0_12027_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12027]) ).

cnf(c_0_12028_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12028]) ).

cnf(c_0_12028_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12028]) ).

cnf(c_0_12028_2,axiom,
    ( ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12028]) ).

cnf(c_0_12028_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12028]) ).

cnf(c_0_12028_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12028]) ).

cnf(c_0_12028_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12028]) ).

cnf(c_0_12029_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12029]) ).

cnf(c_0_12029_1,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12029]) ).

cnf(c_0_12029_2,axiom,
    ( ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12029]) ).

cnf(c_0_12029_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12029]) ).

cnf(c_0_12029_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12029]) ).

cnf(c_0_12029_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12029]) ).

cnf(c_0_12030_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12030]) ).

cnf(c_0_12030_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12030]) ).

cnf(c_0_12030_2,axiom,
    ( ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12030]) ).

cnf(c_0_12030_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12030]) ).

cnf(c_0_12030_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12030]) ).

cnf(c_0_12030_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12030]) ).

cnf(c_0_12031_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12031]) ).

cnf(c_0_12031_1,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12031]) ).

cnf(c_0_12031_2,axiom,
    ( ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12031]) ).

cnf(c_0_12031_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12031]) ).

cnf(c_0_12031_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12031]) ).

cnf(c_0_12031_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12031]) ).

cnf(c_0_12032_0,axiom,
    ( c_minus(c_Suc(c_minus(X1,X2,tc_nat)),X3,tc_nat) = c_minus(c_Suc(X1),c_plus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12032]) ).

cnf(c_0_12032_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_minus(c_Suc(c_minus(X1,X2,tc_nat)),X3,tc_nat) = c_minus(c_Suc(X1),c_plus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12032]) ).

cnf(c_0_12033_0,axiom,
    ( c_minus(c_plus(X1,X3,tc_nat),c_Suc(X2),tc_nat) = c_minus(X1,c_Suc(c_minus(X2,X3,tc_nat)),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12033]) ).

cnf(c_0_12033_1,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | c_minus(c_plus(X1,X3,tc_nat),c_Suc(X2),tc_nat) = c_minus(X1,c_Suc(c_minus(X2,X3,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12033]) ).

cnf(c_0_12034_0,axiom,
    ( X1 = X2
    | c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12034]) ).

cnf(c_0_12034_1,axiom,
    ( c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12034]) ).

cnf(c_0_12035_0,axiom,
    ( X1 = X2
    | c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12035]) ).

cnf(c_0_12035_1,axiom,
    ( c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12035]) ).

cnf(c_0_12036_0,axiom,
    ( c_List_Olist__update(X1,X2,c_List_Onth(X1,X2,X3),X3) = X1
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12036]) ).

cnf(c_0_12036_1,axiom,
    ( ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | c_List_Olist__update(X1,X2,c_List_Onth(X1,X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12036]) ).

cnf(c_0_12039_0,axiom,
    ( c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | X2 = c_Numeral_Obit_OB0
    | c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12039]) ).

cnf(c_0_12039_1,axiom,
    ( X2 = c_Numeral_Obit_OB0
    | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12039]) ).

cnf(c_0_12039_2,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | X2 = c_Numeral_Obit_OB0
    | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12039]) ).

cnf(c_0_12043_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12043]) ).

cnf(c_0_12043_1,axiom,
    ( c_less(c_0,X3,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12043]) ).

cnf(c_0_12043_2,axiom,
    ( ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,X3,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12043]) ).

cnf(c_0_12043_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,X3,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12043]) ).

cnf(c_0_12043_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,X3,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12043]) ).

cnf(c_0_12043_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(c_0,X3,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12043]) ).

cnf(c_0_12044_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12044]) ).

cnf(c_0_12044_1,axiom,
    ( c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12044]) ).

cnf(c_0_12044_2,axiom,
    ( ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12044]) ).

cnf(c_0_12044_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12044]) ).

cnf(c_0_12044_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12044]) ).

cnf(c_0_12044_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_less(X3,c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12044]) ).

cnf(c_0_12045_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12045]) ).

cnf(c_0_12045_1,axiom,
    ( c_lessequals(c_0,X3,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12045]) ).

cnf(c_0_12045_2,axiom,
    ( ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12045]) ).

cnf(c_0_12045_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12045]) ).

cnf(c_0_12045_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12045]) ).

cnf(c_0_12045_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12045]) ).

cnf(c_0_12046_0,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12046]) ).

cnf(c_0_12046_1,axiom,
    ( c_lessequals(X3,c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12046]) ).

cnf(c_0_12046_2,axiom,
    ( ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12046]) ).

cnf(c_0_12046_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12046]) ).

cnf(c_0_12046_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12046]) ).

cnf(c_0_12046_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12046]) ).

cnf(c_0_12047_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12047]) ).

cnf(c_0_12047_1,axiom,
    ( c_less(X3,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12047]) ).

cnf(c_0_12047_2,axiom,
    ( ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12047]) ).

cnf(c_0_12047_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12047]) ).

cnf(c_0_12047_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12047]) ).

cnf(c_0_12047_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(X3,c_0,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12047]) ).

cnf(c_0_12048_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,X3,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12048]) ).

cnf(c_0_12048_1,axiom,
    ( c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12048]) ).

cnf(c_0_12048_2,axiom,
    ( ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12048]) ).

cnf(c_0_12048_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12048]) ).

cnf(c_0_12048_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12048]) ).

cnf(c_0_12048_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_less(c_0,X3,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12048]) ).

cnf(c_0_12049_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12049]) ).

cnf(c_0_12049_1,axiom,
    ( c_lessequals(X3,c_0,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12049]) ).

cnf(c_0_12049_2,axiom,
    ( ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12049]) ).

cnf(c_0_12049_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12049]) ).

cnf(c_0_12049_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12049]) ).

cnf(c_0_12049_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(X3,c_0,X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12049]) ).

cnf(c_0_12050_0,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12050]) ).

cnf(c_0_12050_1,axiom,
    ( c_lessequals(c_0,X3,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12050]) ).

cnf(c_0_12050_2,axiom,
    ( ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12050]) ).

cnf(c_0_12050_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12050]) ).

cnf(c_0_12050_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12050]) ).

cnf(c_0_12050_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | c_lessequals(c_0,X3,X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12050]) ).

cnf(c_0_12051_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12051]) ).

cnf(c_0_12051_1,axiom,
    ( ~ c_less(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12051]) ).

cnf(c_0_12051_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_less(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12051]) ).

cnf(c_0_12052_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12052]) ).

cnf(c_0_12052_1,axiom,
    ( ~ c_less(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12052]) ).

cnf(c_0_12052_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_less(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12052]) ).

cnf(c_0_12053_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12053]) ).

cnf(c_0_12053_1,axiom,
    ( ~ c_lessequals(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12053]) ).

cnf(c_0_12053_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(c_plus(X1,X4,X3),c_plus(X2,X4,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12053]) ).

cnf(c_0_12054_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12054]) ).

cnf(c_0_12054_1,axiom,
    ( ~ c_lessequals(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12054]) ).

cnf(c_0_12054_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(c_plus(X4,X1,X3),c_plus(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12054]) ).

cnf(c_0_12055_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12055_1,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12055_2,axiom,
    ( c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12055_3,axiom,
    ( ~ c_less(X3,c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12055_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12055_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12055_6,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | c_less(X3,c_divide(X4,c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12055]) ).

cnf(c_0_12056_0,axiom,
    ( c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12056_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12056_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ c_lessequals(X1,c_0,X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12056_3,axiom,
    ( ~ c_lessequals(X1,c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12056_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12056_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4)
    | ~ class_Numeral_Onumber(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12056_6,axiom,
    ( ~ class_Numeral_Onumber(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Oordered__field(X4)
    | ~ c_lessequals(X1,c_0,X4)
    | c_less(c_0,c_Numeral_Onumber__of(X3,X4),X4)
    | c_less(c_Numeral_Onumber__of(X3,X4),c_0,X4)
    | c_lessequals(X1,c_divide(X2,c_Numeral_Onumber__of(X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12056]) ).

cnf(c_0_12057_0,axiom,
    ( c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12057_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12057_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_less(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12057_3,axiom,
    ( ~ c_less(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12057_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12057_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12057_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12057]) ).

cnf(c_0_12058_0,axiom,
    ( c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12058_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12058_2,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ c_lessequals(c_0,X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12058_3,axiom,
    ( ~ c_lessequals(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12058_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12058_5,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12058_6,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_lessequals(c_0,X4,X3)
    | c_less(c_0,c_Numeral_Onumber__of(X2,X3),X3)
    | c_less(c_Numeral_Onumber__of(X2,X3),c_0,X3)
    | c_lessequals(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12058]) ).

cnf(c_0_12065_0,axiom,
    ( c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12065]) ).

cnf(c_0_12065_1,axiom,
    ( ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12065]) ).

cnf(c_0_12065_2,axiom,
    ( ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12065]) ).

cnf(c_0_12066_0,axiom,
    ( c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12066]) ).

cnf(c_0_12066_1,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12066]) ).

cnf(c_0_12066_2,axiom,
    ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12066]) ).

cnf(c_0_12066_3,axiom,
    ( ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12066]) ).

cnf(c_0_12067_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12067]) ).

cnf(c_0_12067_1,axiom,
    ( ~ c_less(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12067]) ).

cnf(c_0_12068_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12068]) ).

cnf(c_0_12068_1,axiom,
    ( ~ c_lessequals(c_plus(X3,X1,tc_nat),c_plus(X3,X2,tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12068]) ).

cnf(c_0_12069_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12069]) ).

cnf(c_0_12069_1,axiom,
    ( ~ c_less(c_times(X1,X3,tc_nat),c_times(X2,X3,tc_nat),tc_nat)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12069]) ).

cnf(c_0_12070_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12070]) ).

cnf(c_0_12070_1,axiom,
    ( ~ c_less(c_times(X3,X1,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12070]) ).

cnf(c_0_12073_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_times(X2,X1,tc_nat),c_times(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12073]) ).

cnf(c_0_12073_1,axiom,
    ( ~ c_less(c_times(X2,X1,tc_nat),c_times(X3,X1,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12073]) ).

cnf(c_0_12074_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12074]) ).

cnf(c_0_12074_1,axiom,
    ( ~ c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12074]) ).

cnf(c_0_12075_0,axiom,
    ( c_less(c_0,X1,X2)
    | c_less(X1,c_0,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12075]) ).

cnf(c_0_12075_1,axiom,
    ( c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12075]) ).

cnf(c_0_12075_2,axiom,
    ( ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12075]) ).

cnf(c_0_12075_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12075]) ).

cnf(c_0_12075_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12075]) ).

cnf(c_0_12075_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12075]) ).

cnf(c_0_12076_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12076]) ).

cnf(c_0_12076_1,axiom,
    ( c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12076]) ).

cnf(c_0_12076_2,axiom,
    ( ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12076]) ).

cnf(c_0_12076_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12076]) ).

cnf(c_0_12076_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12076]) ).

cnf(c_0_12076_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12076]) ).

cnf(c_0_12077_0,axiom,
    ( c_less(c_0,X1,X2)
    | c_less(X1,c_0,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12077]) ).

cnf(c_0_12077_1,axiom,
    ( c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12077]) ).

cnf(c_0_12077_2,axiom,
    ( ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12077]) ).

cnf(c_0_12077_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12077]) ).

cnf(c_0_12077_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12077]) ).

cnf(c_0_12077_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | c_less(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12077]) ).

cnf(c_0_12078_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12078]) ).

cnf(c_0_12078_1,axiom,
    ( c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12078]) ).

cnf(c_0_12078_2,axiom,
    ( ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12078]) ).

cnf(c_0_12078_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12078]) ).

cnf(c_0_12078_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12078]) ).

cnf(c_0_12078_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X3,X2),X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12078]) ).

cnf(c_0_12080_0,axiom,
    ( c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X2,X5,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12080]) ).

cnf(c_0_12080_1,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X2,X5,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12080]) ).

cnf(c_0_12080_2,axiom,
    ( ~ c_lessequals(X2,X5,X3)
    | ~ c_lessequals(X4,X1,X3)
    | c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12080]) ).

cnf(c_0_12080_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X2,X5,X3)
    | ~ c_lessequals(X4,X1,X3)
    | c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12080]) ).

cnf(c_0_12081_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12081]) ).

cnf(c_0_12081_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12081]) ).

cnf(c_0_12081_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_12081]) ).

cnf(c_0_12082_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12082]) ).

cnf(c_0_12082_1,axiom,
    ( ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_12082]) ).

cnf(c_0_12084_0,axiom,
    ( c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_less(c_1,X1,X3)
    | ~ c_less(X2,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12084]) ).

cnf(c_0_12084_1,axiom,
    ( ~ c_less(c_1,X1,X3)
    | c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_less(X2,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12084]) ).

cnf(c_0_12084_2,axiom,
    ( ~ c_less(X2,X4,tc_nat)
    | ~ c_less(c_1,X1,X3)
    | c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12084]) ).

cnf(c_0_12084_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_less(X2,X4,tc_nat)
    | ~ c_less(c_1,X1,X3)
    | c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12084]) ).

cnf(c_0_12084_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_less(X2,X4,tc_nat)
    | ~ c_less(c_1,X1,X3)
    | c_less(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12084]) ).

cnf(c_0_12085_0,axiom,
    ( c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_less(c_1,X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12085]) ).

cnf(c_0_12085_1,axiom,
    ( ~ c_lessequals(X2,X4,tc_nat)
    | c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ c_less(c_1,X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12085]) ).

cnf(c_0_12085_2,axiom,
    ( ~ c_less(c_1,X1,X3)
    | ~ c_lessequals(X2,X4,tc_nat)
    | c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12085]) ).

cnf(c_0_12085_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_less(c_1,X1,X3)
    | ~ c_lessequals(X2,X4,tc_nat)
    | c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12085]) ).

cnf(c_0_12085_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_less(c_1,X1,X3)
    | ~ c_lessequals(X2,X4,tc_nat)
    | c_lessequals(c_Nat_Opower(X1,X2,X3),c_Nat_Opower(X1,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12085]) ).

cnf(c_0_12086_0,axiom,
    ( c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Olist__inter(X2,X4,X3),X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12086]) ).

cnf(c_0_12086_1,axiom,
    ( ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Olist__inter(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12086]) ).

cnf(c_0_12087_0,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12087]) ).

cnf(c_0_12087_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12087]) ).

cnf(c_0_12087_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12087]) ).

cnf(c_0_12087_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12087]) ).

cnf(c_0_12088_0,axiom,
    ( c_List_Otake(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(X2,c_plus(X2,X1,tc_nat))
    | ~ c_lessequals(c_plus(X2,X1,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12088]) ).

cnf(c_0_12088_1,axiom,
    ( ~ c_lessequals(c_plus(X2,X1,tc_nat),X3,tc_nat)
    | c_List_Otake(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(X2,c_plus(X2,X1,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_12088]) ).

cnf(c_0_12089_0,axiom,
    ( c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12089]) ).

cnf(c_0_12089_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12089]) ).

cnf(c_0_12089_2,axiom,
    ( ~ c_less(X3,c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12089]) ).

cnf(c_0_12089_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12089]) ).

cnf(c_0_12089_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12089]) ).

cnf(c_0_12089_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12089]) ).

cnf(c_0_12090_0,axiom,
    ( c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12090]) ).

cnf(c_0_12090_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12090]) ).

cnf(c_0_12090_2,axiom,
    ( ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12090]) ).

cnf(c_0_12090_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12090]) ).

cnf(c_0_12090_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12090]) ).

cnf(c_0_12090_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12090]) ).

cnf(c_0_12091_0,axiom,
    ( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12091]) ).

cnf(c_0_12091_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12091]) ).

cnf(c_0_12091_2,axiom,
    ( ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12091]) ).

cnf(c_0_12091_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12091]) ).

cnf(c_0_12091_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12091]) ).

cnf(c_0_12091_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12091]) ).

cnf(c_0_12092_0,axiom,
    ( c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12092]) ).

cnf(c_0_12092_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12092]) ).

cnf(c_0_12092_2,axiom,
    ( ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12092]) ).

cnf(c_0_12092_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12092]) ).

cnf(c_0_12092_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12092]) ).

cnf(c_0_12092_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12092]) ).

cnf(c_0_12093_0,axiom,
    ( c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12093]) ).

cnf(c_0_12093_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12093]) ).

cnf(c_0_12093_2,axiom,
    ( ~ c_less(c_0,X3,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12093]) ).

cnf(c_0_12093_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12093]) ).

cnf(c_0_12093_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12093]) ).

cnf(c_0_12093_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12093]) ).

cnf(c_0_12094_0,axiom,
    ( c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12094]) ).

cnf(c_0_12094_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12094]) ).

cnf(c_0_12094_2,axiom,
    ( ~ c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12094]) ).

cnf(c_0_12094_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12094]) ).

cnf(c_0_12094_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12094]) ).

cnf(c_0_12094_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12094]) ).

cnf(c_0_12095_0,axiom,
    ( c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12095]) ).

cnf(c_0_12095_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12095]) ).

cnf(c_0_12095_2,axiom,
    ( ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12095]) ).

cnf(c_0_12095_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12095]) ).

cnf(c_0_12095_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12095]) ).

cnf(c_0_12095_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X3,X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12095]) ).

cnf(c_0_12096_0,axiom,
    ( c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12096]) ).

cnf(c_0_12096_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12096]) ).

cnf(c_0_12096_2,axiom,
    ( ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12096]) ).

cnf(c_0_12096_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12096]) ).

cnf(c_0_12096_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12096]) ).

cnf(c_0_12096_5,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X3,c_0,X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_divide(c_Numeral_Onumber__of(X1,X2),X3,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12096]) ).

cnf(c_0_12097_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,X2,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12097]) ).

cnf(c_0_12097_1,axiom,
    ( c_less(c_0,X2,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12097]) ).

cnf(c_0_12097_2,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_less(c_0,X2,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12097]) ).

cnf(c_0_12097_3,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_less(c_0,X2,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12097]) ).

cnf(c_0_12097_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_less(c_0,X2,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12097]) ).

cnf(c_0_12097_5,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_less(c_0,X2,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12097]) ).

cnf(c_0_12098_0,axiom,
    ( X1 = c_emptyset
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12098]) ).

cnf(c_0_12098_1,axiom,
    ( c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12098]) ).

cnf(c_0_12098_2,axiom,
    ( ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12098]) ).

cnf(c_0_12098_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12098]) ).

cnf(c_0_12098_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X3),X3)
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12098]) ).

cnf(c_0_12099_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12099]) ).

cnf(c_0_12099_1,axiom,
    ( c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12099]) ).

cnf(c_0_12099_2,axiom,
    ( ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12099]) ).

cnf(c_0_12099_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12099]) ).

cnf(c_0_12099_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X3),X3)
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12099]) ).

cnf(c_0_12100_0,axiom,
    ( X1 = c_emptyset
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12100]) ).

cnf(c_0_12100_1,axiom,
    ( c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12100]) ).

cnf(c_0_12100_2,axiom,
    ( ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12100]) ).

cnf(c_0_12100_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12100]) ).

cnf(c_0_12100_4,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_less(c_Main_OMax__less__iff__1(X1,X3,X2),X3,X2)
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12100]) ).

cnf(c_0_12101_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12101]) ).

cnf(c_0_12101_1,axiom,
    ( c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12101]) ).

cnf(c_0_12101_2,axiom,
    ( ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12101]) ).

cnf(c_0_12101_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12101]) ).

cnf(c_0_12101_4,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X3,X2),X3,X2)
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12101]) ).

cnf(c_0_12106_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12106]) ).

cnf(c_0_12106_1,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12106]) ).

cnf(c_0_12106_2,axiom,
    ( ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12106]) ).

cnf(c_0_12106_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12106]) ).

cnf(c_0_12106_4,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12106]) ).

cnf(c_0_12107_0,axiom,
    ( c_lessequals(X1,c_0,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12107]) ).

cnf(c_0_12107_1,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12107]) ).

cnf(c_0_12107_2,axiom,
    ( ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12107]) ).

cnf(c_0_12107_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12107]) ).

cnf(c_0_12107_4,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_lessequals(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12107]) ).

cnf(c_0_12109_0,axiom,
    ( c_less(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12109]) ).

cnf(c_0_12109_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_less(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_less(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12109]) ).

cnf(c_0_12109_2,axiom,
    ( ~ c_less(X1,X3,tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | c_less(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12109]) ).

cnf(c_0_12110_0,axiom,
    ( c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12110]) ).

cnf(c_0_12110_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12110]) ).

cnf(c_0_12110_2,axiom,
    ( ~ c_less(X2,X3,tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | c_less(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12110]) ).

cnf(c_0_12112_0,axiom,
    ( c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2) = X1
    | ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12112]) ).

cnf(c_0_12112_1,axiom,
    ( ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2))
    | c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12112]) ).

cnf(c_0_12113_0,axiom,
    ( c_minus(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X1,X4,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X4,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12113]) ).

cnf(c_0_12113_1,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | c_minus(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X1,X4,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12113]) ).

cnf(c_0_12113_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_minus(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X1,X4,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12113]) ).

cnf(c_0_12117_0,axiom,
    ( c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12117]) ).

cnf(c_0_12117_1,axiom,
    ( ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12117]) ).

cnf(c_0_12117_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12117]) ).

cnf(c_0_12121_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12121]) ).

cnf(c_0_12121_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12121]) ).

cnf(c_0_12121_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12121]) ).

cnf(c_0_12121_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12121]) ).

cnf(c_0_12123_0,axiom,
    ( c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12123]) ).

cnf(c_0_12123_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X3,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12123]) ).

cnf(c_0_12125_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12125]) ).

cnf(c_0_12125_1,axiom,
    ( ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12125]) ).

cnf(c_0_12125_2,axiom,
    ( ~ c_less(c_0,X1,X3)
    | ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12125]) ).

cnf(c_0_12125_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X1,X3)
    | ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12125]) ).

cnf(c_0_12125_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X1,X3)
    | ~ c_less(c_1,c_divide(X2,X1,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12125]) ).

cnf(c_0_12126_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12126]) ).

cnf(c_0_12126_1,axiom,
    ( ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12126]) ).

cnf(c_0_12126_2,axiom,
    ( ~ c_less(X2,c_0,X3)
    | ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12126]) ).

cnf(c_0_12126_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12126]) ).

cnf(c_0_12126_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(c_1,c_divide(X1,X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12126]) ).

cnf(c_0_12127_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12127]) ).

cnf(c_0_12127_1,axiom,
    ( ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12127]) ).

cnf(c_0_12127_2,axiom,
    ( ~ c_less(c_0,X1,X3)
    | ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12127]) ).

cnf(c_0_12127_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X1,X3)
    | ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12127]) ).

cnf(c_0_12127_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X1,X3)
    | ~ c_lessequals(c_1,c_divide(X2,X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12127]) ).

cnf(c_0_12128_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12128]) ).

cnf(c_0_12128_1,axiom,
    ( ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12128]) ).

cnf(c_0_12128_2,axiom,
    ( ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12128]) ).

cnf(c_0_12128_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12128]) ).

cnf(c_0_12128_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12128]) ).

cnf(c_0_12129_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12129]) ).

cnf(c_0_12129_1,axiom,
    ( ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12129]) ).

cnf(c_0_12129_2,axiom,
    ( ~ c_less(c_0,X2,X3)
    | ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12129]) ).

cnf(c_0_12129_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12129]) ).

cnf(c_0_12129_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_divide(X1,X2,X3),c_1,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12129]) ).

cnf(c_0_12130_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12130]) ).

cnf(c_0_12130_1,axiom,
    ( ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | c_less(X1,X2,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12130]) ).

cnf(c_0_12130_2,axiom,
    ( ~ c_less(X1,c_0,X3)
    | ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12130]) ).

cnf(c_0_12130_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_0,X3)
    | ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12130]) ).

cnf(c_0_12130_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_0,X3)
    | ~ c_less(c_divide(X2,X1,X3),c_1,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12130]) ).

cnf(c_0_12131_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12131]) ).

cnf(c_0_12131_1,axiom,
    ( ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12131]) ).

cnf(c_0_12131_2,axiom,
    ( ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12131]) ).

cnf(c_0_12131_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12131]) ).

cnf(c_0_12131_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12131]) ).

cnf(c_0_12132_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12132]) ).

cnf(c_0_12132_1,axiom,
    ( ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12132]) ).

cnf(c_0_12132_2,axiom,
    ( ~ c_less(X1,c_0,X3)
    | ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12132]) ).

cnf(c_0_12132_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_0,X3)
    | ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12132]) ).

cnf(c_0_12132_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_0,X3)
    | ~ c_lessequals(c_divide(X2,X1,X3),c_1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12132]) ).

cnf(c_0_12133_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_minus(X3,c_Numeral_Onumber__of(X4,X2),X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X4)),X2),X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12133]) ).

cnf(c_0_12133_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_plus(c_Numeral_Onumber__of(X1,X2),c_minus(X3,c_Numeral_Onumber__of(X4,X2),X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X4)),X2),X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12133]) ).

cnf(c_0_12134_0,axiom,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12134]) ).

cnf(c_0_12134_1,axiom,
    ( c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_12134]) ).

cnf(c_0_12135_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12135]) ).

cnf(c_0_12135_1,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12135]) ).

cnf(c_0_12135_2,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12135]) ).

cnf(c_0_12135_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12135]) ).

cnf(c_0_12135_4,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12135]) ).

cnf(c_0_12136_0,axiom,
    ( c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12136]) ).

cnf(c_0_12136_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12136]) ).

cnf(c_0_12136_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12136]) ).

cnf(c_0_12136_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12136]) ).

cnf(c_0_12137_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Onth(c_List_Olist_OCons(X2,X3,X4),c_Numeral_Onumber__of(X1,tc_nat),X4) = c_List_Onth(X3,c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12137]) ).

cnf(c_0_12137_1,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X2,X3,X4),c_Numeral_Onumber__of(X1,tc_nat),X4) = c_List_Onth(X3,c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X4)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12137]) ).

cnf(c_0_12138_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12138]) ).

cnf(c_0_12138_1,axiom,
    ( c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X1,tc_nat),c_1,tc_nat),X3,X4)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12138]) ).

cnf(c_0_12139_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,c_0,X2)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12139]) ).

cnf(c_0_12139_1,axiom,
    ( c_less(c_0,c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12139]) ).

cnf(c_0_12139_2,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_less(c_0,c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12139]) ).

cnf(c_0_12139_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_less(c_0,c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12139]) ).

cnf(c_0_12139_4,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),X2)
    | c_less(c_0,c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12139]) ).

cnf(c_0_12140_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12140]) ).

cnf(c_0_12140_1,axiom,
    ( ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12140]) ).

cnf(c_0_12140_2,axiom,
    ( ~ c_less(X2,c_0,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12140]) ).

cnf(c_0_12140_3,axiom,
    ( ~ c_less(X1,c_0,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12140]) ).

cnf(c_0_12140_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_0,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12140]) ).

cnf(c_0_12141_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12141]) ).

cnf(c_0_12141_1,axiom,
    ( ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12141]) ).

cnf(c_0_12141_2,axiom,
    ( ~ c_less(c_0,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12141]) ).

cnf(c_0_12141_3,axiom,
    ( ~ c_less(c_0,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12141]) ).

cnf(c_0_12141_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12141]) ).

cnf(c_0_12142_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12142]) ).

cnf(c_0_12142_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12142]) ).

cnf(c_0_12142_2,axiom,
    ( ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12142]) ).

cnf(c_0_12142_3,axiom,
    ( ~ c_less(X1,c_0,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12142]) ).

cnf(c_0_12142_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,c_0,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12142]) ).

cnf(c_0_12143_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12143]) ).

cnf(c_0_12143_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12143]) ).

cnf(c_0_12143_2,axiom,
    ( ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12143]) ).

cnf(c_0_12143_3,axiom,
    ( ~ c_less(c_0,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12143]) ).

cnf(c_0_12143_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(c_HOL_Oinverse(X2,X3),c_HOL_Oinverse(X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12143]) ).

cnf(c_0_12144_0,axiom,
    ( c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat) = c_minus(X1,c_minus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12144]) ).

cnf(c_0_12144_1,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat) = c_minus(X1,c_minus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12144]) ).

cnf(c_0_12145_0,axiom,
    ( c_minus(c_plus(X1,X2,tc_nat),X3,tc_nat) = c_plus(X1,c_minus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12145]) ).

cnf(c_0_12145_1,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | c_minus(c_plus(X1,X2,tc_nat),X3,tc_nat) = c_plus(X1,c_minus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12145]) ).

cnf(c_0_12146_0,axiom,
    ( c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat) = c_plus(c_minus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12146]) ).

cnf(c_0_12146_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_minus(c_plus(X1,X3,tc_nat),X2,tc_nat) = c_plus(c_minus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12146]) ).

cnf(c_0_12147_0,axiom,
    ( X1 = c_0
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12147]) ).

cnf(c_0_12147_1,axiom,
    ( ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | X1 = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12147]) ).

cnf(c_0_12147_2,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12147]) ).

cnf(c_0_12147_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | X1 = c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12147]) ).

cnf(c_0_12147_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12147]) ).

cnf(c_0_12149_0,axiom,
    ( c_div(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) = c_div(X1,X3,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12149]) ).

cnf(c_0_12149_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_div(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) = c_div(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12149]) ).

cnf(c_0_12150_0,axiom,
    ( c_div(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) = c_div(X2,X3,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12150]) ).

cnf(c_0_12150_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_div(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) = c_div(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12150]) ).

cnf(c_0_12151_0,axiom,
    ( ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12151]) ).

cnf(c_0_12151_1,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12151]) ).

cnf(c_0_12151_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12151]) ).

cnf(c_0_12151_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12151]) ).

cnf(c_0_12152_0,axiom,
    ( c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_12152]) ).

cnf(c_0_12152_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12152]) ).

cnf(c_0_12153_0,axiom,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12153]) ).

cnf(c_0_12153_1,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12153]) ).

cnf(c_0_12153_2,axiom,
    ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12153]) ).

cnf(c_0_12154_0,axiom,
    ( X1 = c_0
    | c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12154]) ).

cnf(c_0_12154_1,axiom,
    ( c_lessequals(X1,c_0,X2)
    | X1 = c_0
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12154]) ).

cnf(c_0_12154_2,axiom,
    ( ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12154]) ).

cnf(c_0_12154_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | X1 = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12154]) ).

cnf(c_0_12154_4,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12154]) ).

cnf(c_0_12156_0,axiom,
    ( c_List_Olist__update(X1,X2,X3,X4) = X1
    | ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12156]) ).

cnf(c_0_12156_1,axiom,
    ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X4)),X2,tc_nat)
    | c_List_Olist__update(X1,X2,X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12156]) ).

cnf(c_0_12157_0,axiom,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12157]) ).

cnf(c_0_12157_1,axiom,
    ( ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12157]) ).

cnf(c_0_12157_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12157]) ).

cnf(c_0_12157_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2),c_0,X2)
    | c_less(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12157]) ).

cnf(c_0_12158_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12158]) ).

cnf(c_0_12158_1,axiom,
    ( ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12158]) ).

cnf(c_0_12159_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12159]) ).

cnf(c_0_12159_1,axiom,
    ( ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12159]) ).

cnf(c_0_12160_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12160]) ).

cnf(c_0_12160_1,axiom,
    ( ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12160]) ).

cnf(c_0_12161_0,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12161]) ).

cnf(c_0_12161_1,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) != c_0
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12161]) ).

cnf(c_0_12162_0,axiom,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12162]) ).

cnf(c_0_12162_1,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12162]) ).

cnf(c_0_12162_2,axiom,
    ( ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12162]) ).

cnf(c_0_12163_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12163]) ).

cnf(c_0_12163_1,axiom,
    ( c_less(c_0,X2,tc_nat)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12163]) ).

cnf(c_0_12163_2,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),tc_nat),tc_nat)
    | c_less(c_0,X2,tc_nat)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12163]) ).

cnf(c_0_12164_0,axiom,
    ( c_List_Onth(c_List_Oupt(X1,X2),X3,tc_nat) = c_plus(X1,X3,tc_nat)
    | ~ c_less(c_plus(X1,X3,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12164]) ).

cnf(c_0_12164_1,axiom,
    ( ~ c_less(c_plus(X1,X3,tc_nat),X2,tc_nat)
    | c_List_Onth(c_List_Oupt(X1,X2),X3,tc_nat) = c_plus(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12164]) ).

cnf(c_0_12165_0,axiom,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_times(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2),X4,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12165]) ).

cnf(c_0_12165_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_times(c_Numeral_Onumber__of(X1,X2),c_times(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2),X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12165]) ).

cnf(c_0_12166_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_plus(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2),X4,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12166]) ).

cnf(c_0_12166_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_plus(c_Numeral_Onumber__of(X1,X2),c_plus(c_Numeral_Onumber__of(X3,X2),X4,X2),X2) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2),X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12166]) ).

cnf(c_0_12167_0,axiom,
    ( X1 = c_emptyset
    | c_less(X2,X3,X4)
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12167]) ).

cnf(c_0_12167_1,axiom,
    ( c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12167]) ).

cnf(c_0_12167_2,axiom,
    ( ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12167]) ).

cnf(c_0_12167_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12167]) ).

cnf(c_0_12167_4,axiom,
    ( ~ c_in(X3,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12167]) ).

cnf(c_0_12167_5,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_in(X3,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_less(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12167]) ).

cnf(c_0_12168_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(X2,X3,X4)
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12168]) ).

cnf(c_0_12168_1,axiom,
    ( c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12168]) ).

cnf(c_0_12168_2,axiom,
    ( ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12168]) ).

cnf(c_0_12168_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X3,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12168]) ).

cnf(c_0_12168_4,axiom,
    ( ~ c_in(X3,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12168]) ).

cnf(c_0_12168_5,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_in(X3,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_lessequals(X2,c_Finite__Set_OMin(X1,X4),X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12168]) ).

cnf(c_0_12169_0,axiom,
    ( X1 = c_emptyset
    | c_less(X2,X3,X4)
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12169]) ).

cnf(c_0_12169_1,axiom,
    ( c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12169]) ).

cnf(c_0_12169_2,axiom,
    ( ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12169]) ).

cnf(c_0_12169_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12169]) ).

cnf(c_0_12169_4,axiom,
    ( ~ c_in(X2,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12169]) ).

cnf(c_0_12169_5,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_in(X2,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_less(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_less(X2,X3,X4)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12169]) ).

cnf(c_0_12170_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(X2,X3,X4)
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12170]) ).

cnf(c_0_12170_1,axiom,
    ( c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12170]) ).

cnf(c_0_12170_2,axiom,
    ( ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12170]) ).

cnf(c_0_12170_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ c_in(X2,X1,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12170]) ).

cnf(c_0_12170_4,axiom,
    ( ~ c_in(X2,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12170]) ).

cnf(c_0_12170_5,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_in(X2,X1,X4)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_lessequals(c_Finite__Set_OMax(X1,X4),X3,X4)
    | c_lessequals(X2,X3,X4)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12170]) ).

cnf(c_0_12171_0,axiom,
    ( c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12171]) ).

cnf(c_0_12171_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12171]) ).

cnf(c_0_12171_2,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12171]) ).

cnf(c_0_12172_0,axiom,
    ( c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12172]) ).

cnf(c_0_12172_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12172]) ).

cnf(c_0_12172_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12172]) ).

cnf(c_0_12172_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_lessequals(c_1,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12172]) ).

cnf(c_0_12173_0,axiom,
    ( c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12173]) ).

cnf(c_0_12173_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12173]) ).

cnf(c_0_12173_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_SetInterval_OatLeastLessThan(X1,X2,X3),c_SetInterval_OatLeastLessThan(X4,X5,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12173]) ).

cnf(c_0_12174_0,axiom,
    ( c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12174]) ).

cnf(c_0_12174_1,axiom,
    ( ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12174]) ).

cnf(c_0_12174_2,axiom,
    ( ~ c_less(X3,c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12174]) ).

cnf(c_0_12174_3,axiom,
    ( ~ c_less(X3,X1,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12174]) ).

cnf(c_0_12174_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,X1,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12174]) ).

cnf(c_0_12175_0,axiom,
    ( c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12175]) ).

cnf(c_0_12175_1,axiom,
    ( ~ c_less(c_0,X1,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12175]) ).

cnf(c_0_12175_2,axiom,
    ( ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12175]) ).

cnf(c_0_12175_3,axiom,
    ( ~ c_less(X3,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12175]) ).

cnf(c_0_12175_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12175]) ).

cnf(c_0_12176_0,axiom,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12176]) ).

cnf(c_0_12176_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12176]) ).

cnf(c_0_12176_2,axiom,
    ( ~ c_less(X1,c_0,X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(X3,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12176]) ).

cnf(c_0_12176_3,axiom,
    ( ~ c_less(X3,c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12176]) ).

cnf(c_0_12176_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X3,c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12176]) ).

cnf(c_0_12177_0,axiom,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12177]) ).

cnf(c_0_12177_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12177]) ).

cnf(c_0_12177_2,axiom,
    ( ~ c_less(c_0,X1,X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ c_less(c_0,X3,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12177]) ).

cnf(c_0_12177_3,axiom,
    ( ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12177]) ).

cnf(c_0_12177_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X3,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_HOL_Oinverse(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12177]) ).

cnf(c_0_12178_0,axiom,
    ( c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3)
    | ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12178]) ).

cnf(c_0_12178_1,axiom,
    ( ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3))
    | c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12178]) ).

cnf(c_0_12179_0,axiom,
    ( c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2)
    | ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12179]) ).

cnf(c_0_12179_1,axiom,
    ( ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2))
    | c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12179]) ).

cnf(c_0_12180_0,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12180]) ).

cnf(c_0_12180_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12180]) ).

cnf(c_0_12180_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12180]) ).

cnf(c_0_12180_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12180]) ).

cnf(c_0_12181_0,axiom,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12181]) ).

cnf(c_0_12181_1,axiom,
    ( c_in(X1,X4,X3)
    | c_in(X1,X2,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12181]) ).

cnf(c_0_12181_2,axiom,
    ( ~ c_in(X1,c_union(X2,X4,X3),X3)
    | c_in(X1,X4,X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12181]) ).

cnf(c_0_12182_0,axiom,
    ( c_less(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ c_less(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12182]) ).

cnf(c_0_12182_1,axiom,
    ( ~ c_less(X1,X4,X3)
    | c_less(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12182]) ).

cnf(c_0_12182_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_less(X1,X4,X3)
    | c_less(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12182]) ).

cnf(c_0_12183_0,axiom,
    ( c_less(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12183]) ).

cnf(c_0_12183_1,axiom,
    ( ~ c_less(X2,X4,X3)
    | c_less(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12183]) ).

cnf(c_0_12183_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_less(X2,X4,X3)
    | c_less(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12183]) ).

cnf(c_0_12184_0,axiom,
    ( c_lessequals(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12184]) ).

cnf(c_0_12184_1,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12184]) ).

cnf(c_0_12184_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_plus(X1,X2,X3),c_plus(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12184]) ).

cnf(c_0_12185_0,axiom,
    ( c_lessequals(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12185]) ).

cnf(c_0_12185_1,axiom,
    ( ~ c_lessequals(X2,X4,X3)
    | c_lessequals(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12185]) ).

cnf(c_0_12185_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(X2,X4,X3)
    | c_lessequals(c_plus(X1,X2,X3),c_plus(X1,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12185]) ).

cnf(c_0_12186_0,axiom,
    ( c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X1,X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12186]) ).

cnf(c_0_12186_1,axiom,
    ( ~ c_lessequals(X1,X4,tc_set(X3))
    | c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12186]) ).

cnf(c_0_12186_2,axiom,
    ( ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_lessequals(X1,X4,tc_set(X3))
    | c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12186]) ).

cnf(c_0_12187_0,axiom,
    ( c_lessequals(X1,c_inter(X2,X3,X4),tc_set(X4))
    | ~ c_lessequals(X1,X2,tc_set(X4))
    | ~ c_lessequals(X1,X3,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12187]) ).

cnf(c_0_12187_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X4))
    | c_lessequals(X1,c_inter(X2,X3,X4),tc_set(X4))
    | ~ c_lessequals(X1,X3,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12187]) ).

cnf(c_0_12187_2,axiom,
    ( ~ c_lessequals(X1,X3,tc_set(X4))
    | ~ c_lessequals(X1,X2,tc_set(X4))
    | c_lessequals(X1,c_inter(X2,X3,X4),tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12187]) ).

cnf(c_0_12188_0,axiom,
    ( ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12188]) ).

cnf(c_0_12188_1,axiom,
    ( ~ c_in(X1,X3,X4)
    | ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12188]) ).

cnf(c_0_12189_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12189]) ).

cnf(c_0_12189_1,axiom,
    ( ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12189]) ).

cnf(c_0_12190_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12190]) ).

cnf(c_0_12190_1,axiom,
    ( ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12190]) ).

cnf(c_0_12190_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12190]) ).

cnf(c_0_12190_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12190]) ).

cnf(c_0_12193_0,axiom,
    ( c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12193]) ).

cnf(c_0_12193_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12193]) ).

cnf(c_0_12193_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12193]) ).

cnf(c_0_12194_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_lessequals(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12194]) ).

cnf(c_0_12194_1,axiom,
    ( c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_lessequals(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12194]) ).

cnf(c_0_12194_2,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_lessequals(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12194]) ).

cnf(c_0_12194_3,axiom,
    ( ~ c_lessequals(X2,c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12194]) ).

cnf(c_0_12194_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(X2,c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12194]) ).

cnf(c_0_12194_5,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(X2,c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3),c_0,X3)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12194]) ).

cnf(c_0_12195_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12195]) ).

cnf(c_0_12195_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12195]) ).

cnf(c_0_12195_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12195]) ).

cnf(c_0_12196_0,axiom,
    ( c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3))
    | ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12196]) ).

cnf(c_0_12196_1,axiom,
    ( ~ c_lessequals(X2,X4,tc_set(X3))
    | c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12196]) ).

cnf(c_0_12196_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X2,X4,tc_set(X3))
    | c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12196]) ).

cnf(c_0_12197_0,axiom,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Power_Orecpower(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12197]) ).

cnf(c_0_12197_1,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12197]) ).

cnf(c_0_12197_2,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12197]) ).

cnf(c_0_12198_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12198]) ).

cnf(c_0_12198_1,axiom,
    ( c_less(c_0,X2,tc_nat)
    | c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12198]) ).

cnf(c_0_12198_2,axiom,
    ( ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | c_less(c_0,X2,tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12198]) ).

cnf(c_0_12199_0,axiom,
    ( c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12199]) ).

cnf(c_0_12199_1,axiom,
    ( ~ c_less(c_0,X2,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12199]) ).

cnf(c_0_12199_2,axiom,
    ( ~ c_less(X2,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12199]) ).

cnf(c_0_12199_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12199]) ).

cnf(c_0_12199_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12199]) ).

cnf(c_0_12200_0,axiom,
    ( c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12200]) ).

cnf(c_0_12200_1,axiom,
    ( ~ c_less(X2,c_0,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12200]) ).

cnf(c_0_12200_2,axiom,
    ( ~ c_less(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12200]) ).

cnf(c_0_12200_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12200]) ).

cnf(c_0_12200_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | c_less(c_1,c_divide(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12200]) ).

cnf(c_0_12201_0,axiom,
    ( c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12201]) ).

cnf(c_0_12201_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12201]) ).

cnf(c_0_12201_2,axiom,
    ( ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12201]) ).

cnf(c_0_12201_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12201]) ).

cnf(c_0_12201_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12201]) ).

cnf(c_0_12202_0,axiom,
    ( c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12202]) ).

cnf(c_0_12202_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12202]) ).

cnf(c_0_12202_2,axiom,
    ( ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12202]) ).

cnf(c_0_12202_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12202]) ).

cnf(c_0_12202_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_1,c_divide(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12202]) ).

cnf(c_0_12203_0,axiom,
    ( c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12203]) ).

cnf(c_0_12203_1,axiom,
    ( ~ c_less(c_0,X2,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12203]) ).

cnf(c_0_12203_2,axiom,
    ( ~ c_less(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12203]) ).

cnf(c_0_12203_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12203]) ).

cnf(c_0_12203_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12203]) ).

cnf(c_0_12204_0,axiom,
    ( c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12204]) ).

cnf(c_0_12204_1,axiom,
    ( ~ c_less(X2,c_0,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12204]) ).

cnf(c_0_12204_2,axiom,
    ( ~ c_less(X2,X1,X3)
    | ~ c_less(X2,c_0,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12204]) ).

cnf(c_0_12204_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,X1,X3)
    | ~ c_less(X2,c_0,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12204]) ).

cnf(c_0_12204_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,X1,X3)
    | ~ c_less(X2,c_0,X3)
    | c_less(c_divide(X1,X2,X3),c_1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12204]) ).

cnf(c_0_12205_0,axiom,
    ( c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12205]) ).

cnf(c_0_12205_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(c_0,X2,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12205]) ).

cnf(c_0_12205_2,axiom,
    ( ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12205]) ).

cnf(c_0_12205_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12205]) ).

cnf(c_0_12205_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(c_0,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12205]) ).

cnf(c_0_12206_0,axiom,
    ( c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12206]) ).

cnf(c_0_12206_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ c_less(X2,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12206]) ).

cnf(c_0_12206_2,axiom,
    ( ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12206]) ).

cnf(c_0_12206_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12206]) ).

cnf(c_0_12206_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ c_less(X2,c_0,X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_lessequals(c_divide(X1,X2,X3),c_1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12206]) ).

cnf(c_0_12207_0,axiom,
    ( c_less(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat)
    | ~ c_less(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12207]) ).

cnf(c_0_12207_1,axiom,
    ( ~ c_less(X2,X3,tc_nat)
    | c_less(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12207]) ).

cnf(c_0_12208_0,axiom,
    ( c_lessequals(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12208]) ).

cnf(c_0_12208_1,axiom,
    ( ~ c_lessequals(X2,X3,tc_nat)
    | c_lessequals(c_plus(X1,X2,tc_nat),c_plus(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12208]) ).

cnf(c_0_12209_0,axiom,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12209]) ).

cnf(c_0_12209_1,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12209]) ).

cnf(c_0_12210_0,axiom,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12210]) ).

cnf(c_0_12210_1,axiom,
    ( ~ c_lessequals(X2,X3,tc_nat)
    | c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12210]) ).

cnf(c_0_12211_0,axiom,
    ( X1 = c_emptyset
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12211]) ).

cnf(c_0_12211_1,axiom,
    ( c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12211]) ).

cnf(c_0_12211_2,axiom,
    ( c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12211]) ).

cnf(c_0_12211_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12211]) ).

cnf(c_0_12211_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_Main_OMin__gr__iff__1(X1,X2,X3),X1,X3)
    | c_less(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12211]) ).

cnf(c_0_12212_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12212]) ).

cnf(c_0_12212_1,axiom,
    ( c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12212]) ).

cnf(c_0_12212_2,axiom,
    ( c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12212]) ).

cnf(c_0_12212_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12212]) ).

cnf(c_0_12212_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_Main_OMin__ge__iff__1(X1,X2,X3),X1,X3)
    | c_lessequals(X2,c_Finite__Set_OMin(X1,X3),X3)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12212]) ).

cnf(c_0_12213_0,axiom,
    ( X1 = c_emptyset
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12213]) ).

cnf(c_0_12213_1,axiom,
    ( c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12213]) ).

cnf(c_0_12213_2,axiom,
    ( c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12213]) ).

cnf(c_0_12213_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12213]) ).

cnf(c_0_12213_4,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_OMax__less__iff__1(X1,X3,X2),X1,X2)
    | c_less(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12213]) ).

cnf(c_0_12214_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12214]) ).

cnf(c_0_12214_1,axiom,
    ( c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12214]) ).

cnf(c_0_12214_2,axiom,
    ( c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12214]) ).

cnf(c_0_12214_3,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12214]) ).

cnf(c_0_12214_4,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_OMax__le__iff__1(X1,X3,X2),X1,X2)
    | c_lessequals(c_Finite__Set_OMax(X1,X2),X3,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12214]) ).

cnf(c_0_12215_0,axiom,
    ( c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12215]) ).

cnf(c_0_12215_1,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12215]) ).

cnf(c_0_12215_2,axiom,
    ( ~ c_in(c_Message_OHPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12215]) ).

cnf(c_0_12216_0,axiom,
    ( c_in(X1,c_SetInterval_OgreaterThanLessThan(X2,X3,X4),X4)
    | ~ c_less(X2,X1,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12216]) ).

cnf(c_0_12216_1,axiom,
    ( ~ c_less(X2,X1,X4)
    | c_in(X1,c_SetInterval_OgreaterThanLessThan(X2,X3,X4),X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12216]) ).

cnf(c_0_12216_2,axiom,
    ( ~ c_less(X1,X3,X4)
    | ~ c_less(X2,X1,X4)
    | c_in(X1,c_SetInterval_OgreaterThanLessThan(X2,X3,X4),X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12216]) ).

cnf(c_0_12216_3,axiom,
    ( ~ class_Orderings_Oord(X4)
    | ~ c_less(X1,X3,X4)
    | ~ c_less(X2,X1,X4)
    | c_in(X1,c_SetInterval_OgreaterThanLessThan(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12216]) ).

cnf(c_0_12217_0,axiom,
    ( c_in(X1,c_SetInterval_OgreaterThanAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ c_less(X2,X1,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12217]) ).

cnf(c_0_12217_1,axiom,
    ( ~ c_lessequals(X1,X3,X4)
    | c_in(X1,c_SetInterval_OgreaterThanAtMost(X2,X3,X4),X4)
    | ~ c_less(X2,X1,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12217]) ).

cnf(c_0_12217_2,axiom,
    ( ~ c_less(X2,X1,X4)
    | ~ c_lessequals(X1,X3,X4)
    | c_in(X1,c_SetInterval_OgreaterThanAtMost(X2,X3,X4),X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12217]) ).

cnf(c_0_12217_3,axiom,
    ( ~ class_Orderings_Oord(X4)
    | ~ c_less(X2,X1,X4)
    | ~ c_lessequals(X1,X3,X4)
    | c_in(X1,c_SetInterval_OgreaterThanAtMost(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12217]) ).

cnf(c_0_12218_0,axiom,
    ( c_in(X1,c_SetInterval_OatLeastLessThan(X2,X3,X4),X4)
    | ~ c_lessequals(X2,X1,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12218]) ).

cnf(c_0_12218_1,axiom,
    ( ~ c_lessequals(X2,X1,X4)
    | c_in(X1,c_SetInterval_OatLeastLessThan(X2,X3,X4),X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12218]) ).

cnf(c_0_12218_2,axiom,
    ( ~ c_less(X1,X3,X4)
    | ~ c_lessequals(X2,X1,X4)
    | c_in(X1,c_SetInterval_OatLeastLessThan(X2,X3,X4),X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12218]) ).

cnf(c_0_12218_3,axiom,
    ( ~ class_Orderings_Oord(X4)
    | ~ c_less(X1,X3,X4)
    | ~ c_lessequals(X2,X1,X4)
    | c_in(X1,c_SetInterval_OatLeastLessThan(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12218]) ).

cnf(c_0_12219_0,axiom,
    ( c_in(X1,c_SetInterval_OatLeastAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X2,X1,X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12219]) ).

cnf(c_0_12219_1,axiom,
    ( ~ c_lessequals(X2,X1,X4)
    | c_in(X1,c_SetInterval_OatLeastAtMost(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12219]) ).

cnf(c_0_12219_2,axiom,
    ( ~ c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X2,X1,X4)
    | c_in(X1,c_SetInterval_OatLeastAtMost(X2,X3,X4),X4)
    | ~ class_Orderings_Oord(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12219]) ).

cnf(c_0_12219_3,axiom,
    ( ~ class_Orderings_Oord(X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X2,X1,X4)
    | c_in(X1,c_SetInterval_OatLeastAtMost(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12219]) ).

cnf(c_0_12220_0,axiom,
    ( c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12220]) ).

cnf(c_0_12220_1,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12220]) ).

cnf(c_0_12220_2,axiom,
    ( ~ c_lessequals(X2,X4,X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12220]) ).

cnf(c_0_12220_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ c_lessequals(X1,X4,X3)
    | c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12220]) ).

cnf(c_0_12221_0,axiom,
    ( c_lessequals(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12221]) ).

cnf(c_0_12221_1,axiom,
    ( ~ c_lessequals(X1,X2,X4)
    | c_lessequals(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12221]) ).

cnf(c_0_12221_2,axiom,
    ( ~ c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,X2,X4)
    | c_lessequals(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12221]) ).

cnf(c_0_12221_3,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,X2,X4)
    | c_lessequals(X1,c_Orderings_Omin(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12221]) ).

cnf(c_0_12222_0,axiom,
    ( c_less(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_less(X1,X2,X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12222]) ).

cnf(c_0_12222_1,axiom,
    ( ~ c_less(X1,X2,X4)
    | c_less(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ c_less(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12222]) ).

cnf(c_0_12222_2,axiom,
    ( ~ c_less(X1,X3,X4)
    | ~ c_less(X1,X2,X4)
    | c_less(X1,c_Orderings_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12222]) ).

cnf(c_0_12222_3,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_less(X1,X3,X4)
    | ~ c_less(X1,X2,X4)
    | c_less(X1,c_Orderings_Omin(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12222]) ).

cnf(c_0_12223_0,axiom,
    ( c_less(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_less(X1,X4,X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12223]) ).

cnf(c_0_12223_1,axiom,
    ( ~ c_less(X1,X4,X3)
    | c_less(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ c_less(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12223]) ).

cnf(c_0_12223_2,axiom,
    ( ~ c_less(X2,X4,X3)
    | ~ c_less(X1,X4,X3)
    | c_less(c_Orderings_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12223]) ).

cnf(c_0_12223_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_less(X2,X4,X3)
    | ~ c_less(X1,X4,X3)
    | c_less(c_Orderings_Omax(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12223]) ).

cnf(c_0_12224_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12224]) ).

cnf(c_0_12224_1,axiom,
    ( ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3)
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12224]) ).

cnf(c_0_12225_0,axiom,
    ( c_Message_Osynth(c_Message_Oanalz(c_insert(X1,X2,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X2))
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12225]) ).

cnf(c_0_12225_1,axiom,
    ( ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_Message_Osynth(c_Message_Oanalz(c_insert(X1,X2,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12225]) ).

cnf(c_0_12226_0,axiom,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12226]) ).

cnf(c_0_12226_1,axiom,
    ( ~ c_in(X1,X4,X3)
    | c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12226]) ).

cnf(c_0_12227_0,axiom,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12227]) ).

cnf(c_0_12227_1,axiom,
    ( ~ c_in(X1,X4,X3)
    | c_inter(c_insert(X1,X2,X3),X4,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12227]) ).

cnf(c_0_12228_0,axiom,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset
    | ~ c_in(X2,X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12228]) ).

cnf(c_0_12228_1,axiom,
    ( ~ c_in(X2,X1,X4)
    | c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12228]) ).

cnf(c_0_12229_0,axiom,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset
    | ~ c_in(X2,X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12229]) ).

cnf(c_0_12229_1,axiom,
    ( ~ c_in(X2,X1,X4)
    | c_inter(X1,c_insert(X2,X3,X4),X4) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12229]) ).

cnf(c_0_12230_0,axiom,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12230]) ).

cnf(c_0_12230_1,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_less(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12230]) ).

cnf(c_0_12230_2,axiom,
    ( ~ c_less(c_0,X1,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12230]) ).

cnf(c_0_12230_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_0,X1,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12230]) ).

cnf(c_0_12230_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_0,X1,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12230]) ).

cnf(c_0_12231_0,axiom,
    ( c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12231]) ).

cnf(c_0_12231_1,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_lessequals(c_0,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12231]) ).

cnf(c_0_12231_2,axiom,
    ( ~ c_lessequals(c_0,X1,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12231]) ).

cnf(c_0_12231_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(c_0,X1,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12231]) ).

cnf(c_0_12231_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(c_0,X1,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12231]) ).

cnf(c_0_12232_0,axiom,
    ( c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12232]) ).

cnf(c_0_12232_1,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ c_less(X1,c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12232]) ).

cnf(c_0_12232_2,axiom,
    ( ~ c_less(X1,c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12232]) ).

cnf(c_0_12232_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(X1,c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12232]) ).

cnf(c_0_12232_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(X1,c_0,X3)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),c_0,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12232]) ).

cnf(c_0_12233_0,axiom,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X2),X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12233]) ).

cnf(c_0_12233_1,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X2),X1,X2),X2)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12233]) ).

cnf(c_0_12233_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X2),X1,X2),X2)
    | X1 = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12233]) ).

cnf(c_0_12233_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X2),X1,X2),X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12233]) ).

cnf(c_0_12234_0,axiom,
    ( c_divide(c_times(X1,X2,X3),c_times(X4,X2,X3),X3) = c_divide(X1,X4,X3)
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12234]) ).

cnf(c_0_12234_1,axiom,
    ( X2 = c_0
    | c_divide(c_times(X1,X2,X3),c_times(X4,X2,X3),X3) = c_divide(X1,X4,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12234]) ).

cnf(c_0_12234_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X2 = c_0
    | c_divide(c_times(X1,X2,X3),c_times(X4,X2,X3),X3) = c_divide(X1,X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12234]) ).

cnf(c_0_12234_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X2 = c_0
    | c_divide(c_times(X1,X2,X3),c_times(X4,X2,X3),X3) = c_divide(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12234]) ).

cnf(c_0_12235_0,axiom,
    ( c_divide(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) = c_divide(X2,X4,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12235]) ).

cnf(c_0_12235_1,axiom,
    ( X1 = c_0
    | c_divide(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) = c_divide(X2,X4,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12235]) ).

cnf(c_0_12235_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) = c_divide(X2,X4,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12235]) ).

cnf(c_0_12235_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(c_times(X1,X2,X3),c_times(X1,X4,X3),X3) = c_divide(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12235]) ).

cnf(c_0_12236_0,axiom,
    ( c_HOL_Oabs(c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2),X2) = c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12236]) ).

cnf(c_0_12236_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_HOL_Oabs(c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2),X2) = c_plus(c_HOL_Oabs(X1,X2),c_HOL_Oabs(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12236]) ).

cnf(c_0_12237_0,axiom,
    ( c_divide(c_times(X1,X3,X4),X2,X4) = c_divide(X1,c_divide(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12237]) ).

cnf(c_0_12237_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(c_times(X1,X3,X4),X2,X4) = c_divide(X1,c_divide(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12237]) ).

cnf(c_0_12237_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(c_times(X1,X3,X4),X2,X4) = c_divide(X1,c_divide(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12237]) ).

cnf(c_0_12238_0,axiom,
    ( c_divide(c_divide(X1,X2,X3),X4,X3) = c_divide(X1,c_times(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12238]) ).

cnf(c_0_12238_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(c_divide(X1,X2,X3),X4,X3) = c_divide(X1,c_times(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12238]) ).

cnf(c_0_12238_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(c_divide(X1,X2,X3),X4,X3) = c_divide(X1,c_times(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12238]) ).

cnf(c_0_12239_0,axiom,
    ( c_in(c_times(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12239]) ).

cnf(c_0_12239_1,axiom,
    ( ~ c_in(X1,c_IntDef_ONats,X3)
    | c_in(c_times(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12239]) ).

cnf(c_0_12239_2,axiom,
    ( ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | c_in(c_times(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12239]) ).

cnf(c_0_12239_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | c_in(c_times(X1,X2,X3),c_IntDef_ONats,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12239]) ).

cnf(c_0_12240_0,axiom,
    ( c_in(c_plus(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12240]) ).

cnf(c_0_12240_1,axiom,
    ( ~ c_in(X1,c_IntDef_ONats,X3)
    | c_in(c_plus(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12240]) ).

cnf(c_0_12240_2,axiom,
    ( ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | c_in(c_plus(X1,X2,X3),c_IntDef_ONats,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12240]) ).

cnf(c_0_12240_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
    | ~ c_in(X2,c_IntDef_ONats,X3)
    | ~ c_in(X1,c_IntDef_ONats,X3)
    | c_in(c_plus(X1,X2,X3),c_IntDef_ONats,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12240]) ).

cnf(c_0_12241_0,axiom,
    ( c_in(c_times(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12241]) ).

cnf(c_0_12241_1,axiom,
    ( ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_times(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12241]) ).

cnf(c_0_12241_2,axiom,
    ( ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_times(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12241]) ).

cnf(c_0_12241_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_times(X1,X2,X3),c_IntDef_OInts,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12241]) ).

cnf(c_0_12242_0,axiom,
    ( c_in(c_minus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12242]) ).

cnf(c_0_12242_1,axiom,
    ( ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_minus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12242]) ).

cnf(c_0_12242_2,axiom,
    ( ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_minus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12242]) ).

cnf(c_0_12242_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_minus(X1,X2,X3),c_IntDef_OInts,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12242]) ).

cnf(c_0_12243_0,axiom,
    ( c_in(c_plus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12243]) ).

cnf(c_0_12243_1,axiom,
    ( ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_plus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12243]) ).

cnf(c_0_12243_2,axiom,
    ( ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_plus(X1,X2,X3),c_IntDef_OInts,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12243]) ).

cnf(c_0_12243_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | ~ c_in(X2,c_IntDef_OInts,X3)
    | ~ c_in(X1,c_IntDef_OInts,X3)
    | c_in(c_plus(X1,X2,X3),c_IntDef_OInts,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12243]) ).

cnf(c_0_12244_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12244]) ).

cnf(c_0_12244_1,axiom,
    ( ~ c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12244]) ).

cnf(c_0_12244_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12244]) ).

cnf(c_0_12244_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_1,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12244]) ).

cnf(c_0_12245_0,axiom,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInter__iff__1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12245]) ).

cnf(c_0_12245_1,axiom,
    ( ~ c_in(X1,c_Main_OInter__iff__1(X1,X2,X3),X3)
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12245]) ).

cnf(c_0_12246_0,axiom,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12246]) ).

cnf(c_0_12246_1,axiom,
    ( ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3)
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12246]) ).

cnf(c_0_12247_0,axiom,
    ( c_List_Odistinct(c_append(X1,X2,X3),X3)
    | c_inter(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) != c_emptyset
    | ~ c_List_Odistinct(X1,X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12247]) ).

cnf(c_0_12247_1,axiom,
    ( c_inter(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) != c_emptyset
    | c_List_Odistinct(c_append(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X1,X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12247]) ).

cnf(c_0_12247_2,axiom,
    ( ~ c_List_Odistinct(X1,X3)
    | c_inter(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) != c_emptyset
    | c_List_Odistinct(c_append(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12247]) ).

cnf(c_0_12247_3,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | ~ c_List_Odistinct(X1,X3)
    | c_inter(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) != c_emptyset
    | c_List_Odistinct(c_append(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12247]) ).

cnf(c_0_12248_0,axiom,
    ( c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12248]) ).

cnf(c_0_12248_1,axiom,
    ( ~ c_in(X1,X2,X4)
    | c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12248]) ).

cnf(c_0_12248_2,axiom,
    ( ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4)
    | c_in(X1,c_inter(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12248]) ).

cnf(c_0_12249_0,axiom,
    ( c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_nat),tc_IntDef_Oint)) = c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12249]) ).

cnf(c_0_12249_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_nat),tc_IntDef_Oint)) = c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12249]) ).

cnf(c_0_12250_0,axiom,
    ( c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12250]) ).

cnf(c_0_12250_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12250]) ).

cnf(c_0_12251_0,axiom,
    ( c_minus(c_List_Oset(X2,X3),c_insert(X1,c_emptyset,X3),tc_set(X3)) = c_List_Oset(c_List_Oremove1(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12251]) ).

cnf(c_0_12251_1,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | c_minus(c_List_Oset(X2,X3),c_insert(X1,c_emptyset,X3),tc_set(X3)) = c_List_Oset(c_List_Oremove1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12251]) ).

cnf(c_0_12252_0,axiom,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12252]) ).

cnf(c_0_12252_1,axiom,
    ( c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3)
    | c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12252]) ).

cnf(c_0_12253_0,axiom,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12253]) ).

cnf(c_0_12253_1,axiom,
    ( c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3)
    | c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12253]) ).

cnf(c_0_12254_0,axiom,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12254]) ).

cnf(c_0_12254_1,axiom,
    ( ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12254]) ).

cnf(c_0_12254_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12254]) ).

cnf(c_0_12256_0,axiom,
    ( c_in(c_List_Onth(X1,X2,X3),c_List_Oset(X1,X3),X3)
    | ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12256]) ).

cnf(c_0_12256_1,axiom,
    ( ~ c_less(X2,c_Nat_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | c_in(c_List_Onth(X1,X2,X3),c_List_Oset(X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12256]) ).

cnf(c_0_12257_0,axiom,
    ( c_divide(c_times(X1,X4,X3),X2,X3) = c_times(c_divide(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ofield(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12257]) ).

cnf(c_0_12257_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(c_times(X1,X4,X3),X2,X3) = c_times(c_divide(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12257]) ).

cnf(c_0_12258_0,axiom,
    ( c_divide(c_times(X1,X2,X4),X3,X4) = c_times(X1,c_divide(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12258]) ).

cnf(c_0_12258_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(c_times(X1,X2,X4),X3,X4) = c_times(X1,c_divide(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12258]) ).

cnf(c_0_12259_0,axiom,
    ( c_less(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_less(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12259]) ).

cnf(c_0_12259_1,axiom,
    ( ~ c_less(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12259]) ).

cnf(c_0_12259_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12259]) ).

cnf(c_0_12259_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_less(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12259]) ).

cnf(c_0_12260_0,axiom,
    ( c_lessequals(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12260]) ).

cnf(c_0_12260_1,axiom,
    ( ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12260]) ).

cnf(c_0_12260_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12260]) ).

cnf(c_0_12260_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X3,X2),X2),X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12260]) ).

cnf(c_0_12261_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_less(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12261]) ).

cnf(c_0_12261_1,axiom,
    ( ~ c_less(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12261]) ).

cnf(c_0_12261_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12261]) ).

cnf(c_0_12261_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12261]) ).

cnf(c_0_12262_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_lessequals(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12262]) ).

cnf(c_0_12262_1,axiom,
    ( ~ c_lessequals(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12262]) ).

cnf(c_0_12262_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12262]) ).

cnf(c_0_12262_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X3,c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_uminus(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12262]) ).

cnf(c_0_12263_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12263]) ).

cnf(c_0_12263_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12263]) ).

cnf(c_0_12263_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_12263]) ).

cnf(c_0_12266_0,axiom,
    ( c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3)
    | ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12266]) ).

cnf(c_0_12266_1,axiom,
    ( ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3))
    | c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12266]) ).

cnf(c_0_12268_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12268]) ).

cnf(c_0_12268_1,axiom,
    ( ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12268]) ).

cnf(c_0_12270_0,axiom,
    ( X1 = X2
    | c_IntDef_OAbs__Integ(X1) != c_IntDef_OAbs__Integ(X2)
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_12270]) ).

cnf(c_0_12270_1,axiom,
    ( c_IntDef_OAbs__Integ(X1) != c_IntDef_OAbs__Integ(X2)
    | X1 = X2
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_12270]) ).

cnf(c_0_12270_2,axiom,
    ( ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | c_IntDef_OAbs__Integ(X1) != c_IntDef_OAbs__Integ(X2)
    | X1 = X2
    | ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_12270]) ).

cnf(c_0_12270_3,axiom,
    ( ~ c_in(X2,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | c_IntDef_OAbs__Integ(X1) != c_IntDef_OAbs__Integ(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12270]) ).

cnf(c_0_12271_0,axiom,
    ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_insert(X2,c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    inference(literals_permutation,[status(thm)],[c_0_12271]) ).

cnf(c_0_12271_1,axiom,
    ( ~ c_in(X1,c_Event_Obad,tc_Message_Oagent)
    | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_insert(X2,c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12271]) ).

cnf(c_0_12272_0,axiom,
    ( c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12272]) ).

cnf(c_0_12272_1,axiom,
    ( X1 = X2
    | c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12272]) ).

cnf(c_0_12273_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_insert(X4,X1,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12273]) ).

cnf(c_0_12273_1,axiom,
    ( ~ c_lessequals(c_insert(X4,X1,X3),X2,tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12273]) ).

cnf(c_0_12274_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12274]) ).

cnf(c_0_12274_1,axiom,
    ( ~ c_lessequals(c_union(X4,X1,X3),X2,tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12274]) ).

cnf(c_0_12275_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_union(X1,X4,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12275]) ).

cnf(c_0_12275_1,axiom,
    ( ~ c_lessequals(c_union(X1,X4,X3),X2,tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12275]) ).

cnf(c_0_12276_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,c_inter(X4,X2,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12276]) ).

cnf(c_0_12276_1,axiom,
    ( ~ c_lessequals(X1,c_inter(X4,X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12276]) ).

cnf(c_0_12277_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,c_inter(X2,X4,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12277]) ).

cnf(c_0_12277_1,axiom,
    ( ~ c_lessequals(X1,c_inter(X2,X4,X3),tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12277]) ).

cnf(c_0_12278_0,axiom,
    ( c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12278]) ).

cnf(c_0_12278_1,axiom,
    ( ~ c_lessequals(c_1,X1,tc_nat)
    | c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12278]) ).

cnf(c_0_12278_2,axiom,
    ( ~ c_lessequals(c_1,X2,tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat)
    | c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12278]) ).

cnf(c_0_12279_0,axiom,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12279]) ).

cnf(c_0_12279_1,axiom,
    ( ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12279]) ).

cnf(c_0_12279_2,axiom,
    ( ~ c_in(X2,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(c_Message_Oanalz(X3)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12279]) ).

cnf(c_0_12280_0,axiom,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12280]) ).

cnf(c_0_12280_1,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X1)),c_Message_Oanalz(X3),tc_Message_Omsg)
    | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oanalz(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12280]) ).

cnf(c_0_12286_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_insert(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12286]) ).

cnf(c_0_12286_1,axiom,
    ( ~ c_in(c_insert(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12286]) ).

cnf(c_0_12287_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12287]) ).

cnf(c_0_12287_1,axiom,
    ( ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12287]) ).

cnf(c_0_12288_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12288]) ).

cnf(c_0_12288_1,axiom,
    ( ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12288]) ).

cnf(c_0_12289_0,axiom,
    ( c_less(c_minus(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12289]) ).

cnf(c_0_12289_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_less(c_minus(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12289]) ).

cnf(c_0_12289_2,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | c_less(c_minus(X1,X2,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12289]) ).

cnf(c_0_12290_0,axiom,
    ( c_less(c_div(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_1,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12290]) ).

cnf(c_0_12290_1,axiom,
    ( ~ c_less(c_1,X2,tc_nat)
    | c_less(c_div(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12290]) ).

cnf(c_0_12290_2,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(c_1,X2,tc_nat)
    | c_less(c_div(X1,X2,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12290]) ).

cnf(c_0_12295_0,axiom,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12295]) ).

cnf(c_0_12295_1,axiom,
    ( ~ c_less(c_plus(X1,X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12295]) ).

cnf(c_0_12295_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_less(c_plus(X1,X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12295]) ).

cnf(c_0_12295_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_less(c_plus(X1,X1,X2),c_0,X2)
    | c_less(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12295]) ).

cnf(c_0_12296_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_insert(X1,X4,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12296]) ).

cnf(c_0_12296_1,axiom,
    ( ~ c_lessequals(c_insert(X1,X4,X3),X2,tc_set(X3))
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12296]) ).

cnf(c_0_12297_0,axiom,
    ( c_less(c_0,c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12297]) ).

cnf(c_0_12297_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12297]) ).

cnf(c_0_12297_2,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12297]) ).

cnf(c_0_12298_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12298]) ).

cnf(c_0_12298_1,axiom,
    ( ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | c_in(X1,X2,X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12298]) ).

cnf(c_0_12298_2,axiom,
    ( ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12298]) ).

cnf(c_0_12299_0,axiom,
    ( ~ c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12299]) ).

cnf(c_0_12299_1,axiom,
    ( ~ c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3)
    | ~ c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12299]) ).

cnf(c_0_12300_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanLessThan(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12300]) ).

cnf(c_0_12300_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OgreaterThanLessThan(X4,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12300]) ).

cnf(c_0_12300_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanLessThan(X4,X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12300]) ).

cnf(c_0_12301_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanLessThan(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12301]) ).

cnf(c_0_12301_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OgreaterThanLessThan(X1,X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12301]) ).

cnf(c_0_12301_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanLessThan(X1,X4,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12301]) ).

cnf(c_0_12302_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanAtMost(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12302]) ).

cnf(c_0_12302_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OgreaterThanAtMost(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12302]) ).

cnf(c_0_12302_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OgreaterThanAtMost(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12302]) ).

cnf(c_0_12303_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanAtMost(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12303]) ).

cnf(c_0_12303_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OgreaterThanAtMost(X1,X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12303]) ).

cnf(c_0_12303_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThanAtMost(X1,X4,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12303]) ).

cnf(c_0_12304_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatLeastLessThan(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12304]) ).

cnf(c_0_12304_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OatLeastLessThan(X4,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12304]) ).

cnf(c_0_12304_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OatLeastLessThan(X4,X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12304]) ).

cnf(c_0_12305_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeastLessThan(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12305]) ).

cnf(c_0_12305_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OatLeastLessThan(X1,X4,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12305]) ).

cnf(c_0_12305_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OatLeastLessThan(X1,X4,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12305]) ).

cnf(c_0_12306_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatLeastAtMost(X4,X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12306]) ).

cnf(c_0_12306_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OatLeastAtMost(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12306]) ).

cnf(c_0_12306_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OatLeastAtMost(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12306]) ).

cnf(c_0_12307_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeastAtMost(X1,X4,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12307]) ).

cnf(c_0_12307_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OatLeastAtMost(X1,X4,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12307]) ).

cnf(c_0_12307_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OatLeastAtMost(X1,X4,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12307]) ).

cnf(c_0_12308_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12308]) ).

cnf(c_0_12308_1,axiom,
    ( ~ c_lessequals(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12308]) ).

cnf(c_0_12308_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12308]) ).

cnf(c_0_12309_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12309]) ).

cnf(c_0_12309_1,axiom,
    ( ~ c_lessequals(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12309]) ).

cnf(c_0_12309_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12309]) ).

cnf(c_0_12310_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12310]) ).

cnf(c_0_12310_1,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12310]) ).

cnf(c_0_12310_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12310]) ).

cnf(c_0_12311_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12311]) ).

cnf(c_0_12311_1,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12311]) ).

cnf(c_0_12311_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12311]) ).

cnf(c_0_12312_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12312]) ).

cnf(c_0_12312_1,axiom,
    ( ~ c_less(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12312]) ).

cnf(c_0_12312_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_less(X1,c_Orderings_Omin(X4,X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12312]) ).

cnf(c_0_12313_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12313]) ).

cnf(c_0_12313_1,axiom,
    ( ~ c_less(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12313]) ).

cnf(c_0_12313_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_less(X1,c_Orderings_Omin(X2,X4,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12313]) ).

cnf(c_0_12314_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12314]) ).

cnf(c_0_12314_1,axiom,
    ( ~ c_less(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12314]) ).

cnf(c_0_12314_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_less(c_Orderings_Omax(X4,X1,X3),X2,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12314]) ).

cnf(c_0_12315_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12315]) ).

cnf(c_0_12315_1,axiom,
    ( ~ c_less(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12315]) ).

cnf(c_0_12315_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_less(c_Orderings_Omax(X1,X4,X3),X2,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12315]) ).

cnf(c_0_12316_0,axiom,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X3)),c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12316]) ).

cnf(c_0_12316_1,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X3)),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12316]) ).

cnf(c_0_12316_2,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X3)),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12316]) ).

cnf(c_0_12317_0,axiom,
    ( c_minus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_minus(X1,X2,tc_nat),X3)
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12317]) ).

cnf(c_0_12317_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_minus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_minus(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12317]) ).

cnf(c_0_12317_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | ~ c_lessequals(X2,X1,tc_nat)
    | c_minus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_minus(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12317]) ).

cnf(c_0_12318_0,axiom,
    ( c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12318]) ).

cnf(c_0_12318_1,axiom,
    ( c_in(X1,X3,X4)
    | c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12318]) ).

cnf(c_0_12318_2,axiom,
    ( ~ c_in(X1,X2,X4)
    | c_in(X1,X3,X4)
    | c_in(X1,c_minus(X2,X3,tc_set(X4)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12318]) ).

cnf(c_0_12319_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12319]) ).

cnf(c_0_12319_1,axiom,
    ( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12319]) ).

cnf(c_0_12320_0,axiom,
    ( c_less(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ c_less(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12320]) ).

cnf(c_0_12320_1,axiom,
    ( ~ c_less(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12320]) ).

cnf(c_0_12320_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12320]) ).

cnf(c_0_12320_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | c_less(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12320]) ).

cnf(c_0_12321_0,axiom,
    ( c_lessequals(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ c_lessequals(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12321]) ).

cnf(c_0_12321_1,axiom,
    ( ~ c_lessequals(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12321]) ).

cnf(c_0_12321_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12321]) ).

cnf(c_0_12321_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(X3,X2),c_Numeral_Onumber__of(X1,X2),X2)
    | c_lessequals(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12321]) ).

cnf(c_0_12322_0,axiom,
    ( c_less(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12322]) ).

cnf(c_0_12322_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | c_less(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12322]) ).

cnf(c_0_12322_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | c_less(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12322]) ).

cnf(c_0_12322_3,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_less(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | c_less(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12322]) ).

cnf(c_0_12323_0,axiom,
    ( c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12323]) ).

cnf(c_0_12323_1,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12323]) ).

cnf(c_0_12323_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12323]) ).

cnf(c_0_12323_3,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(c_Numeral_Onumber__of(X2,X3),c_uminus(X1,X3),X3)
    | c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12323]) ).

cnf(c_0_12324_0,axiom,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12324]) ).

cnf(c_0_12324_1,axiom,
    ( ~ c_less(c_0,c_divide(c_1,X1,X2),X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12324]) ).

cnf(c_0_12324_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_1,X1,X2),X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12324]) ).

cnf(c_0_12324_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_divide(c_1,X1,X2),X2)
    | c_less(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12324]) ).

cnf(c_0_12325_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12325]) ).

cnf(c_0_12325_1,axiom,
    ( ~ c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12325]) ).

cnf(c_0_12325_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12325]) ).

cnf(c_0_12325_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12325]) ).

cnf(c_0_12326_0,axiom,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12326]) ).

cnf(c_0_12326_1,axiom,
    ( ~ c_less(c_divide(c_1,X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12326]) ).

cnf(c_0_12326_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_1,X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12326]) ).

cnf(c_0_12326_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_divide(c_1,X1,X2),c_0,X2)
    | c_less(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12326]) ).

cnf(c_0_12327_0,axiom,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12327]) ).

cnf(c_0_12327_1,axiom,
    ( ~ c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12327]) ).

cnf(c_0_12327_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12327]) ).

cnf(c_0_12327_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12327]) ).

cnf(c_0_12328_0,axiom,
    ( c_minus(c_insert(X1,X2,X3),X4,tc_set(X3)) = c_minus(X2,X4,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12328]) ).

cnf(c_0_12328_1,axiom,
    ( ~ c_in(X1,X4,X3)
    | c_minus(c_insert(X1,X2,X3),X4,tc_set(X3)) = c_minus(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12328]) ).

cnf(c_0_12329_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12329]) ).

cnf(c_0_12329_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12329]) ).

cnf(c_0_12329_2,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12329]) ).

cnf(c_0_12329_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12329]) ).

cnf(c_0_12330_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12330]) ).

cnf(c_0_12330_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12330]) ).

cnf(c_0_12330_2,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12330]) ).

cnf(c_0_12330_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12330]) ).

cnf(c_0_12331_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12331]) ).

cnf(c_0_12331_1,axiom,
    ( ~ c_less(c_minus(X1,X2,X3),c_0,X3)
    | c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12331]) ).

cnf(c_0_12331_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_less(c_minus(X1,X2,X3),c_0,X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12331]) ).

cnf(c_0_12332_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12332]) ).

cnf(c_0_12332_1,axiom,
    ( ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12332]) ).

cnf(c_0_12332_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12332]) ).

cnf(c_0_12334_0,axiom,
    ( c_div(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_plus(c_div(X1,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X2 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12334]) ).

cnf(c_0_12334_1,axiom,
    ( X2 = c_0
    | c_div(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_plus(c_div(X1,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12334]) ).

cnf(c_0_12335_0,axiom,
    ( c_div(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_plus(c_div(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12335]) ).

cnf(c_0_12335_1,axiom,
    ( X1 = c_0
    | c_div(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_plus(c_div(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12335]) ).

cnf(c_0_12336_0,axiom,
    ( ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12336]) ).

cnf(c_0_12336_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12336]) ).

cnf(c_0_12336_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12336]) ).

cnf(c_0_12336_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12336]) ).

cnf(c_0_12337_0,axiom,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat)
    | c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12337]) ).

cnf(c_0_12337_1,axiom,
    ( c_less(c_0,X2,tc_nat)
    | c_lessequals(c_times(X1,X2,tc_nat),c_times(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12337]) ).

cnf(c_0_12338_0,axiom,
    ( c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12338]) ).

cnf(c_0_12338_1,axiom,
    ( c_less(c_0,X1,tc_nat)
    | c_lessequals(c_times(X1,X2,tc_nat),c_times(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12338]) ).

cnf(c_0_12339_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12339]) ).

cnf(c_0_12339_1,axiom,
    ( ~ c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12339]) ).

cnf(c_0_12339_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12339]) ).

cnf(c_0_12340_0,axiom,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12340]) ).

cnf(c_0_12340_1,axiom,
    ( ~ c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12340]) ).

cnf(c_0_12340_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12340]) ).

cnf(c_0_12341_0,axiom,
    ( X1 = X2
    | c_in(X1,X3,X4)
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12341]) ).

cnf(c_0_12341_1,axiom,
    ( c_in(X1,X3,X4)
    | X1 = X2
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12341]) ).

cnf(c_0_12341_2,axiom,
    ( ~ c_in(X1,c_insert(X2,X3,X4),X4)
    | c_in(X1,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12341]) ).

cnf(c_0_12342_0,axiom,
    ( X1 = X2
    | c_List_Oop_Amem(X2,X3,X4)
    | ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12342]) ).

cnf(c_0_12342_1,axiom,
    ( c_List_Oop_Amem(X2,X3,X4)
    | X1 = X2
    | ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12342]) ).

cnf(c_0_12342_2,axiom,
    ( ~ c_List_Oop_Amem(X2,c_List_Olist_OCons(X1,X3,X4),X4)
    | c_List_Oop_Amem(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12342]) ).

cnf(c_0_12343_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12343]) ).

cnf(c_0_12343_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12343]) ).

cnf(c_0_12343_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12343]) ).

cnf(c_0_12344_0,axiom,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12344]) ).

cnf(c_0_12344_1,axiom,
    ( c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset
    | c_inter(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12344]) ).

cnf(c_0_12345_0,axiom,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12345]) ).

cnf(c_0_12345_1,axiom,
    ( c_inter(c_insert(X4,X1,X3),X2,X3) != c_emptyset
    | c_inter(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12345]) ).

cnf(c_0_12346_0,axiom,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12346]) ).

cnf(c_0_12346_1,axiom,
    ( c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset
    | c_inter(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12346]) ).

cnf(c_0_12347_0,axiom,
    ( c_inter(X1,X2,X3) = c_emptyset
    | c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12347]) ).

cnf(c_0_12347_1,axiom,
    ( c_inter(X1,c_insert(X4,X2,X3),X3) != c_emptyset
    | c_inter(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12347]) ).

cnf(c_0_12348_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12348]) ).

cnf(c_0_12348_1,axiom,
    ( ~ c_in(X1,c_inter(X4,X2,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12348]) ).

cnf(c_0_12349_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12349]) ).

cnf(c_0_12349_1,axiom,
    ( ~ c_in(X1,c_inter(X2,X4,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12349]) ).

cnf(c_0_12350_0,axiom,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12350]) ).

cnf(c_0_12350_1,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12350]) ).

cnf(c_0_12352_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12352]) ).

cnf(c_0_12352_1,axiom,
    ( c_Numeral_Onumber__of(X1,X2) != c_1
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12352]) ).

cnf(c_0_12352_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12352]) ).

cnf(c_0_12354_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12354]) ).

cnf(c_0_12354_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12354]) ).

cnf(c_0_12354_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12354]) ).

cnf(c_0_12354_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12354]) ).

cnf(c_0_12355_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12355]) ).

cnf(c_0_12355_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12355]) ).

cnf(c_0_12355_2,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12355]) ).

cnf(c_0_12356_0,axiom,
    ( c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_0),c_times(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12356]) ).

cnf(c_0_12356_1,axiom,
    ( ~ c_lessequals(c_Suc(c_0),c_times(X2,X1,tc_nat),tc_nat)
    | c_lessequals(c_1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12356]) ).

cnf(c_0_12357_0,axiom,
    ( c_lessequals(c_1,X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12357]) ).

cnf(c_0_12357_1,axiom,
    ( ~ c_lessequals(c_Suc(c_0),c_times(X1,X2,tc_nat),tc_nat)
    | c_lessequals(c_1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12357]) ).

cnf(c_0_12358_0,axiom,
    ( c_Orderings_Omin(X1,c_Finite__Set_OMin(X2,X3),X3) = c_Finite__Set_OMin(c_insert(X1,X2,X3),X3)
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12358]) ).

cnf(c_0_12358_1,axiom,
    ( X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMin(X2,X3),X3) = c_Finite__Set_OMin(c_insert(X1,X2,X3),X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12358]) ).

cnf(c_0_12358_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMin(X2,X3),X3) = c_Finite__Set_OMin(c_insert(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12358]) ).

cnf(c_0_12358_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMin(X2,X3),X3) = c_Finite__Set_OMin(c_insert(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12358]) ).

cnf(c_0_12359_0,axiom,
    ( c_Orderings_Omax(X1,c_Finite__Set_OMax(X2,X3),X3) = c_Finite__Set_OMax(c_insert(X1,X2,X3),X3)
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12359]) ).

cnf(c_0_12359_1,axiom,
    ( X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMax(X2,X3),X3) = c_Finite__Set_OMax(c_insert(X1,X2,X3),X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12359]) ).

cnf(c_0_12359_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMax(X2,X3),X3) = c_Finite__Set_OMax(c_insert(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12359]) ).

cnf(c_0_12359_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMax(X2,X3),X3) = c_Finite__Set_OMax(c_insert(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12359]) ).

cnf(c_0_12360_0,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12360]) ).

cnf(c_0_12360_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12360]) ).

cnf(c_0_12360_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12360]) ).

cnf(c_0_12360_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12360]) ).

cnf(c_0_12361_0,axiom,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(X2,X4,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12361]) ).

cnf(c_0_12361_1,axiom,
    ( c_in(X1,X4,X3)
    | c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_inter(X2,X4,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12361]) ).

cnf(c_0_12361_2,axiom,
    ( c_inter(X2,X4,X3) != c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12361]) ).

cnf(c_0_12362_0,axiom,
    ( c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(X2,X4,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12362]) ).

cnf(c_0_12362_1,axiom,
    ( c_in(X1,X4,X3)
    | c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset
    | c_inter(X2,X4,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12362]) ).

cnf(c_0_12362_2,axiom,
    ( c_inter(X2,X4,X3) != c_emptyset
    | c_in(X1,X4,X3)
    | c_inter(c_insert(X1,X2,X3),X4,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12362]) ).

cnf(c_0_12363_0,axiom,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,X3,X4) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12363]) ).

cnf(c_0_12363_1,axiom,
    ( c_in(X2,X1,X4)
    | c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_inter(X1,X3,X4) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12363]) ).

cnf(c_0_12363_2,axiom,
    ( c_inter(X1,X3,X4) != c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12363]) ).

cnf(c_0_12364_0,axiom,
    ( c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,X3,X4) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12364]) ).

cnf(c_0_12364_1,axiom,
    ( c_in(X2,X1,X4)
    | c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset
    | c_inter(X1,X3,X4) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12364]) ).

cnf(c_0_12364_2,axiom,
    ( c_inter(X1,X3,X4) != c_emptyset
    | c_in(X2,X1,X4)
    | c_inter(X1,c_insert(X2,X3,X4),X4) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12364]) ).

cnf(c_0_12365_0,axiom,
    ( c_List_Onth(c_List_Otake(X1,X2,X3),X4,X3) = c_List_Onth(X2,X4,X3)
    | ~ c_less(X4,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12365]) ).

cnf(c_0_12365_1,axiom,
    ( ~ c_less(X4,X1,tc_nat)
    | c_List_Onth(c_List_Otake(X1,X2,X3),X4,X3) = c_List_Onth(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12365]) ).

cnf(c_0_12366_0,axiom,
    ( c_Finite__Set_Ocard(c_insert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12366]) ).

cnf(c_0_12366_1,axiom,
    ( c_in(X1,X2,X3)
    | c_Finite__Set_Ocard(c_insert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12366]) ).

cnf(c_0_12366_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(X1,X2,X3)
    | c_Finite__Set_Ocard(c_insert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12366]) ).

cnf(c_0_12367_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | ~ c_less(c_Numeral_Onumber__of(X1,X3),c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12367]) ).

cnf(c_0_12367_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X3),c_Numeral_Onumber__of(X2,X3),X3)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12367]) ).

cnf(c_0_12367_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_Numeral_Onumber__of(X1,X3),c_Numeral_Onumber__of(X2,X3),X3)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12367]) ).

cnf(c_0_12367_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_Numeral_Onumber__of(X1,X3),c_Numeral_Onumber__of(X2,X3),X3)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12367]) ).

cnf(c_0_12368_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_0,c_minus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12368]) ).

cnf(c_0_12368_1,axiom,
    ( ~ c_less(c_0,c_minus(X2,X1,tc_nat),tc_nat)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12368]) ).

cnf(c_0_12369_0,axiom,
    ( c_inter(c_List_Oset(X1,X2),c_List_Oset(X3,X2),X2) = c_emptyset
    | ~ c_List_Odistinct(c_append(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12369]) ).

cnf(c_0_12369_1,axiom,
    ( ~ c_List_Odistinct(c_append(X1,X3,X2),X2)
    | c_inter(c_List_Oset(X1,X2),c_List_Oset(X3,X2),X2) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12369]) ).

cnf(c_0_12370_0,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X3,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12370]) ).

cnf(c_0_12370_1,axiom,
    ( c_in(X3,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_OHPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12370]) ).

cnf(c_0_12370_2,axiom,
    ( ~ c_in(c_Message_OHPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X3,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12370]) ).

cnf(c_0_12371_0,axiom,
    ( c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist__inter(X2,X4,X3)
    | c_in(X1,c_List_Oset(X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12371]) ).

cnf(c_0_12371_1,axiom,
    ( c_in(X1,c_List_Oset(X4,X3),X3)
    | c_List_Olist__inter(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist__inter(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12371]) ).

cnf(c_0_12372_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_times(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12372]) ).

cnf(c_0_12372_1,axiom,
    ( ~ c_less(c_0,c_times(X2,X1,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12372]) ).

cnf(c_0_12373_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12373]) ).

cnf(c_0_12373_1,axiom,
    ( ~ c_less(c_0,c_times(X1,X2,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12373]) ).

cnf(c_0_12374_0,axiom,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12374]) ).

cnf(c_0_12374_1,axiom,
    ( ~ c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12374]) ).

cnf(c_0_12375_0,axiom,
    ( c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12375]) ).

cnf(c_0_12375_1,axiom,
    ( ~ c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_lessequals(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12375]) ).

cnf(c_0_12376_0,axiom,
    ( c_in(c_Main_OUnion__iff__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12376]) ).

cnf(c_0_12376_1,axiom,
    ( ~ c_in(X1,c_Union(X2,X3),X3)
    | c_in(c_Main_OUnion__iff__1(X1,X2,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12376]) ).

cnf(c_0_12377_0,axiom,
    ( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12377]) ).

cnf(c_0_12377_1,axiom,
    ( ~ c_in(X1,c_Union(X2,X3),X3)
    | c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12377]) ).

cnf(c_0_12378_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12378]) ).

cnf(c_0_12378_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12378]) ).

cnf(c_0_12378_2,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12378]) ).

cnf(c_0_12378_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12378]) ).

cnf(c_0_12379_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12379]) ).

cnf(c_0_12379_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12379]) ).

cnf(c_0_12379_2,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12379]) ).

cnf(c_0_12379_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12379]) ).

cnf(c_0_12380_0,axiom,
    ( X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12380]) ).

cnf(c_0_12380_1,axiom,
    ( c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3)
    | X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12380]) ).

cnf(c_0_12381_0,axiom,
    ( c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2)
    | ~ c_in(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12381]) ).

cnf(c_0_12381_1,axiom,
    ( ~ c_in(c_0,X3,tc_nat)
    | c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12381]) ).

cnf(c_0_12383_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12383]) ).

cnf(c_0_12383_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12383]) ).

cnf(c_0_12383_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12383]) ).

cnf(c_0_12383_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12383]) ).

cnf(c_0_12385_0,axiom,
    ( c_in(X1,c_Main_OUnion__iff__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12385]) ).

cnf(c_0_12385_1,axiom,
    ( ~ c_in(X1,c_Union(X2,X3),X3)
    | c_in(X1,c_Main_OUnion__iff__1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12385]) ).

cnf(c_0_12386_0,axiom,
    ( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12386]) ).

cnf(c_0_12386_1,axiom,
    ( ~ c_in(X1,c_Union(X2,X3),X3)
    | c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12386]) ).

cnf(c_0_12387_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12387]) ).

cnf(c_0_12387_1,axiom,
    ( c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12387]) ).

cnf(c_0_12387_2,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12387]) ).

cnf(c_0_12387_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12387]) ).

cnf(c_0_12387_4,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2),c_0,X2)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12387]) ).

cnf(c_0_12388_0,axiom,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12388]) ).

cnf(c_0_12388_1,axiom,
    ( c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12388]) ).

cnf(c_0_12388_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12388]) ).

cnf(c_0_12389_0,axiom,
    ( c_append(c_List_Oupt(X1,X2),c_List_Olist_OCons(X2,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X1,c_Suc(X2))
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12389]) ).

cnf(c_0_12389_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_append(c_List_Oupt(X1,X2),c_List_Olist_OCons(X2,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X1,c_Suc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12389]) ).

cnf(c_0_12390_0,axiom,
    ( c_in(c_Message_Omsg_OKey(v_sko__uhi(X1,X2)),X1,tc_Message_Omsg)
    | c_in(X2,c_Message_OkeysFor(X1),tc_nat)
    | ~ c_in(X2,c_Message_OkeysFor(c_Message_Osynth(X1)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12390]) ).

cnf(c_0_12390_1,axiom,
    ( c_in(X2,c_Message_OkeysFor(X1),tc_nat)
    | c_in(c_Message_Omsg_OKey(v_sko__uhi(X1,X2)),X1,tc_Message_Omsg)
    | ~ c_in(X2,c_Message_OkeysFor(c_Message_Osynth(X1)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12390]) ).

cnf(c_0_12390_2,axiom,
    ( ~ c_in(X2,c_Message_OkeysFor(c_Message_Osynth(X1)),tc_nat)
    | c_in(X2,c_Message_OkeysFor(X1),tc_nat)
    | c_in(c_Message_Omsg_OKey(v_sko__uhi(X1,X2)),X1,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12390]) ).

cnf(c_0_12391_0,axiom,
    ( c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)) = c_minus(X1,X3,tc_set(X4))
    | c_in(X2,X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12391]) ).

cnf(c_0_12391_1,axiom,
    ( c_in(X2,X1,X4)
    | c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)) = c_minus(X1,X3,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12391]) ).

cnf(c_0_12392_0,axiom,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12392]) ).

cnf(c_0_12392_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12392]) ).

cnf(c_0_12393_0,axiom,
    ( c_List_Olist_OCons(X1,c_List_Oremdups(X2,X3),X3) = c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12393]) ).

cnf(c_0_12393_1,axiom,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | c_List_Olist_OCons(X1,c_List_Oremdups(X2,X3),X3) = c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12393]) ).

cnf(c_0_12394_0,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12394]) ).

cnf(c_0_12394_1,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12394]) ).

cnf(c_0_12395_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Event_Obad,tc_Message_Oagent) ),
    inference(literals_permutation,[status(thm)],[c_0_12395]) ).

cnf(c_0_12395_1,axiom,
    ( ~ c_in(X2,c_Event_Obad,tc_Message_Oagent)
    | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12395]) ).

cnf(c_0_12396_0,axiom,
    ( c_List_Olast(c_List_Odrop(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | ~ c_less(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12396]) ).

cnf(c_0_12396_1,axiom,
    ( ~ c_less(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat)
    | c_List_Olast(c_List_Odrop(X1,X2,X3),X3) = c_List_Olast(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12396]) ).

cnf(c_0_12397_0,axiom,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12397]) ).

cnf(c_0_12397_1,axiom,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | X1 = c_0
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12397]) ).

cnf(c_0_12397_2,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12397]) ).

cnf(c_0_12397_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | X1 = c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12397]) ).

cnf(c_0_12397_4,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12397]) ).

cnf(c_0_12398_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12398]) ).

cnf(c_0_12398_1,axiom,
    ( ~ c_in(X1,c_Inter(X4,X3),X3)
    | c_in(X1,X2,X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12398]) ).

cnf(c_0_12398_2,axiom,
    ( ~ c_in(X2,X4,tc_set(X3))
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12398]) ).

cnf(c_0_12399_0,axiom,
    ( c_List_Otl(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_minus(X1,c_1,tc_nat),X2,X3)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12399]) ).

cnf(c_0_12399_1,axiom,
    ( X1 = c_0
    | c_List_Otl(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_minus(X1,c_1,tc_nat),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12399]) ).

cnf(c_0_12400_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12400]) ).

cnf(c_0_12400_1,axiom,
    ( ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12400]) ).

cnf(c_0_12401_0,axiom,
    ( c_divide(c_times(X1,c_0,X2),c_times(X3,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12401]) ).

cnf(c_0_12401_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X1,c_0,X2),c_times(X3,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12401]) ).

cnf(c_0_12401_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X1,c_0,X2),c_times(X3,c_0,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12401]) ).

cnf(c_0_12402_0,axiom,
    ( c_divide(c_times(c_0,X1,X2),c_times(c_0,X3,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12402]) ).

cnf(c_0_12402_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,X1,X2),c_times(c_0,X3,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12402]) ).

cnf(c_0_12402_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,X1,X2),c_times(c_0,X3,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12402]) ).

cnf(c_0_12403_0,axiom,
    ( c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12403]) ).

cnf(c_0_12403_1,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12403]) ).

cnf(c_0_12403_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12403]) ).

cnf(c_0_12403_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_lessequals(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12403]) ).

cnf(c_0_12404_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12404]) ).

cnf(c_0_12404_1,axiom,
    ( c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12404]) ).

cnf(c_0_12404_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12404]) ).

cnf(c_0_12404_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12404]) ).

cnf(c_0_12404_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12404]) ).

cnf(c_0_12405_0,axiom,
    ( c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12405]) ).

cnf(c_0_12405_1,axiom,
    ( c_Numeral_Onumber__of(X2,X3) = c_0
    | c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12405]) ).

cnf(c_0_12405_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12405]) ).

cnf(c_0_12405_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12405]) ).

cnf(c_0_12405_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | c_times(c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12405]) ).

cnf(c_0_12406_0,axiom,
    ( c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12406]) ).

cnf(c_0_12406_1,axiom,
    ( c_Numeral_Onumber__of(X2,X3) = c_0
    | c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12406]) ).

cnf(c_0_12406_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12406]) ).

cnf(c_0_12406_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12406]) ).

cnf(c_0_12406_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) = c_0
    | c_divide(c_times(X1,c_Numeral_Onumber__of(X2,X3),X3),c_Numeral_Onumber__of(X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12406]) ).

cnf(c_0_12407_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12407]) ).

cnf(c_0_12407_1,axiom,
    ( c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12407]) ).

cnf(c_0_12407_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12407]) ).

cnf(c_0_12407_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12407]) ).

cnf(c_0_12407_4,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_divide(X3,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_Numeral_Onumber__of(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12407]) ).

cnf(c_0_12408_0,axiom,
    ( c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
    | c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12408]) ).

cnf(c_0_12408_1,axiom,
    ( c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3))
    | c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12408]) ).

cnf(c_0_12409_0,axiom,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12409]) ).

cnf(c_0_12409_1,axiom,
    ( c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12409]) ).

cnf(c_0_12409_2,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12409]) ).

cnf(c_0_12410_0,axiom,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12410]) ).

cnf(c_0_12410_1,axiom,
    ( c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12410]) ).

cnf(c_0_12410_2,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12410]) ).

cnf(c_0_12411_0,axiom,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12411]) ).

cnf(c_0_12411_1,axiom,
    ( c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12411]) ).

cnf(c_0_12411_2,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12411]) ).

cnf(c_0_12412_0,axiom,
    ( c_in(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12412]) ).

cnf(c_0_12412_1,axiom,
    ( c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12412]) ).

cnf(c_0_12412_2,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12412]) ).

cnf(c_0_12413_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12413]) ).

cnf(c_0_12413_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12413]) ).

cnf(c_0_12413_2,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12413]) ).

cnf(c_0_12413_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12413]) ).

cnf(c_0_12414_0,axiom,
    ( c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12414]) ).

cnf(c_0_12414_1,axiom,
    ( ~ c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12414]) ).

cnf(c_0_12414_2,axiom,
    ( ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X3),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12414]) ).

cnf(c_0_12415_0,axiom,
    ( c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X3,tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12415]) ).

cnf(c_0_12415_1,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(X1),X3,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12415]) ).

cnf(c_0_12415_2,axiom,
    ( ~ c_in(X2,c_Message_Osynth(X3),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X3,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X2),c_Message_Osynth(X3),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12415]) ).

cnf(c_0_12416_0,axiom,
    ( X1 = X2
    | c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12416]) ).

cnf(c_0_12416_1,axiom,
    ( c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | X1 = X2
    | ~ c_less(c_1,X3,X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12416]) ).

cnf(c_0_12416_2,axiom,
    ( ~ c_less(c_1,X3,X4)
    | c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12416]) ).

cnf(c_0_12416_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ c_less(c_1,X3,X4)
    | c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | X1 = X2
    | ~ class_Power_Orecpower(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12416]) ).

cnf(c_0_12416_4,axiom,
    ( ~ class_Power_Orecpower(X4)
    | ~ class_Ring__and__Field_Oordered__semidom(X4)
    | ~ c_less(c_1,X3,X4)
    | c_Nat_Opower(X3,X1,X4) != c_Nat_Opower(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12416]) ).

cnf(c_0_12417_0,axiom,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12417]) ).

cnf(c_0_12417_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12417]) ).

cnf(c_0_12418_0,axiom,
    ( c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12418]) ).

cnf(c_0_12418_1,axiom,
    ( X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12418]) ).

cnf(c_0_12418_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12418]) ).

cnf(c_0_12418_3,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12418]) ).

cnf(c_0_12418_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omax(X1,c_Finite__Set_OMin(X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12418]) ).

cnf(c_0_12419_0,axiom,
    ( c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1
    | X2 = c_emptyset
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12419]) ).

cnf(c_0_12419_1,axiom,
    ( X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12419]) ).

cnf(c_0_12419_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1
    | ~ c_in(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12419]) ).

cnf(c_0_12419_3,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12419]) ).

cnf(c_0_12419_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | X2 = c_emptyset
    | c_Orderings_Omin(X1,c_Finite__Set_OMax(X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12419]) ).

cnf(c_0_12420_0,axiom,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12420]) ).

cnf(c_0_12420_1,axiom,
    ( c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12420]) ).

cnf(c_0_12420_2,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(X1,X3),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(X1,X3),c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12420]) ).

cnf(c_0_12421_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12421]) ).

cnf(c_0_12421_1,axiom,
    ( c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12421]) ).

cnf(c_0_12421_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ c_in(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12421]) ).

cnf(c_0_12421_3,axiom,
    ( ~ c_in(X3,X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12421]) ).

cnf(c_0_12421_4,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X3,X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_lessequals(c_Finite__Set_OMin(X1,X2),X3,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12421]) ).

cnf(c_0_12422_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12422]) ).

cnf(c_0_12422_1,axiom,
    ( c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12422]) ).

cnf(c_0_12422_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | X1 = c_emptyset
    | ~ c_in(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12422]) ).

cnf(c_0_12422_3,axiom,
    ( ~ c_in(X2,X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12422]) ).

cnf(c_0_12422_4,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_lessequals(X2,c_Finite__Set_OMax(X1,X3),X3)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12422]) ).

cnf(c_0_12424_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12424]) ).

cnf(c_0_12424_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12424]) ).

cnf(c_0_12424_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12424]) ).

cnf(c_0_12424_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12424]) ).

cnf(c_0_12425_0,axiom,
    ( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12425]) ).

cnf(c_0_12425_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12425]) ).

cnf(c_0_12426_0,axiom,
    ( c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12426]) ).

cnf(c_0_12426_1,axiom,
    ( ~ c_in(X4,X2,tc_set(X3))
    | c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12426]) ).

cnf(c_0_12426_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12426]) ).

cnf(c_0_12427_0,axiom,
    ( c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oremdups(X2,X3)
    | ~ c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12427]) ).

cnf(c_0_12427_1,axiom,
    ( ~ c_in(X1,c_List_Oset(X2,X3),X3)
    | c_List_Oremdups(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oremdups(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12427]) ).

cnf(c_0_12428_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12428]) ).

cnf(c_0_12428_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12428]) ).

cnf(c_0_12428_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12428]) ).

cnf(c_0_12429_0,axiom,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12429]) ).

cnf(c_0_12429_1,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12429]) ).

cnf(c_0_12430_0,axiom,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12430]) ).

cnf(c_0_12430_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12430]) ).

cnf(c_0_12431_0,axiom,
    ( c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12431]) ).

cnf(c_0_12431_1,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12431]) ).

cnf(c_0_12432_0,axiom,
    ( c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,X3,X4)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12432]) ).

cnf(c_0_12432_1,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | c_List_Odrop(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12432]) ).

cnf(c_0_12433_0,axiom,
    ( c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12433]) ).

cnf(c_0_12433_1,axiom,
    ( ~ c_less(X1,c_0,X2)
    | c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12433]) ).

cnf(c_0_12433_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12433]) ).

cnf(c_0_12433_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_Orderings_Olinorder(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_plus(X1,X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12433]) ).

cnf(c_0_12434_0,axiom,
    ( c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12434]) ).

cnf(c_0_12434_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12434]) ).

cnf(c_0_12434_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12434]) ).

cnf(c_0_12434_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12434]) ).

cnf(c_0_12435_0,axiom,
    ( c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12435]) ).

cnf(c_0_12435_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12435]) ).

cnf(c_0_12435_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12435]) ).

cnf(c_0_12435_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,c_Numeral_Onumber__of(X1,X2),X2),c_Numeral_Onumber__of(X1,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12435]) ).

cnf(c_0_12436_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12436]) ).

cnf(c_0_12436_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12436]) ).

cnf(c_0_12436_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12436]) ).

cnf(c_0_12436_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12436]) ).

cnf(c_0_12439_0,axiom,
    ( c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_OkeysFor(c_Message_Oanalz(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12439]) ).

cnf(c_0_12439_1,axiom,
    ( c_in(X1,c_Message_OkeysFor(c_Message_Oanalz(X2)),tc_nat)
    | c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12439]) ).

cnf(c_0_12441_0,axiom,
    ( c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12441]) ).

cnf(c_0_12441_1,axiom,
    ( ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12441]) ).

cnf(c_0_12441_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12441]) ).

cnf(c_0_12441_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_divide(c_1,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12441]) ).

cnf(c_0_12442_0,axiom,
    ( c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12442]) ).

cnf(c_0_12442_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12442]) ).

cnf(c_0_12442_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_divide(c_1,X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12442]) ).

cnf(c_0_12442_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_divide(c_1,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12442]) ).

cnf(c_0_12443_0,axiom,
    ( c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12443]) ).

cnf(c_0_12443_1,axiom,
    ( ~ c_less(X1,c_0,X2)
    | c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12443]) ).

cnf(c_0_12443_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12443]) ).

cnf(c_0_12443_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_divide(c_1,X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12443]) ).

cnf(c_0_12444_0,axiom,
    ( c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12444]) ).

cnf(c_0_12444_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12444]) ).

cnf(c_0_12444_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_divide(c_1,X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12444]) ).

cnf(c_0_12444_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_divide(c_1,X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12444]) ).

cnf(c_0_12445_0,axiom,
    ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12445]) ).

cnf(c_0_12445_1,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) != c_0
    | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12445]) ).

cnf(c_0_12446_0,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12446]) ).

cnf(c_0_12446_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12446]) ).

cnf(c_0_12447_0,axiom,
    ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12447]) ).

cnf(c_0_12447_1,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) != c_0
    | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12447]) ).

cnf(c_0_12448_0,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_0
    | ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12448]) ).

cnf(c_0_12448_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12448]) ).

cnf(c_0_12449_0,axiom,
    ( c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12449]) ).

cnf(c_0_12449_1,axiom,
    ( ~ c_less(X1,X2,X3)
    | c_less(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12449]) ).

cnf(c_0_12449_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_less(X1,X2,X3)
    | c_less(c_minus(X1,X2,X3),c_0,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12449]) ).

cnf(c_0_12450_0,axiom,
    ( c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12450]) ).

cnf(c_0_12450_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12450]) ).

cnf(c_0_12450_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_minus(X1,X2,X3),c_0,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12450]) ).

cnf(c_0_12451_0,axiom,
    ( X1 = X2
    | ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12451]) ).

cnf(c_0_12451_1,axiom,
    ( ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12451]) ).

cnf(c_0_12452_0,axiom,
    ( c_Nat_Opower(c_HOL_Oabs(X1,X2),c_Numeral_Onumber__of(X3,tc_nat),X2) = c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12452]) ).

cnf(c_0_12452_1,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_Nat_Opower(c_HOL_Oabs(X1,X2),c_Numeral_Onumber__of(X3,tc_nat),X2) = c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12452]) ).

cnf(c_0_12452_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_Nat_Opower(c_HOL_Oabs(X1,X2),c_Numeral_Onumber__of(X3,tc_nat),X2) = c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12452]) ).

cnf(c_0_12452_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
    | c_Nat_Opower(c_HOL_Oabs(X1,X2),c_Numeral_Onumber__of(X3,tc_nat),X2) = c_Nat_Opower(X1,c_Numeral_Onumber__of(X3,tc_nat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12452]) ).

cnf(c_0_12453_0,axiom,
    ( c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12453]) ).

cnf(c_0_12453_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_plus(X1,X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12453]) ).

cnf(c_0_12453_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_plus(X1,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12453]) ).

cnf(c_0_12454_0,axiom,
    ( c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12454]) ).

cnf(c_0_12454_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_plus(X1,X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12454]) ).

cnf(c_0_12454_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_plus(X1,X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12454]) ).

cnf(c_0_12455_0,axiom,
    ( c_less(c_minus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12455]) ).

cnf(c_0_12455_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_minus(X1,c_Suc(X2),tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12455]) ).

cnf(c_0_12456_0,axiom,
    ( c_minus(c_insert(X1,c_emptyset,X2),c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_insert(X1,c_emptyset,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12456]) ).

cnf(c_0_12456_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_minus(c_insert(X1,c_emptyset,X2),c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_insert(X1,c_emptyset,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12456]) ).

cnf(c_0_12457_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12457]) ).

cnf(c_0_12457_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12457]) ).

cnf(c_0_12457_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12457]) ).

cnf(c_0_12457_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12457]) ).

cnf(c_0_12458_0,axiom,
    ( c_in(c_Main_OInter__iff__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12458]) ).

cnf(c_0_12458_1,axiom,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | c_in(c_Main_OInter__iff__1(X1,X2,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12458]) ).

cnf(c_0_12459_0,axiom,
    ( c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12459]) ).

cnf(c_0_12459_1,axiom,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12459]) ).

cnf(c_0_12460_0,axiom,
    ( c_in(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12460]) ).

cnf(c_0_12460_1,axiom,
    ( ~ c_in(X1,X3,X4)
    | c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12460]) ).

cnf(c_0_12461_0,axiom,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12461]) ).

cnf(c_0_12461_1,axiom,
    ( ~ c_in(X1,X3,X4)
    | c_in(X1,c_union(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12461]) ).

cnf(c_0_12462_0,axiom,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12462]) ).

cnf(c_0_12462_1,axiom,
    ( ~ c_in(X1,X2,X4)
    | c_in(X1,c_union(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12462]) ).

cnf(c_0_12463_0,axiom,
    ( c_List_Oop_Amem(X1,c_List_Olist_OCons(X2,X3,X4),X4)
    | ~ c_List_Oop_Amem(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12463]) ).

cnf(c_0_12463_1,axiom,
    ( ~ c_List_Oop_Amem(X1,X3,X4)
    | c_List_Oop_Amem(X1,c_List_Olist_OCons(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12463]) ).

cnf(c_0_12482_0,axiom,
    ( c_List_Onth(c_List_Oreplicate(X1,X2,X3),X4,X3) = X2
    | ~ c_less(X4,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12482]) ).

cnf(c_0_12482_1,axiom,
    ( ~ c_less(X4,X1,tc_nat)
    | c_List_Onth(c_List_Oreplicate(X1,X2,X3),X4,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12482]) ).

cnf(c_0_12486_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12486]) ).

cnf(c_0_12486_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12486]) ).

cnf(c_0_12486_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12486]) ).

cnf(c_0_12486_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12486]) ).

cnf(c_0_12487_0,axiom,
    ( c_plus(X1,c_minus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12487]) ).

cnf(c_0_12487_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_plus(X1,c_minus(X2,X1,tc_nat),tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12487]) ).

cnf(c_0_12488_0,axiom,
    ( c_plus(c_minus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12488]) ).

cnf(c_0_12488_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_plus(c_minus(X1,X2,tc_nat),X2,tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12488]) ).

cnf(c_0_12489_0,axiom,
    ( c_minus(X1,c_minus(X1,X2,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12489]) ).

cnf(c_0_12489_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_minus(X1,c_minus(X1,X2,tc_nat),tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12489]) ).

cnf(c_0_12490_0,axiom,
    ( c_times(c_HOL_Oinverse(X1,X3),c_HOL_Oinverse(X2,X3),X3) = c_HOL_Oinverse(c_times(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12490]) ).

cnf(c_0_12490_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_times(c_HOL_Oinverse(X1,X3),c_HOL_Oinverse(X2,X3),X3) = c_HOL_Oinverse(c_times(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12490]) ).

cnf(c_0_12490_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_times(c_HOL_Oinverse(X1,X3),c_HOL_Oinverse(X2,X3),X3) = c_HOL_Oinverse(c_times(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12490]) ).

cnf(c_0_12491_0,axiom,
    ( c_divide(c_HOL_Oabs(X1,X3),c_HOL_Oabs(X2,X3),X3) = c_HOL_Oabs(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12491]) ).

cnf(c_0_12491_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | c_divide(c_HOL_Oabs(X1,X3),c_HOL_Oabs(X2,X3),X3) = c_HOL_Oabs(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12491]) ).

cnf(c_0_12491_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | c_divide(c_HOL_Oabs(X1,X3),c_HOL_Oabs(X2,X3),X3) = c_HOL_Oabs(c_divide(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12491]) ).

cnf(c_0_12492_0,axiom,
    ( c_lessequals(c_Suc(c_0),c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12492]) ).

cnf(c_0_12492_1,axiom,
    ( ~ c_lessequals(c_1,X1,tc_nat)
    | c_lessequals(c_Suc(c_0),c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12492]) ).

cnf(c_0_12493_0,axiom,
    ( X1 = c_0
    | ~ c_less(c_0,c_Nat_Opower(c_0,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12493]) ).

cnf(c_0_12493_1,axiom,
    ( ~ c_less(c_0,c_Nat_Opower(c_0,X1,tc_nat),tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12493]) ).

cnf(c_0_12494_0,axiom,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12494]) ).

cnf(c_0_12494_1,axiom,
    ( c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12494]) ).

cnf(c_0_12494_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12494]) ).

cnf(c_0_12494_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12494]) ).

cnf(c_0_12497_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12497]) ).

cnf(c_0_12497_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12497]) ).

cnf(c_0_12497_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12497]) ).

cnf(c_0_12498_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12498]) ).

cnf(c_0_12498_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12498]) ).

cnf(c_0_12498_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12498]) ).

cnf(c_0_12499_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12499]) ).

cnf(c_0_12499_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12499]) ).

cnf(c_0_12499_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12499]) ).

cnf(c_0_12500_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12500]) ).

cnf(c_0_12500_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12500]) ).

cnf(c_0_12500_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12500]) ).

cnf(c_0_12501_0,axiom,
    ( c_less(c_0,c_minus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12501]) ).

cnf(c_0_12501_1,axiom,
    ( ~ c_less(X2,X1,tc_nat)
    | c_less(c_0,c_minus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12501]) ).

cnf(c_0_12503_0,axiom,
    ( c_div(c_times(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12503]) ).

cnf(c_0_12503_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_div(c_times(X1,X2,tc_nat),X2,tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12503]) ).

cnf(c_0_12504_0,axiom,
    ( c_div(c_times(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12504]) ).

cnf(c_0_12504_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_div(c_times(X1,X2,tc_nat),X1,tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12504]) ).

cnf(c_0_12505_0,axiom,
    ( c_append(c_List_Obutlast(X1,X2),c_List_Olist_OCons(c_List_Olast(X1,X2),c_List_Olist_ONil,X2),X2) = X1
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12505]) ).

cnf(c_0_12505_1,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(c_List_Obutlast(X1,X2),c_List_Olist_OCons(c_List_Olast(X1,X2),c_List_Olist_ONil,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12505]) ).

cnf(c_0_12506_0,axiom,
    ( c_less(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12506]) ).

cnf(c_0_12506_1,axiom,
    ( ~ c_less(c_0,X2,tc_IntDef_Oint)
    | c_less(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12506]) ).

cnf(c_0_12507_0,axiom,
    ( c_less(X1,c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(X1,c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12507]) ).

cnf(c_0_12507_1,axiom,
    ( ~ c_less(X1,c_0,tc_IntDef_Oint)
    | c_less(X1,c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12507]) ).

cnf(c_0_12508_0,axiom,
    ( c_less(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12508]) ).

cnf(c_0_12508_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_less(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12508]) ).

cnf(c_0_12509_0,axiom,
    ( c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12509]) ).

cnf(c_0_12509_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12509]) ).

cnf(c_0_12510_0,axiom,
    ( c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12510]) ).

cnf(c_0_12510_1,axiom,
    ( ~ c_less(X1,X2,tc_IntDef_Oint)
    | c_lessequals(X1,c_minus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12510]) ).

cnf(c_0_12511_0,axiom,
    ( c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_lessequals(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12511]) ).

cnf(c_0_12511_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_IntDef_Oint)
    | c_less(X1,c_plus(X2,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12511]) ).

cnf(c_0_12512_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12512]) ).

cnf(c_0_12512_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12512]) ).

cnf(c_0_12512_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12512]) ).

cnf(c_0_12512_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12512]) ).

cnf(c_0_12513_0,axiom,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12513]) ).

cnf(c_0_12513_1,axiom,
    ( c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | X1 = X2
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12513]) ).

cnf(c_0_12513_2,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4))
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12513]) ).

cnf(c_0_12514_0,axiom,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12514]) ).

cnf(c_0_12514_1,axiom,
    ( c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | X1 = X2
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12514]) ).

cnf(c_0_12514_2,axiom,
    ( c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4))
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12514]) ).

cnf(c_0_12515_0,axiom,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12515]) ).

cnf(c_0_12515_1,axiom,
    ( c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | X1 = X2
    | c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12515]) ).

cnf(c_0_12515_2,axiom,
    ( c_Nat_Osize(X3,tc_List_Olist(X4)) != c_Nat_Osize(X5,tc_List_Olist(X4))
    | c_append(X3,X1,X4) != c_append(X5,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12515]) ).

cnf(c_0_12516_0,axiom,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12516]) ).

cnf(c_0_12516_1,axiom,
    ( c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | X1 = X2
    | c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_12516]) ).

cnf(c_0_12516_2,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X4)) != c_Nat_Osize(X2,tc_List_Olist(X4))
    | c_append(X1,X3,X4) != c_append(X2,X5,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12516]) ).

cnf(c_0_12517_0,axiom,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12517]) ).

cnf(c_0_12517_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12517]) ).

cnf(c_0_12518_0,axiom,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12518]) ).

cnf(c_0_12518_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12518]) ).

cnf(c_0_12519_0,axiom,
    ( c_lessequals(c_0,c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12519]) ).

cnf(c_0_12519_1,axiom,
    ( ~ c_less(c_0,X2,tc_IntDef_Oint)
    | c_lessequals(c_0,c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12519]) ).

cnf(c_0_12520_0,axiom,
    ( c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ c_less(X2,c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12520]) ).

cnf(c_0_12520_1,axiom,
    ( ~ c_less(X2,c_0,tc_IntDef_Oint)
    | c_lessequals(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12520]) ).

cnf(c_0_12521_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12521]) ).

cnf(c_0_12521_1,axiom,
    ( ~ c_lessequals(X4,X2,tc_set(X3))
    | c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12521]) ).

cnf(c_0_12521_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12521]) ).

cnf(c_0_12522_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12522]) ).

cnf(c_0_12522_1,axiom,
    ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12522]) ).

cnf(c_0_12523_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12523]) ).

cnf(c_0_12523_1,axiom,
    ( ~ c_Parity_Oeven(c_Nat_Opower(X2,X1,tc_nat),tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12523]) ).

cnf(c_0_12524_0,axiom,
    ( c_LOrder_Ojoin(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_LOrder_Omeet(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12524]) ).

cnf(c_0_12524_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X3)
    | c_LOrder_Ojoin(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_LOrder_Omeet(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12524]) ).

cnf(c_0_12525_0,axiom,
    ( c_LOrder_Omeet(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_LOrder_Ojoin(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12525]) ).

cnf(c_0_12525_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X3)
    | c_LOrder_Omeet(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_LOrder_Ojoin(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12525]) ).

cnf(c_0_12526_0,axiom,
    ( c_plus(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_plus(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12526]) ).

cnf(c_0_12526_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_plus(c_uminus(X1,X3),c_uminus(X2,X3),X3) = c_uminus(c_plus(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12526]) ).

cnf(c_0_12527_0,axiom,
    ( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
    | ~ c_in(X1,X2,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12527]) ).

cnf(c_0_12527_1,axiom,
    ( ~ c_in(X1,X2,tc_prod(X3,X3))
    | c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12527]) ).

cnf(c_0_12530_0,axiom,
    ( c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2))
    | ~ c_lessequals(X3,X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12530]) ).

cnf(c_0_12530_1,axiom,
    ( ~ c_lessequals(X3,X1,tc_set(X2))
    | c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12530]) ).

cnf(c_0_12531_0,axiom,
    ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3)
    | c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    inference(literals_permutation,[status(thm)],[c_0_12531]) ).

cnf(c_0_12531_1,axiom,
    ( c_in(X1,c_Event_Obad,tc_Message_Oagent)
    | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12531]) ).

cnf(c_0_12532_0,axiom,
    ( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | ~ c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12532]) ).

cnf(c_0_12532_1,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12532]) ).

cnf(c_0_12533_0,axiom,
    ( c_times(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2),X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12533]) ).

cnf(c_0_12533_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_times(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X3,X2) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2),X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12533]) ).

cnf(c_0_12535_0,axiom,
    ( c_times(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_times(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12535]) ).

cnf(c_0_12535_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
    | c_times(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_times(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12535]) ).

cnf(c_0_12536_0,axiom,
    ( c_plus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_plus(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12536]) ).

cnf(c_0_12536_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
    | c_plus(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3) = c_NatArith_Oof__nat(c_plus(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12536]) ).

cnf(c_0_12537_0,axiom,
    ( c_times(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_times(X1,X2,tc_IntDef_Oint),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12537]) ).

cnf(c_0_12537_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | c_times(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_times(X1,X2,tc_IntDef_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12537]) ).

cnf(c_0_12538_0,axiom,
    ( c_minus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_minus(X1,X2,tc_IntDef_Oint),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12538]) ).

cnf(c_0_12538_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | c_minus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_minus(X1,X2,tc_IntDef_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12538]) ).

cnf(c_0_12539_0,axiom,
    ( c_plus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_plus(X1,X2,tc_IntDef_Oint),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12539]) ).

cnf(c_0_12539_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | c_plus(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3) = c_IntDef_Oof__int(c_plus(X1,X2,tc_IntDef_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12539]) ).

cnf(c_0_12540_0,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12540]) ).

cnf(c_0_12540_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12540]) ).

cnf(c_0_12540_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X2),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12540]) ).

cnf(c_0_12541_0,axiom,
    ( c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
    | ~ c_less(c_0,X2,tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12541]) ).

cnf(c_0_12541_1,axiom,
    ( ~ c_less(c_0,X2,tc_IntDef_Oint)
    | c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
    | ~ c_less(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12541]) ).

cnf(c_0_12541_2,axiom,
    ( ~ c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_IntDef_Oint)
    | c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12541]) ).

cnf(c_0_12542_0,axiom,
    ( c_divide(X1,c_times(X2,X1,X3),X3) = c_divide(c_1,X2,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12542]) ).

cnf(c_0_12542_1,axiom,
    ( X1 = c_0
    | c_divide(X1,c_times(X2,X1,X3),X3) = c_divide(c_1,X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12542]) ).

cnf(c_0_12542_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(X1,c_times(X2,X1,X3),X3) = c_divide(c_1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12542]) ).

cnf(c_0_12542_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(X1,c_times(X2,X1,X3),X3) = c_divide(c_1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12542]) ).

cnf(c_0_12543_0,axiom,
    ( c_divide(X1,c_times(X1,X2,X3),X3) = c_divide(c_1,X2,X3)
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12543]) ).

cnf(c_0_12543_1,axiom,
    ( X1 = c_0
    | c_divide(X1,c_times(X1,X2,X3),X3) = c_divide(c_1,X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12543]) ).

cnf(c_0_12543_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(X1,c_times(X1,X2,X3),X3) = c_divide(c_1,X2,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12543]) ).

cnf(c_0_12543_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(X1,c_times(X1,X2,X3),X3) = c_divide(c_1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12543]) ).

cnf(c_0_12544_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_less(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12544]) ).

cnf(c_0_12544_1,axiom,
    ( ~ c_less(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12544]) ).

cnf(c_0_12544_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_less(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12544]) ).

cnf(c_0_12545_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12545]) ).

cnf(c_0_12545_1,axiom,
    ( ~ c_lessequals(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12545]) ).

cnf(c_0_12545_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(c_uminus(X2,X3),c_uminus(X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12545]) ).

cnf(c_0_12547_0,axiom,
    ( c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X2,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12547]) ).

cnf(c_0_12547_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Nat_Opower(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12547]) ).

cnf(c_0_12548_0,axiom,
    ( c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_uminus(c_Nat_Opower(X1,X3,X2),X2)
    | c_Parity_Oeven(X3,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12548]) ).

cnf(c_0_12548_1,axiom,
    ( c_Parity_Oeven(X3,tc_nat)
    | c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_uminus(c_Nat_Opower(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12548]) ).

cnf(c_0_12548_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_Parity_Oeven(X3,tc_nat)
    | c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_uminus(c_Nat_Opower(X1,X3,X2),X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12548]) ).

cnf(c_0_12548_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_Parity_Oeven(X3,tc_nat)
    | c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_uminus(c_Nat_Opower(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12548]) ).

cnf(c_0_12549_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12549]) ).

cnf(c_0_12549_1,axiom,
    ( ~ c_less(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | c_less(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12549]) ).

cnf(c_0_12549_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_less(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12549]) ).

cnf(c_0_12550_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12550]) ).

cnf(c_0_12550_1,axiom,
    ( ~ c_lessequals(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12550]) ).

cnf(c_0_12550_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X3),c_NatArith_Oof__nat(X2,X3),X3)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12550]) ).

cnf(c_0_12551_0,axiom,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12551]) ).

cnf(c_0_12551_1,axiom,
    ( ~ c_less(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | c_less(X1,X2,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12551]) ).

cnf(c_0_12551_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_less(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | c_less(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12551]) ).

cnf(c_0_12552_0,axiom,
    ( c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12552]) ).

cnf(c_0_12552_1,axiom,
    ( ~ c_lessequals(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | c_lessequals(X1,X2,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12552]) ).

cnf(c_0_12552_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X3),c_IntDef_Oof__int(X2,X3),X3)
    | c_lessequals(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12552]) ).

cnf(c_0_12556_0,axiom,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12556]) ).

cnf(c_0_12556_1,axiom,
    ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12556]) ).

cnf(c_0_12556_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | X1 = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12556]) ).

cnf(c_0_12556_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12556]) ).

cnf(c_0_12559_0,axiom,
    ( c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12559]) ).

cnf(c_0_12559_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12559]) ).

cnf(c_0_12559_2,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12559]) ).

cnf(c_0_12560_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12560]) ).

cnf(c_0_12560_1,axiom,
    ( c_Numeral_Onumber__of(X1,X2) != c_1
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12560]) ).

cnf(c_0_12560_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_Numeral_Onumber__of(X1,X2) != c_1
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12560]) ).

cnf(c_0_12561_0,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12561]) ).

cnf(c_0_12561_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12561]) ).

cnf(c_0_12562_0,axiom,
    ( c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12562]) ).

cnf(c_0_12562_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12562]) ).

cnf(c_0_12564_0,axiom,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12564]) ).

cnf(c_0_12564_1,axiom,
    ( ~ c_in(X1,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X2)),tc_Message_Omsg)
    | c_in(X1,c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12564]) ).

cnf(c_0_12565_0,axiom,
    ( c_in(X1,c_List_Oset(X2,X3),X3)
    | c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12565]) ).

cnf(c_0_12565_1,axiom,
    ( c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12565]) ).

cnf(c_0_12565_2,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | c_List_Odistinct(c_List_Olist_OCons(X1,X2,X3),X3)
    | c_in(X1,c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12565]) ).

cnf(c_0_12568_0,axiom,
    ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),c_0,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12568]) ).

cnf(c_0_12568_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),c_0,X2),X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12568]) ).

cnf(c_0_12568_2,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,X2),c_0,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12568]) ).

cnf(c_0_12569_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12569]) ).

cnf(c_0_12569_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12569]) ).

cnf(c_0_12569_2,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12569]) ).

cnf(c_0_12569_3,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12569]) ).

cnf(c_0_12570_0,axiom,
    ( c_Orderings_Omax(X1,c_Orderings_Omax(X1,X2,X3),X3) = c_Orderings_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12570]) ).

cnf(c_0_12570_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Omax(X1,c_Orderings_Omax(X1,X2,X3),X3) = c_Orderings_Omax(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12570]) ).

cnf(c_0_12571_0,axiom,
    ( c_Orderings_Omin(X1,c_Orderings_Omin(X1,X2,X3),X3) = c_Orderings_Omin(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12571]) ).

cnf(c_0_12571_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Omin(X1,c_Orderings_Omin(X1,X2,X3),X3) = c_Orderings_Omin(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12571]) ).

cnf(c_0_12572_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12572]) ).

cnf(c_0_12572_1,axiom,
    ( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12572]) ).

cnf(c_0_12573_0,axiom,
    ( c_in(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12573]) ).

cnf(c_0_12573_1,axiom,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12573]) ).

cnf(c_0_12573_2,axiom,
    ( ~ c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12573]) ).

cnf(c_0_12577_0,axiom,
    ( c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12577]) ).

cnf(c_0_12577_1,axiom,
    ( c_Numeral_Onumber__of(X2,tc_nat) != c_0
    | c_less(c_0,c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12577]) ).

cnf(c_0_12579_0,axiom,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_uminus(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12579]) ).

cnf(c_0_12579_1,axiom,
    ( ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_uminus(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12579]) ).

cnf(c_0_12579_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_uminus(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12579]) ).

cnf(c_0_12579_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_uminus(c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12579]) ).

cnf(c_0_12580_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_Numeral_Onumber__of(X3,X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12580]) ).

cnf(c_0_12580_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_Numeral_Onumber__of(X3,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12580]) ).

cnf(c_0_12580_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_Numeral_Onumber__of(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12580]) ).

cnf(c_0_12581_0,axiom,
    ( c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12581]) ).

cnf(c_0_12581_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12581]) ).

cnf(c_0_12581_2,axiom,
    ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_less(c_0,X2,tc_nat)
    | c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12581]) ).

cnf(c_0_12582_0,axiom,
    ( c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12582]) ).

cnf(c_0_12582_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12582]) ).

cnf(c_0_12582_2,axiom,
    ( ~ c_Parity_Oeven(X1,tc_nat)
    | ~ c_less(c_0,X2,tc_nat)
    | c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12582]) ).

cnf(c_0_12585_0,axiom,
    ( c_minus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12585]) ).

cnf(c_0_12585_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_minus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12585]) ).

cnf(c_0_12586_0,axiom,
    ( c_less(c_uminus(c_1,X1),X2,X1)
    | ~ c_less(c_uminus(X2,X1),c_1,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12586]) ).

cnf(c_0_12586_1,axiom,
    ( ~ c_less(c_uminus(X2,X1),c_1,X1)
    | c_less(c_uminus(c_1,X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12586]) ).

cnf(c_0_12586_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_less(c_uminus(X2,X1),c_1,X1)
    | c_less(c_uminus(c_1,X1),X2,X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12586]) ).

cnf(c_0_12586_3,axiom,
    ( ~ class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_less(c_uminus(X2,X1),c_1,X1)
    | c_less(c_uminus(c_1,X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12586]) ).

cnf(c_0_12587_0,axiom,
    ( c_lessequals(c_uminus(c_1,X1),X2,X1)
    | ~ c_lessequals(c_uminus(X2,X1),c_1,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12587]) ).

cnf(c_0_12587_1,axiom,
    ( ~ c_lessequals(c_uminus(X2,X1),c_1,X1)
    | c_lessequals(c_uminus(c_1,X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12587]) ).

cnf(c_0_12587_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_uminus(X2,X1),c_1,X1)
    | c_lessequals(c_uminus(c_1,X1),X2,X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12587]) ).

cnf(c_0_12587_3,axiom,
    ( ~ class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_uminus(X2,X1),c_1,X1)
    | c_lessequals(c_uminus(c_1,X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12587]) ).

cnf(c_0_12588_0,axiom,
    ( c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(c_divide(c_1,X2,X1),X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12588]) ).

cnf(c_0_12588_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(c_divide(c_1,X2,X1),X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12588]) ).

cnf(c_0_12588_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(c_divide(c_1,X2,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12588]) ).

cnf(c_0_12588_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(c_divide(c_1,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12588]) ).

cnf(c_0_12589_0,axiom,
    ( c_less(X1,c_uminus(c_1,X2),X2)
    | ~ c_less(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12589]) ).

cnf(c_0_12589_1,axiom,
    ( ~ c_less(c_1,c_uminus(X1,X2),X2)
    | c_less(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12589]) ).

cnf(c_0_12589_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_1,c_uminus(X1,X2),X2)
    | c_less(X1,c_uminus(c_1,X2),X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12589]) ).

cnf(c_0_12589_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_1,c_uminus(X1,X2),X2)
    | c_less(X1,c_uminus(c_1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12589]) ).

cnf(c_0_12590_0,axiom,
    ( c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12590]) ).

cnf(c_0_12590_1,axiom,
    ( ~ c_lessequals(c_1,c_uminus(X1,X2),X2)
    | c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12590]) ).

cnf(c_0_12590_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_1,c_uminus(X1,X2),X2)
    | c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12590]) ).

cnf(c_0_12590_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_1,c_uminus(X1,X2),X2)
    | c_lessequals(X1,c_uminus(c_1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12590]) ).

cnf(c_0_12591_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12591]) ).

cnf(c_0_12591_1,axiom,
    ( ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12591]) ).

cnf(c_0_12591_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12591]) ).

cnf(c_0_12592_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12592]) ).

cnf(c_0_12592_1,axiom,
    ( ~ c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12592]) ).

cnf(c_0_12592_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12592]) ).

cnf(c_0_12593_0,axiom,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12593]) ).

cnf(c_0_12593_1,axiom,
    ( ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12593]) ).

cnf(c_0_12593_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X2,X1,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12593]) ).

cnf(c_0_12594_0,axiom,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12594]) ).

cnf(c_0_12594_1,axiom,
    ( ~ c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12594]) ).

cnf(c_0_12594_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12594]) ).

cnf(c_0_12595_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12595]) ).

cnf(c_0_12595_1,axiom,
    ( ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12595]) ).

cnf(c_0_12595_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12595]) ).

cnf(c_0_12596_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12596]) ).

cnf(c_0_12596_1,axiom,
    ( ~ c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12596]) ).

cnf(c_0_12596_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12596]) ).

cnf(c_0_12597_0,axiom,
    ( c_less(c_uminus(X1,X2),c_1,X2)
    | ~ c_less(c_uminus(c_1,X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12597]) ).

cnf(c_0_12597_1,axiom,
    ( ~ c_less(c_uminus(c_1,X2),X1,X2)
    | c_less(c_uminus(X1,X2),c_1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12597]) ).

cnf(c_0_12597_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(c_1,X2),X1,X2)
    | c_less(c_uminus(X1,X2),c_1,X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12597]) ).

cnf(c_0_12597_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(c_1,X2),X1,X2)
    | c_less(c_uminus(X1,X2),c_1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12597]) ).

cnf(c_0_12598_0,axiom,
    ( c_lessequals(c_uminus(X1,X2),c_1,X2)
    | ~ c_lessequals(c_uminus(c_1,X2),X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12598]) ).

cnf(c_0_12598_1,axiom,
    ( ~ c_lessequals(c_uminus(c_1,X2),X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12598]) ).

cnf(c_0_12598_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(c_1,X2),X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_1,X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12598]) ).

cnf(c_0_12598_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(c_1,X2),X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12598]) ).

cnf(c_0_12599_0,axiom,
    ( c_less(c_1,c_uminus(X1,X2),X2)
    | ~ c_less(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12599]) ).

cnf(c_0_12599_1,axiom,
    ( ~ c_less(X1,c_uminus(c_1,X2),X2)
    | c_less(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12599]) ).

cnf(c_0_12599_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(X1,c_uminus(c_1,X2),X2)
    | c_less(c_1,c_uminus(X1,X2),X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12599]) ).

cnf(c_0_12599_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(X1,c_uminus(c_1,X2),X2)
    | c_less(c_1,c_uminus(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12599]) ).

cnf(c_0_12600_0,axiom,
    ( c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ c_lessequals(X1,c_uminus(c_1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12600]) ).

cnf(c_0_12600_1,axiom,
    ( ~ c_lessequals(X1,c_uminus(c_1,X2),X2)
    | c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12600]) ).

cnf(c_0_12600_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X1,c_uminus(c_1,X2),X2)
    | c_lessequals(c_1,c_uminus(X1,X2),X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12600]) ).

cnf(c_0_12600_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X1,c_uminus(c_1,X2),X2)
    | c_lessequals(c_1,c_uminus(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12600]) ).

cnf(c_0_12607_0,axiom,
    ( c_divide(X1,c_uminus(X2,X3),X3) = c_uminus(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12607]) ).

cnf(c_0_12607_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,c_uminus(X2,X3),X3) = c_uminus(c_divide(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12607]) ).

cnf(c_0_12607_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,c_uminus(X2,X3),X3) = c_uminus(c_divide(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12607]) ).

cnf(c_0_12613_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12613]) ).

cnf(c_0_12613_1,axiom,
    ( ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12613]) ).

cnf(c_0_12614_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12614]) ).

cnf(c_0_12614_1,axiom,
    ( c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3) != c_0
    | c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12614]) ).

cnf(c_0_12614_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3) != c_0
    | c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12614]) ).

cnf(c_0_12614_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X2,c_Numeral_Onumber__of(X1,tc_nat),X3) != c_0
    | c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12614]) ).

cnf(c_0_12617_0,axiom,
    ( c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_ONil
    | c_in(c_0,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12617]) ).

cnf(c_0_12617_1,axiom,
    ( c_in(c_0,X3,tc_nat)
    | c_List_Osublist(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X3,X2) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12617]) ).

cnf(c_0_12624_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12624]) ).

cnf(c_0_12624_1,axiom,
    ( c_Parity_Oeven(X2,tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12624]) ).

cnf(c_0_12624_2,axiom,
    ( ~ c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12624]) ).

cnf(c_0_12625_0,axiom,
    ( c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12625]) ).

cnf(c_0_12625_1,axiom,
    ( c_Parity_Oeven(X2,tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12625]) ).

cnf(c_0_12625_2,axiom,
    ( ~ c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X2,tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12625]) ).

cnf(c_0_12626_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12626]) ).

cnf(c_0_12626_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12626]) ).

cnf(c_0_12626_2,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12626]) ).

cnf(c_0_12627_0,axiom,
    ( X1 = c_emptyset
    | c_lessequals(c_Finite__Set_OMin(X1,X2),c_Finite__Set_OMax(X1,X2),X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12627]) ).

cnf(c_0_12627_1,axiom,
    ( c_lessequals(c_Finite__Set_OMin(X1,X2),c_Finite__Set_OMax(X1,X2),X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12627]) ).

cnf(c_0_12627_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_lessequals(c_Finite__Set_OMin(X1,X2),c_Finite__Set_OMax(X1,X2),X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12627]) ).

cnf(c_0_12627_3,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_lessequals(c_Finite__Set_OMin(X1,X2),c_Finite__Set_OMax(X1,X2),X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12627]) ).

cnf(c_0_12628_0,axiom,
    ( c_times(X1,c_uminus(X2,X3),X3) = c_uminus(c_times(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12628]) ).

cnf(c_0_12628_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X3)
    | c_times(X1,c_uminus(X2,X3),X3) = c_uminus(c_times(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12628]) ).

cnf(c_0_12629_0,axiom,
    ( c_times(c_uminus(X1,X2),X3,X2) = c_uminus(c_times(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Oring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12629]) ).

cnf(c_0_12629_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X2)
    | c_times(c_uminus(X1,X2),X3,X2) = c_uminus(c_times(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12629]) ).

cnf(c_0_12630_0,axiom,
    ( c_divide(c_uminus(X1,X2),X3,X2) = c_uminus(c_divide(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12630]) ).

cnf(c_0_12630_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_uminus(X1,X2),X3,X2) = c_uminus(c_divide(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12630]) ).

cnf(c_0_12631_0,axiom,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_0
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12631]) ).

cnf(c_0_12631_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12631]) ).

cnf(c_0_12632_0,axiom,
    ( c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_1
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12632]) ).

cnf(c_0_12632_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | c_Nat_Opower(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_12632]) ).

cnf(c_0_12633_0,axiom,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12633]) ).

cnf(c_0_12633_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12633]) ).

cnf(c_0_12633_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12633]) ).

cnf(c_0_12633_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12633]) ).

cnf(c_0_12634_0,axiom,
    ( c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12634]) ).

cnf(c_0_12634_1,axiom,
    ( ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12634]) ).

cnf(c_0_12634_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12634]) ).

cnf(c_0_12635_0,axiom,
    ( c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12635]) ).

cnf(c_0_12635_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12635]) ).

cnf(c_0_12635_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12635]) ).

cnf(c_0_12636_0,axiom,
    ( c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12636]) ).

cnf(c_0_12636_1,axiom,
    ( ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12636]) ).

cnf(c_0_12636_2,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12636]) ).

cnf(c_0_12637_0,axiom,
    ( c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12637]) ).

cnf(c_0_12637_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12637]) ).

cnf(c_0_12637_2,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12637]) ).

cnf(c_0_12638_0,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Numeral_Onumber__of(X4,tc_nat),X3) = X1
    | c_Numeral_Onumber__of(X4,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12638]) ).

cnf(c_0_12638_1,axiom,
    ( c_Numeral_Onumber__of(X4,tc_nat) != c_0
    | c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Numeral_Onumber__of(X4,tc_nat),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12638]) ).

cnf(c_0_12639_0,axiom,
    ( c_Message_Oparts(c_insert(X1,X2,tc_Message_Omsg)) = c_Message_Oparts(X2)
    | ~ c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12639]) ).

cnf(c_0_12639_1,axiom,
    ( ~ c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | c_Message_Oparts(c_insert(X1,X2,tc_Message_Omsg)) = c_Message_Oparts(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12639]) ).

cnf(c_0_12640_0,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12640]) ).

cnf(c_0_12640_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12640]) ).

cnf(c_0_12641_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate(X3,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12641]) ).

cnf(c_0_12641_1,axiom,
    ( ~ c_List_Odistinct(c_List_Orotate(X3,X1,X2),X2)
    | c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12641]) ).

cnf(c_0_12642_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_append(X3,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12642]) ).

cnf(c_0_12642_1,axiom,
    ( ~ c_List_Odistinct(c_append(X3,X1,X2),X2)
    | c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12642]) ).

cnf(c_0_12643_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_append(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12643]) ).

cnf(c_0_12643_1,axiom,
    ( ~ c_List_Odistinct(c_append(X1,X3,X2),X2)
    | c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12643]) ).

cnf(c_0_12644_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X3,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12644]) ).

cnf(c_0_12644_1,axiom,
    ( ~ c_List_Odistinct(c_List_Olist_OCons(X3,X1,X2),X2)
    | c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12644]) ).

cnf(c_0_12645_0,axiom,
    ( c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_ONil
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12645]) ).

cnf(c_0_12645_1,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | c_List_Otake(c_Numeral_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12645]) ).

cnf(c_0_12646_0,axiom,
    ( c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12646]) ).

cnf(c_0_12646_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12646]) ).

cnf(c_0_12646_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12646]) ).

cnf(c_0_12646_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_lessequals(c_Numeral_Onumber__of(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12646]) ).

cnf(c_0_12647_0,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12647]) ).

cnf(c_0_12647_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12647]) ).

cnf(c_0_12647_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12647]) ).

cnf(c_0_12648_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12648]) ).

cnf(c_0_12648_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12648]) ).

cnf(c_0_12648_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12648]) ).

cnf(c_0_12649_0,axiom,
    ( c_Message_OinvKey(v_sko__uhi(X2,X1)) = X1
    | c_in(X1,c_Message_OkeysFor(X2),tc_nat)
    | ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12649]) ).

cnf(c_0_12649_1,axiom,
    ( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
    | c_Message_OinvKey(v_sko__uhi(X2,X1)) = X1
    | ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12649]) ).

cnf(c_0_12649_2,axiom,
    ( ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | c_in(X1,c_Message_OkeysFor(X2),tc_nat)
    | c_Message_OinvKey(v_sko__uhi(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12649]) ).

cnf(c_0_12650_0,axiom,
    ( c_append(c_List_Otl(X1,X3),X2,X3) = c_List_Otl(c_append(X1,X2,X3),X3)
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12650]) ).

cnf(c_0_12650_1,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(c_List_Otl(X1,X3),X2,X3) = c_List_Otl(c_append(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12650]) ).

cnf(c_0_12651_0,axiom,
    ( c_List_Olist_OCons(X1,c_List_Obutlast(X2,X3),X3) = c_List_Obutlast(c_List_Olist_OCons(X1,X2,X3),X3)
    | X2 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12651]) ).

cnf(c_0_12651_1,axiom,
    ( X2 = c_List_Olist_ONil
    | c_List_Olist_OCons(X1,c_List_Obutlast(X2,X3),X3) = c_List_Obutlast(c_List_Olist_OCons(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12651]) ).

cnf(c_0_12652_0,axiom,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12652]) ).

cnf(c_0_12652_1,axiom,
    ( c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12652]) ).

cnf(c_0_12655_0,axiom,
    ( c_lessequals(c_OrderedGroup_Opprt(X1,X2),c_OrderedGroup_Opprt(X3,X2),X2)
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12655]) ).

cnf(c_0_12655_1,axiom,
    ( ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_OrderedGroup_Opprt(X1,X2),c_OrderedGroup_Opprt(X3,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12655]) ).

cnf(c_0_12655_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_OrderedGroup_Opprt(X1,X2),c_OrderedGroup_Opprt(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12655]) ).

cnf(c_0_12656_0,axiom,
    ( c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_OrderedGroup_Onprt(X3,X2),X2)
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12656]) ).

cnf(c_0_12656_1,axiom,
    ( ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_OrderedGroup_Onprt(X3,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12656]) ).

cnf(c_0_12656_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_OrderedGroup_Onprt(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12656]) ).

cnf(c_0_12657_0,axiom,
    ( c_less(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_less(X3,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12657]) ).

cnf(c_0_12657_1,axiom,
    ( ~ c_less(X3,X1,X2)
    | c_less(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12657]) ).

cnf(c_0_12657_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(X3,X1,X2)
    | c_less(c_uminus(X1,X2),c_uminus(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12657]) ).

cnf(c_0_12658_0,axiom,
    ( c_lessequals(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12658]) ).

cnf(c_0_12658_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_uminus(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12658]) ).

cnf(c_0_12658_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_uminus(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12658]) ).

cnf(c_0_12659_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X3),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12659]) ).

cnf(c_0_12659_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X3),X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12659]) ).

cnf(c_0_12659_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X3),X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12659]) ).

cnf(c_0_12659_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X3),X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12659]) ).

cnf(c_0_12660_0,axiom,
    ( c_List_Otake(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12660]) ).

cnf(c_0_12660_1,axiom,
    ( ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
    | c_List_Otake(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12660]) ).

cnf(c_0_12661_0,axiom,
    ( c_List_Orotate(X1,X2,X3) = X2
    | c_Divides_Oop_Amod(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12661]) ).

cnf(c_0_12661_1,axiom,
    ( c_Divides_Oop_Amod(X1,c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) != c_0
    | c_List_Orotate(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12661]) ).

cnf(c_0_12662_0,axiom,
    ( c_List_Odrop(X1,X2,X3) = c_List_Olist_ONil
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12662]) ).

cnf(c_0_12662_1,axiom,
    ( ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
    | c_List_Odrop(X1,X2,X3) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12662]) ).

cnf(c_0_12664_0,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12664]) ).

cnf(c_0_12664_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12664]) ).

cnf(c_0_12664_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12664]) ).

cnf(c_0_12664_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12664]) ).

cnf(c_0_12665_0,axiom,
    ( c_less(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ c_less(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12665]) ).

cnf(c_0_12665_1,axiom,
    ( ~ c_less(X1,X3,tc_nat)
    | c_less(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12665]) ).

cnf(c_0_12665_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_less(X1,X3,tc_nat)
    | c_less(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12665]) ).

cnf(c_0_12666_0,axiom,
    ( c_lessequals(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12666]) ).

cnf(c_0_12666_1,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | c_lessequals(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12666]) ).

cnf(c_0_12666_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_lessequals(X1,X3,tc_nat)
    | c_lessequals(c_NatArith_Oof__nat(X1,X2),c_NatArith_Oof__nat(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12666]) ).

cnf(c_0_12667_0,axiom,
    ( c_less(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ c_less(X1,X3,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12667]) ).

cnf(c_0_12667_1,axiom,
    ( ~ c_less(X1,X3,tc_IntDef_Oint)
    | c_less(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12667]) ).

cnf(c_0_12667_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(X1,X3,tc_IntDef_Oint)
    | c_less(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12667]) ).

cnf(c_0_12668_0,axiom,
    ( c_lessequals(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ c_lessequals(X1,X3,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12668]) ).

cnf(c_0_12668_1,axiom,
    ( ~ c_lessequals(X1,X3,tc_IntDef_Oint)
    | c_lessequals(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12668]) ).

cnf(c_0_12668_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(X1,X3,tc_IntDef_Oint)
    | c_lessequals(c_IntDef_Oof__int(X1,X2),c_IntDef_Oof__int(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12668]) ).

cnf(c_0_12669_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12669]) ).

cnf(c_0_12669_1,axiom,
    ( ~ c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12669]) ).

cnf(c_0_12670_0,axiom,
    ( X1 = X2
    | ~ c_in(X2,X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12670]) ).

cnf(c_0_12670_1,axiom,
    ( ~ c_in(X2,X3,X4)
    | X1 = X2
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12670]) ).

cnf(c_0_12670_2,axiom,
    ( ~ c_in(X1,X3,X4)
    | ~ c_in(X2,X3,X4)
    | X1 = X2
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12670]) ).

cnf(c_0_12670_3,axiom,
    ( ~ c_Infinite__Set_Oatmost__one(X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12670]) ).

cnf(c_0_12671_0,axiom,
    ( c_List_Orotate(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),c_1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12671]) ).

cnf(c_0_12671_1,axiom,
    ( ~ c_lessequals(c_Nat_Osize(X2,tc_List_Olist(X3)),c_1,tc_nat)
    | c_List_Orotate(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12671]) ).

cnf(c_0_12673_0,axiom,
    ( c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12673]) ).

cnf(c_0_12673_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12673]) ).

cnf(c_0_12674_0,axiom,
    ( ~ c_lessequals(v_sko__urX(X1),X2,tc_nat)
    | ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(X1),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12674]) ).

cnf(c_0_12674_1,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(X1),tc_Message_Omsg)
    | ~ c_lessequals(v_sko__urX(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12674]) ).

cnf(c_0_12675_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12675]) ).

cnf(c_0_12675_1,axiom,
    ( ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12675]) ).

cnf(c_0_12676_0,axiom,
    ( c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12676]) ).

cnf(c_0_12676_1,axiom,
    ( ~ c_Parity_Oeven(c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12676]) ).

cnf(c_0_12677_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12677]) ).

cnf(c_0_12677_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12677]) ).

cnf(c_0_12677_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12677]) ).

cnf(c_0_12678_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12678]) ).

cnf(c_0_12678_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12678]) ).

cnf(c_0_12678_2,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12678]) ).

cnf(c_0_12678_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12678]) ).

cnf(c_0_12679_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12679]) ).

cnf(c_0_12679_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12679]) ).

cnf(c_0_12679_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12679]) ).

cnf(c_0_12679_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12679]) ).

cnf(c_0_12680_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12680]) ).

cnf(c_0_12680_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | X1 = X2
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12680]) ).

cnf(c_0_12680_2,axiom,
    ( ~ c_lessequals(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12680]) ).

cnf(c_0_12681_0,axiom,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12681]) ).

cnf(c_0_12681_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Event_Oused(X2),tc_Message_Omsg)
    | c_in(X1,c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12681]) ).

cnf(c_0_12682_0,axiom,
    ( c_in(X1,c_Event_Oused(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12682]) ).

cnf(c_0_12682_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Event_Oused(X2),tc_Message_Omsg)
    | c_in(X1,c_Event_Oused(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12682]) ).

cnf(c_0_12683_0,axiom,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12683]) ).

cnf(c_0_12683_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12683]) ).

cnf(c_0_12684_0,axiom,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12684]) ).

cnf(c_0_12684_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12684]) ).

cnf(c_0_12685_0,axiom,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12685]) ).

cnf(c_0_12685_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X1,X3),c_Message_Oparts(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12685]) ).

cnf(c_0_12686_0,axiom,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12686]) ).

cnf(c_0_12686_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(X3,X1),c_Message_Oparts(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12686]) ).

cnf(c_0_12687_0,axiom,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12687]) ).

cnf(c_0_12687_1,axiom,
    ( ~ c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12687]) ).

cnf(c_0_12687_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12687]) ).

cnf(c_0_12687_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | c_less(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12687]) ).

cnf(c_0_12688_0,axiom,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12688]) ).

cnf(c_0_12688_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12688]) ).

cnf(c_0_12688_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12688]) ).

cnf(c_0_12688_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12688]) ).

cnf(c_0_12689_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12689]) ).

cnf(c_0_12689_1,axiom,
    ( ~ c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12689]) ).

cnf(c_0_12689_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12689]) ).

cnf(c_0_12689_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12689]) ).

cnf(c_0_12690_0,axiom,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12690]) ).

cnf(c_0_12690_1,axiom,
    ( ~ c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12690]) ).

cnf(c_0_12690_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12690]) ).

cnf(c_0_12690_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | c_less(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12690]) ).

cnf(c_0_12691_0,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X2,X1,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12691]) ).

cnf(c_0_12691_1,axiom,
    ( ~ c_less(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12691]) ).

cnf(c_0_12692_0,axiom,
    ( c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12692]) ).

cnf(c_0_12692_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_12692]) ).

cnf(c_0_12694_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12694]) ).

cnf(c_0_12694_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12694]) ).

cnf(c_0_12694_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12694]) ).

cnf(c_0_12694_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12694]) ).

cnf(c_0_12695_0,axiom,
    ( c_HOL_Oinverse(c_divide(X1,X2,X3),X3) = c_divide(X2,X1,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12695]) ).

cnf(c_0_12695_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_HOL_Oinverse(c_divide(X1,X2,X3),X3) = c_divide(X2,X1,X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12695]) ).

cnf(c_0_12695_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_HOL_Oinverse(c_divide(X1,X2,X3),X3) = c_divide(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12695]) ).

cnf(c_0_12696_0,axiom,
    ( X1 = c_0
    | X2 = X3
    | c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12696]) ).

cnf(c_0_12696_1,axiom,
    ( X2 = X3
    | X1 = c_0
    | c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12696]) ).

cnf(c_0_12696_2,axiom,
    ( c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | X2 = X3
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12696]) ).

cnf(c_0_12696_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | X2 = X3
    | X1 = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12696]) ).

cnf(c_0_12696_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(X2,X1,X4) != c_divide(X3,X1,X4)
    | X2 = X3
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12696]) ).

cnf(c_0_12697_0,axiom,
    ( X1 = c_0
    | X2 = X3
    | c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12697]) ).

cnf(c_0_12697_1,axiom,
    ( X2 = X3
    | X1 = c_0
    | c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12697]) ).

cnf(c_0_12697_2,axiom,
    ( c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | X2 = X3
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X4)
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12697]) ).

cnf(c_0_12697_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | X2 = X3
    | X1 = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12697]) ).

cnf(c_0_12697_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X4)
    | ~ class_Ring__and__Field_Ofield(X4)
    | c_divide(X1,X2,X4) != c_divide(X1,X3,X4)
    | X2 = X3
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12697]) ).

cnf(c_0_12698_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12698]) ).

cnf(c_0_12698_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12698]) ).

cnf(c_0_12698_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12698]) ).

cnf(c_0_12699_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12699]) ).

cnf(c_0_12699_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12699]) ).

cnf(c_0_12699_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12699]) ).

cnf(c_0_12700_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12700]) ).

cnf(c_0_12700_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12700]) ).

cnf(c_0_12700_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12700]) ).

cnf(c_0_12701_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12701]) ).

cnf(c_0_12701_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12701]) ).

cnf(c_0_12701_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12701]) ).

cnf(c_0_12702_0,axiom,
    ( c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1),X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12702]) ).

cnf(c_0_12702_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1),X1) = c_1
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12702]) ).

cnf(c_0_12702_2,axiom,
    ( ~ class_Power_Orecpower(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1),X1) = c_1
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12702]) ).

cnf(c_0_12702_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1),X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_12702]) ).

cnf(c_0_12703_0,axiom,
    ( c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12703]) ).

cnf(c_0_12703_1,axiom,
    ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oint(c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint))) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12703]) ).

cnf(c_0_12704_0,axiom,
    ( c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12704]) ).

cnf(c_0_12704_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12704]) ).

cnf(c_0_12704_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12704]) ).

cnf(c_0_12714_0,axiom,
    ( c_less(c_0,X1,X2)
    | ~ c_less(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12714]) ).

cnf(c_0_12714_1,axiom,
    ( ~ c_less(c_uminus(X1,X2),c_0,X2)
    | c_less(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12714]) ).

cnf(c_0_12714_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_uminus(X1,X2),c_0,X2)
    | c_less(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12714]) ).

cnf(c_0_12715_0,axiom,
    ( c_lessequals(c_0,X1,X2)
    | ~ c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12715]) ).

cnf(c_0_12715_1,axiom,
    ( ~ c_lessequals(c_uminus(X1,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12715]) ).

cnf(c_0_12715_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_uminus(X1,X2),c_0,X2)
    | c_lessequals(c_0,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12715]) ).

cnf(c_0_12716_0,axiom,
    ( c_less(X1,c_0,X2)
    | ~ c_less(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12716]) ).

cnf(c_0_12716_1,axiom,
    ( ~ c_less(c_0,c_uminus(X1,X2),X2)
    | c_less(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12716]) ).

cnf(c_0_12716_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_0,c_uminus(X1,X2),X2)
    | c_less(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12716]) ).

cnf(c_0_12717_0,axiom,
    ( c_lessequals(X1,c_0,X2)
    | ~ c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12717]) ).

cnf(c_0_12717_1,axiom,
    ( ~ c_lessequals(c_0,c_uminus(X1,X2),X2)
    | c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12717]) ).

cnf(c_0_12717_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_0,c_uminus(X1,X2),X2)
    | c_lessequals(X1,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12717]) ).

cnf(c_0_12720_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12720]) ).

cnf(c_0_12720_1,axiom,
    ( ~ c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12720]) ).

cnf(c_0_12720_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12720]) ).

cnf(c_0_12721_0,axiom,
    ( c_less(X1,c_0,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12721]) ).

cnf(c_0_12721_1,axiom,
    ( ~ c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | c_less(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12721]) ).

cnf(c_0_12721_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | c_less(X1,c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12721]) ).

cnf(c_0_12722_0,axiom,
    ( c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12722]) ).

cnf(c_0_12722_1,axiom,
    ( ~ c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12722]) ).

cnf(c_0_12722_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | c_lessequals(X1,c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12722]) ).

cnf(c_0_12723_0,axiom,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12723]) ).

cnf(c_0_12723_1,axiom,
    ( ~ c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | c_less(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12723]) ).

cnf(c_0_12723_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | c_less(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12723]) ).

cnf(c_0_12724_0,axiom,
    ( c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12724]) ).

cnf(c_0_12724_1,axiom,
    ( ~ c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12724]) ).

cnf(c_0_12724_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12724]) ).

cnf(c_0_12725_0,axiom,
    ( X1 = c_emptyset
    | c_in(c_Finite__Set_OMin(X1,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12725]) ).

cnf(c_0_12725_1,axiom,
    ( c_in(c_Finite__Set_OMin(X1,X2),X1,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12725]) ).

cnf(c_0_12725_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Finite__Set_OMin(X1,X2),X1,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12725]) ).

cnf(c_0_12725_3,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Finite__Set_OMin(X1,X2),X1,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12725]) ).

cnf(c_0_12726_0,axiom,
    ( X1 = c_emptyset
    | c_in(c_Finite__Set_OMax(X1,X2),X1,X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12726]) ).

cnf(c_0_12726_1,axiom,
    ( c_in(c_Finite__Set_OMax(X1,X2),X1,X2)
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12726]) ).

cnf(c_0_12726_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Finite__Set_OMax(X1,X2),X1,X2)
    | X1 = c_emptyset
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12726]) ).

cnf(c_0_12726_3,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Finite__Set_OMax(X1,X2),X1,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12726]) ).

cnf(c_0_12727_0,axiom,
    ( c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12727]) ).

cnf(c_0_12727_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12727]) ).

cnf(c_0_12728_0,axiom,
    ( c_uminus(c_minus(X1,X2,X3),X3) = c_minus(X2,X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12728]) ).

cnf(c_0_12728_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_uminus(c_minus(X1,X2,X3),X3) = c_minus(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12728]) ).

cnf(c_0_12729_0,axiom,
    ( X1 = c_0
    | X2 = X3
    | c_times(X2,X1,X4) != c_times(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12729]) ).

cnf(c_0_12729_1,axiom,
    ( X2 = X3
    | X1 = c_0
    | c_times(X2,X1,X4) != c_times(X3,X1,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12729]) ).

cnf(c_0_12729_2,axiom,
    ( c_times(X2,X1,X4) != c_times(X3,X1,X4)
    | X2 = X3
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12729]) ).

cnf(c_0_12729_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(X4)
    | c_times(X2,X1,X4) != c_times(X3,X1,X4)
    | X2 = X3
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12729]) ).

cnf(c_0_12730_0,axiom,
    ( X1 = c_0
    | X2 = X3
    | c_times(X1,X2,X4) != c_times(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12730]) ).

cnf(c_0_12730_1,axiom,
    ( X2 = X3
    | X1 = c_0
    | c_times(X1,X2,X4) != c_times(X1,X3,X4)
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12730]) ).

cnf(c_0_12730_2,axiom,
    ( c_times(X1,X2,X4) != c_times(X1,X3,X4)
    | X2 = X3
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12730]) ).

cnf(c_0_12730_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(X4)
    | c_times(X1,X2,X4) != c_times(X1,X3,X4)
    | X2 = X3
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12730]) ).

cnf(c_0_12735_0,axiom,
    ( X1 = X2
    | c_plus(X1,X3,X4) != c_plus(X2,X3,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12735]) ).

cnf(c_0_12735_1,axiom,
    ( c_plus(X1,X3,X4) != c_plus(X2,X3,X4)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12735]) ).

cnf(c_0_12735_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
    | c_plus(X1,X3,X4) != c_plus(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12735]) ).

cnf(c_0_12736_0,axiom,
    ( X1 = X2
    | c_plus(X3,X1,X4) != c_plus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12736]) ).

cnf(c_0_12736_1,axiom,
    ( c_plus(X3,X1,X4) != c_plus(X3,X2,X4)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12736]) ).

cnf(c_0_12736_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
    | c_plus(X3,X1,X4) != c_plus(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12736]) ).

cnf(c_0_12738_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12738]) ).

cnf(c_0_12738_1,axiom,
    ( c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12738]) ).

cnf(c_0_12738_2,axiom,
    ( ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3))
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12738]) ).

cnf(c_0_12739_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12739]) ).

cnf(c_0_12739_1,axiom,
    ( c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil
    | ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12739]) ).

cnf(c_0_12739_2,axiom,
    ( ~ c_in(X1,c_List_Oset(X2,tc_List_Olist(X3)),tc_List_Olist(X3))
    | c_List_Oconcat(X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12739]) ).

cnf(c_0_12740_0,axiom,
    ( c_times(X1,c_divide(X2,X1,X3),X3) = X2
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12740]) ).

cnf(c_0_12740_1,axiom,
    ( X1 = c_0
    | c_times(X1,c_divide(X2,X1,X3),X3) = X2
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12740]) ).

cnf(c_0_12740_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_times(X1,c_divide(X2,X1,X3),X3) = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12740]) ).

cnf(c_0_12740_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_times(X1,c_divide(X2,X1,X3),X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12740]) ).

cnf(c_0_12741_0,axiom,
    ( c_times(c_divide(X1,X2,X3),X2,X3) = X1
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12741]) ).

cnf(c_0_12741_1,axiom,
    ( X2 = c_0
    | c_times(c_divide(X1,X2,X3),X2,X3) = X1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12741]) ).

cnf(c_0_12741_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X2 = c_0
    | c_times(c_divide(X1,X2,X3),X2,X3) = X1
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12741]) ).

cnf(c_0_12741_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X2 = c_0
    | c_times(c_divide(X1,X2,X3),X2,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12741]) ).

cnf(c_0_12742_0,axiom,
    ( c_divide(c_times(X1,X2,X3),X2,X3) = X1
    | X2 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12742]) ).

cnf(c_0_12742_1,axiom,
    ( X2 = c_0
    | c_divide(c_times(X1,X2,X3),X2,X3) = X1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12742]) ).

cnf(c_0_12742_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X2 = c_0
    | c_divide(c_times(X1,X2,X3),X2,X3) = X1
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12742]) ).

cnf(c_0_12742_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X2 = c_0
    | c_divide(c_times(X1,X2,X3),X2,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12742]) ).

cnf(c_0_12743_0,axiom,
    ( c_divide(c_times(X1,X2,X3),X1,X3) = X2
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12743]) ).

cnf(c_0_12743_1,axiom,
    ( X1 = c_0
    | c_divide(c_times(X1,X2,X3),X1,X3) = X2
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12743]) ).

cnf(c_0_12743_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(c_times(X1,X2,X3),X1,X3) = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12743]) ).

cnf(c_0_12743_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | X1 = c_0
    | c_divide(c_times(X1,X2,X3),X1,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12743]) ).

cnf(c_0_12744_0,axiom,
    ( c_minus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12744]) ).

cnf(c_0_12744_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_minus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12744]) ).

cnf(c_0_12745_0,axiom,
    ( c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),X3,tc_nat)
    | c_List_Odrop(X3,X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12745]) ).

cnf(c_0_12745_1,axiom,
    ( c_List_Odrop(X3,X1,X2) != c_List_Olist_ONil
    | c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12745]) ).

cnf(c_0_12746_0,axiom,
    ( c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12746]) ).

cnf(c_0_12746_1,axiom,
    ( ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12746]) ).

cnf(c_0_12746_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12746]) ).

cnf(c_0_12746_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_0,c_HOL_Oinverse(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12746]) ).

cnf(c_0_12747_0,axiom,
    ( c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12747]) ).

cnf(c_0_12747_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12747]) ).

cnf(c_0_12747_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12747]) ).

cnf(c_0_12747_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_HOL_Oinverse(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12747]) ).

cnf(c_0_12748_0,axiom,
    ( c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12748]) ).

cnf(c_0_12748_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12748]) ).

cnf(c_0_12748_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12748]) ).

cnf(c_0_12748_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_0,c_HOL_Oinverse(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12748]) ).

cnf(c_0_12749_0,axiom,
    ( c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12749]) ).

cnf(c_0_12749_1,axiom,
    ( ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12749]) ).

cnf(c_0_12749_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12749]) ).

cnf(c_0_12749_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_HOL_Oinverse(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12749]) ).

cnf(c_0_12750_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(c_Message_Oagent_OSpy,X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Event_Obad,tc_Message_Oagent) ),
    inference(literals_permutation,[status(thm)],[c_0_12750]) ).

cnf(c_0_12750_1,axiom,
    ( ~ c_in(X1,c_Event_Obad,tc_Message_Oagent)
    | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(c_Message_Oagent_OSpy,X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12750]) ).

cnf(c_0_12753_0,axiom,
    ( c_List_Oset(c_List_Oreplicate(X1,X2,X3),X3) = c_insert(X2,c_emptyset,X3)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12753]) ).

cnf(c_0_12753_1,axiom,
    ( X1 = c_0
    | c_List_Oset(c_List_Oreplicate(X1,X2,X3),X3) = c_insert(X2,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12753]) ).

cnf(c_0_12755_0,axiom,
    ( c_divide(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_divide(X1,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12755]) ).

cnf(c_0_12755_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_divide(X1,X3,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12755]) ).

cnf(c_0_12755_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_divide(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12755]) ).

cnf(c_0_12757_0,axiom,
    ( c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12757]) ).

cnf(c_0_12757_1,axiom,
    ( ~ c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12757]) ).

cnf(c_0_12758_0,axiom,
    ( c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12758]) ).

cnf(c_0_12758_1,axiom,
    ( ~ c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12758]) ).

cnf(c_0_12759_0,axiom,
    ( c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12759]) ).

cnf(c_0_12759_1,axiom,
    ( ~ c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12759]) ).

cnf(c_0_12760_0,axiom,
    ( c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12760]) ).

cnf(c_0_12760_1,axiom,
    ( ~ c_less(X1,X2,X3)
    | c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12760]) ).

cnf(c_0_12760_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_less(X1,X2,X3)
    | c_in(X1,c_SetInterval_OlessThan(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12760]) ).

cnf(c_0_12761_0,axiom,
    ( c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12761]) ).

cnf(c_0_12761_1,axiom,
    ( ~ c_less(X2,X1,X3)
    | c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12761]) ).

cnf(c_0_12761_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_less(X2,X1,X3)
    | c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12761]) ).

cnf(c_0_12762_0,axiom,
    ( c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12762]) ).

cnf(c_0_12762_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12762]) ).

cnf(c_0_12762_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_in(X1,c_SetInterval_OatMost(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12762]) ).

cnf(c_0_12763_0,axiom,
    ( c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12763]) ).

cnf(c_0_12763_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12763]) ).

cnf(c_0_12763_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_in(X1,c_SetInterval_OatLeast(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12763]) ).

cnf(c_0_12765_0,axiom,
    ( c_List_Olast(c_List_Oupt(X1,X2),tc_nat) = c_minus(X2,c_1,tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12765]) ).

cnf(c_0_12765_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_List_Olast(c_List_Oupt(X1,X2),tc_nat) = c_minus(X2,c_1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12765]) ).

cnf(c_0_12766_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_OSays(X3,X4,X1) != c_Event_Oevent_OSays(X5,X6,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12766]) ).

cnf(c_0_12766_1,axiom,
    ( c_Event_Oevent_OSays(X3,X4,X1) != c_Event_Oevent_OSays(X5,X6,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12766]) ).

cnf(c_0_12767_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_OSays(X3,X1,X4) != c_Event_Oevent_OSays(X5,X2,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_12767]) ).

cnf(c_0_12767_1,axiom,
    ( c_Event_Oevent_OSays(X3,X1,X4) != c_Event_Oevent_OSays(X5,X2,X6)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12767]) ).

cnf(c_0_12768_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_OSays(X1,X3,X4) != c_Event_Oevent_OSays(X2,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_12768]) ).

cnf(c_0_12768_1,axiom,
    ( c_Event_Oevent_OSays(X1,X3,X4) != c_Event_Oevent_OSays(X2,X5,X6)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12768]) ).

cnf(c_0_12769_0,axiom,
    ( X1 = X2
    | c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12769]) ).

cnf(c_0_12769_1,axiom,
    ( c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12769]) ).

cnf(c_0_12770_0,axiom,
    ( X1 = X2
    | c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12770]) ).

cnf(c_0_12770_1,axiom,
    ( c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12770]) ).

cnf(c_0_12771_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12771]) ).

cnf(c_0_12771_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12771]) ).

cnf(c_0_12771_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12771]) ).

cnf(c_0_12771_3,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12771]) ).

cnf(c_0_12772_0,axiom,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X3,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12772]) ).

cnf(c_0_12772_1,axiom,
    ( c_append(X3,X1,X4) != c_append(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12772]) ).

cnf(c_0_12773_0,axiom,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12773]) ).

cnf(c_0_12773_1,axiom,
    ( c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12773]) ).

cnf(c_0_12774_0,axiom,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12774]) ).

cnf(c_0_12774_1,axiom,
    ( c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12774]) ).

cnf(c_0_12775_0,axiom,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12775]) ).

cnf(c_0_12775_1,axiom,
    ( c_append(X1,X3,X4) != c_append(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12775]) ).

cnf(c_0_12776_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12776]) ).

cnf(c_0_12776_1,axiom,
    ( c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12776]) ).

cnf(c_0_12777_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12777]) ).

cnf(c_0_12777_1,axiom,
    ( c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12777]) ).

cnf(c_0_12778_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12778]) ).

cnf(c_0_12778_1,axiom,
    ( c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12778]) ).

cnf(c_0_12779_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12779]) ).

cnf(c_0_12779_1,axiom,
    ( c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12779]) ).

cnf(c_0_12780_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12780]) ).

cnf(c_0_12780_1,axiom,
    ( c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12780]) ).

cnf(c_0_12781_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12781]) ).

cnf(c_0_12781_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12781]) ).

cnf(c_0_12782_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12782]) ).

cnf(c_0_12782_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12782]) ).

cnf(c_0_12787_0,axiom,
    ( c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X2),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12787]) ).

cnf(c_0_12787_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12787]) ).

cnf(c_0_12790_0,axiom,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(c_Message_Osynth(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12790]) ).

cnf(c_0_12790_1,axiom,
    ( ~ c_in(X1,c_Message_Osynth(c_Message_Osynth(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12790]) ).

cnf(c_0_12791_0,axiom,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oparts(c_Message_Oparts(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12791]) ).

cnf(c_0_12791_1,axiom,
    ( ~ c_in(X1,c_Message_Oparts(c_Message_Oparts(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12791]) ).

cnf(c_0_12792_0,axiom,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oanalz(c_Message_Oanalz(X2)),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12792]) ).

cnf(c_0_12792_1,axiom,
    ( ~ c_in(X1,c_Message_Oanalz(c_Message_Oanalz(X2)),tc_Message_Omsg)
    | c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12792]) ).

cnf(c_0_12793_0,axiom,
    ( c_times(c_0,c_divide(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12793]) ).

cnf(c_0_12793_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_0,c_divide(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12793]) ).

cnf(c_0_12793_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_0,c_divide(X1,c_0,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12793]) ).

cnf(c_0_12794_0,axiom,
    ( c_times(c_divide(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12794]) ).

cnf(c_0_12794_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_divide(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12794]) ).

cnf(c_0_12794_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_divide(X1,c_0,X2),c_0,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12794]) ).

cnf(c_0_12795_0,axiom,
    ( c_divide(c_times(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12795]) ).

cnf(c_0_12795_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X1,c_0,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12795]) ).

cnf(c_0_12795_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(X1,c_0,X2),c_0,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12795]) ).

cnf(c_0_12796_0,axiom,
    ( c_divide(c_0,c_times(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12796]) ).

cnf(c_0_12796_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,c_times(X1,c_0,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12796]) ).

cnf(c_0_12796_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,c_times(X1,c_0,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12796]) ).

cnf(c_0_12797_0,axiom,
    ( c_divide(c_times(c_0,X1,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12797]) ).

cnf(c_0_12797_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,X1,X2),c_0,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12797]) ).

cnf(c_0_12797_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_times(c_0,X1,X2),c_0,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12797]) ).

cnf(c_0_12798_0,axiom,
    ( c_divide(c_0,c_times(c_0,X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12798]) ).

cnf(c_0_12798_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,c_times(c_0,X1,X2),X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12798]) ).

cnf(c_0_12798_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,c_times(c_0,X1,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12798]) ).

cnf(c_0_12805_0,axiom,
    ( c_in(c_Message_OinvKey(X1),c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12805]) ).

cnf(c_0_12805_1,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_OinvKey(X1),c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12805]) ).

cnf(c_0_12806_0,axiom,
    ( X1 = X2
    | c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_12806]) ).

cnf(c_0_12806_1,axiom,
    ( c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12806]) ).

cnf(c_0_12807_0,axiom,
    ( X1 = X2
    | c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12807]) ).

cnf(c_0_12807_1,axiom,
    ( c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12807]) ).

cnf(c_0_12808_0,axiom,
    ( c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12808]) ).

cnf(c_0_12808_1,axiom,
    ( ~ c_lessequals(X1,c_Message_Osynth(X2),tc_set(tc_Message_Omsg))
    | c_lessequals(c_Message_Osynth(X1),c_Message_Osynth(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12808]) ).

cnf(c_0_12809_0,axiom,
    ( c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12809]) ).

cnf(c_0_12809_1,axiom,
    ( ~ c_lessequals(X1,c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
    | c_lessequals(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12809]) ).

cnf(c_0_12810_0,axiom,
    ( c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12810]) ).

cnf(c_0_12810_1,axiom,
    ( ~ c_lessequals(X1,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
    | c_lessequals(c_Message_Oanalz(X1),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)) ),
    inference(literals_permutation,[status(thm)],[c_0_12810]) ).

cnf(c_0_12813_0,axiom,
    ( c_less(c_uminus(X1,X2),c_0,X2)
    | ~ c_less(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12813]) ).

cnf(c_0_12813_1,axiom,
    ( ~ c_less(c_0,X1,X2)
    | c_less(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12813]) ).

cnf(c_0_12813_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(c_0,X1,X2)
    | c_less(c_uminus(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12813]) ).

cnf(c_0_12814_0,axiom,
    ( c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12814]) ).

cnf(c_0_12814_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12814]) ).

cnf(c_0_12814_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_lessequals(c_uminus(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12814]) ).

cnf(c_0_12815_0,axiom,
    ( c_less(c_0,c_uminus(X1,X2),X2)
    | ~ c_less(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12815]) ).

cnf(c_0_12815_1,axiom,
    ( ~ c_less(X1,c_0,X2)
    | c_less(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12815]) ).

cnf(c_0_12815_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_less(X1,c_0,X2)
    | c_less(c_0,c_uminus(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12815]) ).

cnf(c_0_12816_0,axiom,
    ( c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12816]) ).

cnf(c_0_12816_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,c_uminus(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12816]) ).

cnf(c_0_12816_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_lessequals(c_0,c_uminus(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12816]) ).

cnf(c_0_12817_0,axiom,
    ( X1 = c_0
    | X2 = X3
    | c_times(X2,X1,tc_nat) != c_times(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12817]) ).

cnf(c_0_12817_1,axiom,
    ( X2 = X3
    | X1 = c_0
    | c_times(X2,X1,tc_nat) != c_times(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12817]) ).

cnf(c_0_12817_2,axiom,
    ( c_times(X2,X1,tc_nat) != c_times(X3,X1,tc_nat)
    | X2 = X3
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12817]) ).

cnf(c_0_12818_0,axiom,
    ( X1 = c_0
    | X2 = X3
    | c_times(X1,X2,tc_nat) != c_times(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12818]) ).

cnf(c_0_12818_1,axiom,
    ( X2 = X3
    | X1 = c_0
    | c_times(X1,X2,tc_nat) != c_times(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12818]) ).

cnf(c_0_12818_2,axiom,
    ( c_times(X1,X2,tc_nat) != c_times(X1,X3,tc_nat)
    | X2 = X3
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12818]) ).

cnf(c_0_12819_0,axiom,
    ( c_in(c_uminus(X1,X2),c_IntDef_OInts,X2)
    | ~ c_in(X1,c_IntDef_OInts,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12819]) ).

cnf(c_0_12819_1,axiom,
    ( ~ c_in(X1,c_IntDef_OInts,X2)
    | c_in(c_uminus(X1,X2),c_IntDef_OInts,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12819]) ).

cnf(c_0_12819_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ c_in(X1,c_IntDef_OInts,X2)
    | c_in(c_uminus(X1,X2),c_IntDef_OInts,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12819]) ).

cnf(c_0_12820_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),X3),X3)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12820]) ).

cnf(c_0_12820_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X3),X3)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12820]) ).

cnf(c_0_12820_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X3),X3)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),X3),X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12820]) ).

cnf(c_0_12820_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X3),X3)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X1,X2),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12820]) ).

cnf(c_0_12821_0,axiom,
    ( c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_Nat_Opower(X1,X3,X2)
    | ~ c_Parity_Oeven(X3,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12821]) ).

cnf(c_0_12821_1,axiom,
    ( ~ c_Parity_Oeven(X3,tc_nat)
    | c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_Nat_Opower(X1,X3,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12821]) ).

cnf(c_0_12821_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ c_Parity_Oeven(X3,tc_nat)
    | c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_Nat_Opower(X1,X3,X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12821]) ).

cnf(c_0_12821_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | ~ c_Parity_Oeven(X3,tc_nat)
    | c_Nat_Opower(c_uminus(X1,X2),X3,X2) = c_Nat_Opower(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12821]) ).

cnf(c_0_12824_0,axiom,
    ( X1 = X2
    | c_plus(X1,X3,tc_nat) != c_plus(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12824]) ).

cnf(c_0_12824_1,axiom,
    ( c_plus(X1,X3,tc_nat) != c_plus(X2,X3,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12824]) ).

cnf(c_0_12825_0,axiom,
    ( X1 = X2
    | c_plus(X3,X1,tc_nat) != c_plus(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12825]) ).

cnf(c_0_12825_1,axiom,
    ( c_plus(X3,X1,tc_nat) != c_plus(X3,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12825]) ).

cnf(c_0_12826_0,axiom,
    ( X1 = X2
    | c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12826]) ).

cnf(c_0_12826_1,axiom,
    ( c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12826]) ).

cnf(c_0_12827_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | c_Numeral_Onumber__of(X1,X3) != c_Numeral_Onumber__of(X2,X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12827]) ).

cnf(c_0_12827_1,axiom,
    ( c_Numeral_Onumber__of(X1,X3) != c_Numeral_Onumber__of(X2,X3)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3)
    | ~ class_Numeral_Onumber__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12827]) ).

cnf(c_0_12827_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X3)
    | c_Numeral_Onumber__of(X1,X3) != c_Numeral_Onumber__of(X2,X3)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X2)),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12827]) ).

cnf(c_0_12828_0,axiom,
    ( c_times(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_times(X1,X3,X2)
    | ~ class_Ring__and__Field_Oring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12828]) ).

cnf(c_0_12828_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X2)
    | c_times(c_uminus(X1,X2),c_uminus(X3,X2),X2) = c_times(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12828]) ).

cnf(c_0_12829_0,axiom,
    ( c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12829]) ).

cnf(c_0_12829_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12829]) ).

cnf(c_0_12829_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_NatArith_Oof__nat(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12829]) ).

cnf(c_0_12830_0,axiom,
    ( c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ c_less(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12830]) ).

cnf(c_0_12830_1,axiom,
    ( ~ c_less(X1,c_0,tc_IntDef_Oint)
    | c_less(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12830]) ).

cnf(c_0_12830_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(X1,c_0,tc_IntDef_Oint)
    | c_less(c_IntDef_Oof__int(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12830]) ).

cnf(c_0_12831_0,axiom,
    ( c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12831]) ).

cnf(c_0_12831_1,axiom,
    ( ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
    | c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12831]) ).

cnf(c_0_12831_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
    | c_lessequals(c_IntDef_Oof__int(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12831]) ).

cnf(c_0_12832_0,axiom,
    ( c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ c_less(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12832]) ).

cnf(c_0_12832_1,axiom,
    ( ~ c_less(c_0,X1,tc_IntDef_Oint)
    | c_less(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12832]) ).

cnf(c_0_12832_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,X1,tc_IntDef_Oint)
    | c_less(c_0,c_IntDef_Oof__int(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12832]) ).

cnf(c_0_12833_0,axiom,
    ( c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12833]) ).

cnf(c_0_12833_1,axiom,
    ( ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
    | c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12833]) ).

cnf(c_0_12833_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
    | c_lessequals(c_0,c_IntDef_Oof__int(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12833]) ).

cnf(c_0_12834_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12834]) ).

cnf(c_0_12834_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_plus(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12834]) ).

cnf(c_0_12835_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12835]) ).

cnf(c_0_12835_1,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12835]) ).

cnf(c_0_12835_2,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12835]) ).

cnf(c_0_12835_3,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_Numeral_Onumber__of(X2,tc_nat)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12835]) ).

cnf(c_0_12836_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12836]) ).

cnf(c_0_12836_1,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_Numeral_Onumber__of(X1,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12836]) ).

cnf(c_0_12836_2,axiom,
    ( c_Numeral_Onumber__of(X2,tc_nat) != c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12836]) ).

cnf(c_0_12836_3,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X2,tc_nat) != c_Numeral_Onumber__of(X1,tc_nat)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12836]) ).

cnf(c_0_12837_0,axiom,
    ( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1
    | ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_12837]) ).

cnf(c_0_12837_1,axiom,
    ( ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
    | c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12837]) ).

cnf(c_0_12840_0,axiom,
    ( c_minus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12840]) ).

cnf(c_0_12840_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_minus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12840]) ).

cnf(c_0_12841_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12841]) ).

cnf(c_0_12841_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_plus(c_Numeral_Onumber__of(X1,X2),c_1,X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12841]) ).

cnf(c_0_12842_0,axiom,
    ( c_plus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12842]) ).

cnf(c_0_12842_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_plus(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12842]) ).

cnf(c_0_12843_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12843]) ).

cnf(c_0_12843_1,axiom,
    ( ~ c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12843]) ).

cnf(c_0_12844_0,axiom,
    ( c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
    | ~ c_in(X1,c_Message_OkeysFor(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12844]) ).

cnf(c_0_12844_1,axiom,
    ( ~ c_in(X1,c_Message_OkeysFor(X2),tc_nat)
    | c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12844]) ).

cnf(c_0_12845_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12845]) ).

cnf(c_0_12845_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12845]) ).

cnf(c_0_12845_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12845]) ).

cnf(c_0_12845_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,X2),X2)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12845]) ).

cnf(c_0_12849_0,axiom,
    ( c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12849]) ).

cnf(c_0_12849_1,axiom,
    ( c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0
    | c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12849]) ).

cnf(c_0_12850_0,axiom,
    ( c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12850]) ).

cnf(c_0_12850_1,axiom,
    ( c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0
    | c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12850]) ).

cnf(c_0_12852_0,axiom,
    ( c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12852]) ).

cnf(c_0_12852_1,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12852]) ).

cnf(c_0_12853_0,axiom,
    ( c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12853]) ).

cnf(c_0_12853_1,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12853]) ).

cnf(c_0_12859_0,axiom,
    ( c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12859]) ).

cnf(c_0_12859_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12859]) ).

cnf(c_0_12860_0,axiom,
    ( c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12860]) ).

cnf(c_0_12860_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12860]) ).

cnf(c_0_12869_0,axiom,
    ( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) != c_List_Orev(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12869]) ).

cnf(c_0_12869_1,axiom,
    ( c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) != c_List_Orev(X1,X3)
    | X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12869]) ).

cnf(c_0_12870_0,axiom,
    ( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12870]) ).

cnf(c_0_12870_1,axiom,
    ( c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil,X3)
    | X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12870]) ).

cnf(c_0_12871_0,axiom,
    ( c_div(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12871]) ).

cnf(c_0_12871_1,axiom,
    ( X1 = c_0
    | c_div(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12871]) ).

cnf(c_0_12872_0,axiom,
    ( c_div(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = X1
    | X2 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12872]) ).

cnf(c_0_12872_1,axiom,
    ( X2 = c_0
    | c_div(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12872]) ).

cnf(c_0_12873_0,axiom,
    ( X1 = X2
    | c_less(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12873]) ).

cnf(c_0_12873_1,axiom,
    ( c_less(X1,X2,tc_set(X3))
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12873]) ).

cnf(c_0_12873_2,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | c_less(X1,X2,tc_set(X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_12873]) ).

cnf(c_0_12874_0,axiom,
    ( c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12874]) ).

cnf(c_0_12874_1,axiom,
    ( ~ c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12874]) ).

cnf(c_0_12875_0,axiom,
    ( c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12875]) ).

cnf(c_0_12875_1,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_ONonce(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12875]) ).

cnf(c_0_12876_0,axiom,
    ( c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12876]) ).

cnf(c_0_12876_1,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(X1),c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12876]) ).

cnf(c_0_12878_0,axiom,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12878]) ).

cnf(c_0_12878_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12878]) ).

cnf(c_0_12878_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12878]) ).

cnf(c_0_12879_0,axiom,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12879]) ).

cnf(c_0_12879_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12879]) ).

cnf(c_0_12879_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12879]) ).

cnf(c_0_12880_0,axiom,
    ( c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12880]) ).

cnf(c_0_12880_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12880]) ).

cnf(c_0_12880_2,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12880]) ).

cnf(c_0_12883_0,axiom,
    ( X1 = c_0
    | c_less(c_0,c_Nat_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12883]) ).

cnf(c_0_12883_1,axiom,
    ( c_less(c_0,c_Nat_Opower(X1,X2,tc_nat),tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12883]) ).

cnf(c_0_12896_0,axiom,
    ( c_minus(X1,X2,tc_set(X3)) = c_emptyset
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12896]) ).

cnf(c_0_12896_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | c_minus(X1,X2,tc_set(X3)) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12896]) ).

cnf(c_0_12897_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_minus(X1,X2,tc_set(X3)) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12897]) ).

cnf(c_0_12897_1,axiom,
    ( c_minus(X1,X2,tc_set(X3)) != c_emptyset
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12897]) ).

cnf(c_0_12898_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12898]) ).

cnf(c_0_12898_1,axiom,
    ( ~ c_less(X1,X2,tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_12898]) ).

cnf(c_0_12899_0,axiom,
    ( c_List_Orotate1(X1,X2) = X1
    | ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12899]) ).

cnf(c_0_12899_1,axiom,
    ( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat)
    | c_List_Orotate1(X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12899]) ).

cnf(c_0_12900_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12900]) ).

cnf(c_0_12900_1,axiom,
    ( ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12900]) ).

cnf(c_0_12901_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12901]) ).

cnf(c_0_12901_1,axiom,
    ( ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12901]) ).

cnf(c_0_12902_0,axiom,
    ( c_less(X1,X2,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12902]) ).

cnf(c_0_12902_1,axiom,
    ( ~ c_less(c_IntDef_Onat(X1),c_IntDef_Onat(X2),tc_nat)
    | c_less(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12902]) ).

cnf(c_0_12903_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12903]) ).

cnf(c_0_12903_1,axiom,
    ( ~ c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12903]) ).

cnf(c_0_12904_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12904]) ).

cnf(c_0_12904_1,axiom,
    ( ~ c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12904]) ).

cnf(c_0_12905_0,axiom,
    ( c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12905]) ).

cnf(c_0_12905_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_times(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12905]) ).

cnf(c_0_12906_0,axiom,
    ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12906]) ).

cnf(c_0_12906_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12906]) ).

cnf(c_0_12907_0,axiom,
    ( c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12907]) ).

cnf(c_0_12907_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_div(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12907]) ).

cnf(c_0_12908_0,axiom,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_IntDef_Onat(X2),c_IntDef_Onat(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12908]) ).

cnf(c_0_12908_1,axiom,
    ( ~ c_less(c_IntDef_Onat(X2),c_IntDef_Onat(X1),tc_nat)
    | c_less(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12908]) ).

cnf(c_0_12909_0,axiom,
    ( c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12909]) ).

cnf(c_0_12909_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_times(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12909]) ).

cnf(c_0_12910_0,axiom,
    ( c_plus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12910]) ).

cnf(c_0_12910_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_plus(c_Numeral_Onumber__of(X1,X2),c_Numeral_Onumber__of(X3,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12910]) ).

cnf(c_0_12912_0,axiom,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12912]) ).

cnf(c_0_12912_1,axiom,
    ( ~ c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12912]) ).

cnf(c_0_12913_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | c_Nat_Opower(X2,X1,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12913]) ).

cnf(c_0_12913_1,axiom,
    ( c_Nat_Opower(X2,X1,X3) != c_0
    | c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12913]) ).

cnf(c_0_12913_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X2,X1,X3) != c_0
    | c_less(c_0,X1,tc_nat)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12913]) ).

cnf(c_0_12913_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X2,X1,X3) != c_0
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12913]) ).

cnf(c_0_12916_0,axiom,
    ( c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12916]) ).

cnf(c_0_12916_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),tc_IntDef_Oint),tc_IntDef_Oint)
    | c_less(c_0,c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12916]) ).

cnf(c_0_12917_0,axiom,
    ( c_less(c_1,X1,tc_IntDef_Oint)
    | ~ c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12917]) ).

cnf(c_0_12917_1,axiom,
    ( ~ c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat)
    | c_less(c_1,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12917]) ).

cnf(c_0_12918_0,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12918]) ).

cnf(c_0_12918_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12918]) ).

cnf(c_0_12918_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12918]) ).

cnf(c_0_12919_0,axiom,
    ( c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12919]) ).

cnf(c_0_12919_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12919]) ).

cnf(c_0_12920_0,axiom,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12920]) ).

cnf(c_0_12920_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12920]) ).

cnf(c_0_12921_0,axiom,
    ( c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12921]) ).

cnf(c_0_12921_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_less(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12921]) ).

cnf(c_0_12922_0,axiom,
    ( c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12922]) ).

cnf(c_0_12922_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12922]) ).

cnf(c_0_12923_0,axiom,
    ( c_Nat_Opower(c_0,X1,X2) = c_0
    | ~ c_less(c_0,X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12923]) ).

cnf(c_0_12923_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_Nat_Opower(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12923]) ).

cnf(c_0_12923_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,X1,tc_nat)
    | c_Nat_Opower(c_0,X1,X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12923]) ).

cnf(c_0_12923_3,axiom,
    ( ~ class_Power_Orecpower(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_less(c_0,X1,tc_nat)
    | c_Nat_Opower(c_0,X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12923]) ).

cnf(c_0_12925_0,axiom,
    ( c_SetInterval_OgreaterThanAtMost(X1,X2,X3) = c_emptyset
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12925]) ).

cnf(c_0_12925_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_SetInterval_OgreaterThanAtMost(X1,X2,X3) = c_emptyset
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12925]) ).

cnf(c_0_12925_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_SetInterval_OgreaterThanAtMost(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12925]) ).

cnf(c_0_12926_0,axiom,
    ( c_SetInterval_OatLeastLessThan(X1,X2,X3) = c_emptyset
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12926]) ).

cnf(c_0_12926_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_SetInterval_OatLeastLessThan(X1,X2,X3) = c_emptyset
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12926]) ).

cnf(c_0_12926_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_SetInterval_OatLeastLessThan(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12926]) ).

cnf(c_0_12927_0,axiom,
    ( c_SetInterval_OatLeastAtMost(X1,X2,X3) = c_emptyset
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12927]) ).

cnf(c_0_12927_1,axiom,
    ( ~ c_less(X2,X1,X3)
    | c_SetInterval_OatLeastAtMost(X1,X2,X3) = c_emptyset
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12927]) ).

cnf(c_0_12927_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_less(X2,X1,X3)
    | c_SetInterval_OatLeastAtMost(X1,X2,X3) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_12927]) ).

cnf(c_0_12928_0,axiom,
    ( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12928]) ).

cnf(c_0_12928_1,axiom,
    ( c_in(X1,X2,X3)
    | c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12928]) ).

cnf(c_0_12929_0,axiom,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12929]) ).

cnf(c_0_12929_1,axiom,
    ( c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12929]) ).

cnf(c_0_12929_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12929]) ).

cnf(c_0_12929_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_less(c_Numeral_Onumber__of(X1,X2),c_0,X2)
    | c_HOL_Oabs(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12929]) ).

cnf(c_0_12933_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_less(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12933]) ).

cnf(c_0_12933_1,axiom,
    ( ~ c_less(X1,c_Suc(X2),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12933]) ).

cnf(c_0_12934_0,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12934]) ).

cnf(c_0_12934_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12934]) ).

cnf(c_0_12935_0,axiom,
    ( c_List_Odistinct(c_List_Otake(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12935]) ).

cnf(c_0_12935_1,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | c_List_Odistinct(c_List_Otake(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12935]) ).

cnf(c_0_12936_0,axiom,
    ( c_List_Odistinct(c_List_Osublist(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12936]) ).

cnf(c_0_12936_1,axiom,
    ( ~ c_List_Odistinct(X1,X3)
    | c_List_Odistinct(c_List_Osublist(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12936]) ).

cnf(c_0_12937_0,axiom,
    ( c_List_Odistinct(c_List_Orotate(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12937]) ).

cnf(c_0_12937_1,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | c_List_Odistinct(c_List_Orotate(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12937]) ).

cnf(c_0_12938_0,axiom,
    ( c_List_Odistinct(c_List_Oremove1(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12938]) ).

cnf(c_0_12938_1,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | c_List_Odistinct(c_List_Oremove1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12938]) ).

cnf(c_0_12939_0,axiom,
    ( c_List_Odistinct(c_List_Odrop(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12939]) ).

cnf(c_0_12939_1,axiom,
    ( ~ c_List_Odistinct(X2,X3)
    | c_List_Odistinct(c_List_Odrop(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12939]) ).

cnf(c_0_12940_0,axiom,
    ( c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat)
    | ~ c_less(c_1,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12940]) ).

cnf(c_0_12940_1,axiom,
    ( ~ c_less(c_1,X1,tc_IntDef_Oint)
    | c_less(c_Suc(c_0),c_IntDef_Onat(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12940]) ).

cnf(c_0_12941_0,axiom,
    ( c_less(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12941]) ).

cnf(c_0_12941_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_less(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12941]) ).

cnf(c_0_12942_0,axiom,
    ( c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12942]) ).

cnf(c_0_12942_1,axiom,
    ( ~ c_in(X1,X2,tc_Message_Omsg)
    | c_in(X1,c_Message_Osynth(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12942]) ).

cnf(c_0_12943_0,axiom,
    ( c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12943]) ).

cnf(c_0_12943_1,axiom,
    ( ~ c_in(X1,X2,tc_Message_Omsg)
    | c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12943]) ).

cnf(c_0_12944_0,axiom,
    ( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
    | ~ c_in(X1,X2,tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12944]) ).

cnf(c_0_12944_1,axiom,
    ( ~ c_in(X1,X2,tc_Message_Omsg)
    | c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg) ),
    inference(literals_permutation,[status(thm)],[c_0_12944]) ).

cnf(c_0_12946_0,axiom,
    ( c_in(X1,c_Message_OsymKeys,tc_nat)
    | ~ c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12946]) ).

cnf(c_0_12946_1,axiom,
    ( ~ c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat)
    | c_in(X1,c_Message_OsymKeys,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12946]) ).

cnf(c_0_12947_0,axiom,
    ( c_less(c_0,X1,tc_IntDef_Oint)
    | ~ c_less(c_0,c_IntDef_Onat(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12947]) ).

cnf(c_0_12947_1,axiom,
    ( ~ c_less(c_0,c_IntDef_Onat(X1),tc_nat)
    | c_less(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12947]) ).

cnf(c_0_12948_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12948]) ).

cnf(c_0_12948_1,axiom,
    ( ~ c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12948]) ).

cnf(c_0_12949_0,axiom,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12949]) ).

cnf(c_0_12949_1,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12949]) ).

cnf(c_0_12949_2,axiom,
    ( c_Parity_Oeven(X2,tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_plus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12949]) ).

cnf(c_0_12950_0,axiom,
    ( c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12950]) ).

cnf(c_0_12950_1,axiom,
    ( c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12950]) ).

cnf(c_0_12950_2,axiom,
    ( c_Parity_Oeven(X2,tc_nat)
    | c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12950]) ).

cnf(c_0_12951_0,axiom,
    ( c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12951]) ).

cnf(c_0_12951_1,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12951]) ).

cnf(c_0_12951_2,axiom,
    ( c_Parity_Oeven(X2,tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_minus(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12951]) ).

cnf(c_0_12952_0,axiom,
    ( X1 = c_Datatype_Ooption_OSome(X2,X3)
    | ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12952]) ).

cnf(c_0_12952_1,axiom,
    ( ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3)
    | X1 = c_Datatype_Ooption_OSome(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12952]) ).

cnf(c_0_12953_0,axiom,
    ( c_minus(X1,c_uminus(X2,X3),X3) = c_plus(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12953]) ).

cnf(c_0_12953_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_minus(X1,c_uminus(X2,X3),X3) = c_plus(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12953]) ).

cnf(c_0_12954_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12954]) ).

cnf(c_0_12954_1,axiom,
    ( c_Numeral_Onumber__of(X1,X2) != c_0
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12954]) ).

cnf(c_0_12954_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12954]) ).

cnf(c_0_12955_0,axiom,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_in(c_Main_Oconcat__eq__Nil__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12955]) ).

cnf(c_0_12955_1,axiom,
    ( c_in(c_Main_Oconcat__eq__Nil__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2))
    | c_List_Oconcat(X1,X2) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12955]) ).

cnf(c_0_12956_0,axiom,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_in(c_Main_ONil__eq__concat__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_12956]) ).

cnf(c_0_12956_1,axiom,
    ( c_in(c_Main_ONil__eq__concat__conv__1(X1,X2),c_List_Oset(X1,tc_List_Olist(X2)),tc_List_Olist(X2))
    | c_List_Oconcat(X1,X2) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12956]) ).

cnf(c_0_12957_0,axiom,
    ( c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat)
    | ~ c_in(X1,c_Message_OsymKeys,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12957]) ).

cnf(c_0_12957_1,axiom,
    ( ~ c_in(X1,c_Message_OsymKeys,tc_nat)
    | c_in(c_Message_OinvKey(X1),c_Message_OsymKeys,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12957]) ).

cnf(c_0_12958_0,axiom,
    ( c_less(c_0,c_IntDef_Onat(X1),tc_nat)
    | ~ c_less(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12958]) ).

cnf(c_0_12958_1,axiom,
    ( ~ c_less(c_0,X1,tc_IntDef_Oint)
    | c_less(c_0,c_IntDef_Onat(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12958]) ).

cnf(c_0_12959_0,axiom,
    ( c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12959]) ).

cnf(c_0_12959_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12959]) ).

cnf(c_0_12960_0,axiom,
    ( X1 = c_0
    | c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12960]) ).

cnf(c_0_12960_1,axiom,
    ( c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12960]) ).

cnf(c_0_12960_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3) != c_0
    | X1 = c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12960]) ).

cnf(c_0_12960_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X1,c_Numeral_Onumber__of(X2,tc_nat),X3) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12960]) ).

cnf(c_0_12961_0,axiom,
    ( c_Divides_Oop_Amod(X1,X2,tc_nat) = X1
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12961]) ).

cnf(c_0_12961_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_Divides_Oop_Amod(X1,X2,tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_12961]) ).

cnf(c_0_12962_0,axiom,
    ( c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) = c_Suc(c_0)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12962]) ).

cnf(c_0_12962_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat) = c_Suc(c_0) ),
    inference(literals_permutation,[status(thm)],[c_0_12962]) ).

cnf(c_0_12963_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12963]) ).

cnf(c_0_12963_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12963]) ).

cnf(c_0_12963_2,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12963]) ).

cnf(c_0_12964_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12964]) ).

cnf(c_0_12964_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12964]) ).

cnf(c_0_12964_2,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_Numeral_Onumber__of(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12964]) ).

cnf(c_0_12965_0,axiom,
    ( c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12965]) ).

cnf(c_0_12965_1,axiom,
    ( ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint)
    | c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12965]) ).

cnf(c_0_12966_0,axiom,
    ( c_minus(X1,X2,tc_nat) = c_0
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12966]) ).

cnf(c_0_12966_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_minus(X1,X2,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12966]) ).

cnf(c_0_12967_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_minus(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12967]) ).

cnf(c_0_12967_1,axiom,
    ( c_minus(X1,X2,tc_nat) != c_0
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12967]) ).

cnf(c_0_12968_0,axiom,
    ( c_div(X1,X2,tc_nat) = c_0
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12968]) ).

cnf(c_0_12968_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_div(X1,X2,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12968]) ).

cnf(c_0_12969_0,axiom,
    ( c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12969]) ).

cnf(c_0_12969_1,axiom,
    ( ~ c_Parity_Oeven(X2,tc_IntDef_Oint)
    | c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12969]) ).

cnf(c_0_12970_0,axiom,
    ( c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12970]) ).

cnf(c_0_12970_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_12970]) ).

cnf(c_0_12971_0,axiom,
    ( c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12971]) ).

cnf(c_0_12971_1,axiom,
    ( ~ c_Parity_Oeven(X2,tc_nat)
    | c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12971]) ).

cnf(c_0_12972_0,axiom,
    ( c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12972]) ).

cnf(c_0_12972_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(c_times(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12972]) ).

cnf(c_0_12974_0,axiom,
    ( c_List_Olast(c_append(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12974]) ).

cnf(c_0_12974_1,axiom,
    ( X2 = c_List_Olist_ONil
    | c_List_Olast(c_append(X1,X2,X3),X3) = c_List_Olast(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12974]) ).

cnf(c_0_12975_0,axiom,
    ( c_List_Olast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12975]) ).

cnf(c_0_12975_1,axiom,
    ( X2 = c_List_Olist_ONil
    | c_List_Olast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olast(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12975]) ).

cnf(c_0_12976_0,axiom,
    ( c_List_Ohd(c_append(X1,X2,X3),X3) = c_List_Ohd(X1,X3)
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_12976]) ).

cnf(c_0_12976_1,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Ohd(c_append(X1,X2,X3),X3) = c_List_Ohd(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_12976]) ).

cnf(c_0_12977_0,axiom,
    ( X1 = c_0
    | c_LOrder_Omeet(X1,c_uminus(X1,X2),X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12977]) ).

cnf(c_0_12977_1,axiom,
    ( c_LOrder_Omeet(X1,c_uminus(X1,X2),X2) != c_0
    | X1 = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12977]) ).

cnf(c_0_12977_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | c_LOrder_Omeet(X1,c_uminus(X1,X2),X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12977]) ).

cnf(c_0_12978_0,axiom,
    ( X1 = c_0
    | c_LOrder_Ojoin(X1,c_uminus(X1,X2),X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12978]) ).

cnf(c_0_12978_1,axiom,
    ( c_LOrder_Ojoin(X1,c_uminus(X1,X2),X2) != c_0
    | X1 = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12978]) ).

cnf(c_0_12978_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | c_LOrder_Ojoin(X1,c_uminus(X1,X2),X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12978]) ).

cnf(c_0_12981_0,axiom,
    ( c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) = c_plus(c_1,c_1,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12981]) ).

cnf(c_0_12981_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) = c_plus(c_1,c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_12981]) ).

cnf(c_0_12986_0,axiom,
    ( c_div(X1,X1,tc_nat) = c_1
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_12986]) ).

cnf(c_0_12986_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_div(X1,X1,tc_nat) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_12986]) ).

cnf(c_0_12987_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12987]) ).

cnf(c_0_12987_1,axiom,
    ( c_Numeral_Onumber__of(X1,X2) != c_0
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12987]) ).

cnf(c_0_12987_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_Numeral_Onumber__of(X1,X2) != c_0
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12987]) ).

cnf(c_0_12989_0,axiom,
    ( X1 = c_0
    | ~ c_lessequals(c_HOL_Oabs(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12989]) ).

cnf(c_0_12989_1,axiom,
    ( ~ c_lessequals(c_HOL_Oabs(X1,X2),c_0,X2)
    | X1 = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12989]) ).

cnf(c_0_12989_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | ~ c_lessequals(c_HOL_Oabs(X1,X2),c_0,X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12989]) ).

cnf(c_0_12990_0,axiom,
    ( c_divide(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_HOL_Oinverse(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12990]) ).

cnf(c_0_12990_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_HOL_Oinverse(c_Numeral_Onumber__of(X1,X2),X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12990]) ).

cnf(c_0_12990_2,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_1,c_Numeral_Onumber__of(X1,X2),X2) = c_HOL_Oinverse(c_Numeral_Onumber__of(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12990]) ).

cnf(c_0_12991_0,axiom,
    ( X1 = c_0
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12991]) ).

cnf(c_0_12991_1,axiom,
    ( ~ c_lessequals(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12991]) ).

cnf(c_0_12991_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_lessequals(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_12991]) ).

cnf(c_0_12995_0,axiom,
    ( ~ c_less(c_HOL_Oabs(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12995]) ).

cnf(c_0_12995_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | ~ c_less(c_HOL_Oabs(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12995]) ).

cnf(c_0_12996_0,axiom,
    ( ~ c_less(c_NatArith_Oof__nat(X1,X2),c_0,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12996]) ).

cnf(c_0_12996_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_less(c_NatArith_Oof__nat(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_12996]) ).

cnf(c_0_13000_0,axiom,
    ( ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13000]) ).

cnf(c_0_13000_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13000]) ).

cnf(c_0_13001_0,axiom,
    ( c_Finite__Set_OMin(c_insert(X1,c_emptyset,X2),X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13001]) ).

cnf(c_0_13001_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Finite__Set_OMin(c_insert(X1,c_emptyset,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13001]) ).

cnf(c_0_13002_0,axiom,
    ( c_Finite__Set_OMax(c_insert(X1,c_emptyset,X2),X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13002]) ).

cnf(c_0_13002_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Finite__Set_OMax(c_insert(X1,c_emptyset,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13002]) ).

cnf(c_0_13004_0,axiom,
    ( c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13004]) ).

cnf(c_0_13004_1,axiom,
    ( c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13004]) ).

cnf(c_0_13004_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13004]) ).

cnf(c_0_13004_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13004]) ).

cnf(c_0_13004_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13004]) ).

cnf(c_0_13005_0,axiom,
    ( c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13005]) ).

cnf(c_0_13005_1,axiom,
    ( c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13005]) ).

cnf(c_0_13005_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13005]) ).

cnf(c_0_13005_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13005]) ).

cnf(c_0_13005_4,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_0
    | c_divide(X1,c_Numeral_Onumber__of(X2,X3),X3) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13005]) ).

cnf(c_0_13011_0,axiom,
    ( c_List_Olast(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13011]) ).

cnf(c_0_13011_1,axiom,
    ( X1 = c_0
    | c_List_Olast(c_List_Oreplicate(X1,X2,X3),X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13011]) ).

cnf(c_0_13012_0,axiom,
    ( c_List_Ohd(c_List_Oupt(X1,X2),tc_nat) = X1
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13012]) ).

cnf(c_0_13012_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_List_Ohd(c_List_Oupt(X1,X2),tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13012]) ).

cnf(c_0_13013_0,axiom,
    ( c_List_Ohd(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13013]) ).

cnf(c_0_13013_1,axiom,
    ( X1 = c_0
    | c_List_Ohd(c_List_Oreplicate(X1,X2,X3),X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13013]) ).

cnf(c_0_13018_0,axiom,
    ( c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13018]) ).

cnf(c_0_13018_1,axiom,
    ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
    | c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13018]) ).

cnf(c_0_13019_0,axiom,
    ( c_divide(X1,c_0,X2) = c_divide(X3,c_0,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13019]) ).

cnf(c_0_13019_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_0,X2) = c_divide(X3,c_0,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13019]) ).

cnf(c_0_13019_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_0,X2) = c_divide(X3,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13019]) ).

cnf(c_0_13020_0,axiom,
    ( c_divide(c_0,X1,X2) = c_divide(c_0,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13020]) ).

cnf(c_0_13020_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,X1,X2) = c_divide(c_0,X3,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13020]) ).

cnf(c_0_13020_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,X1,X2) = c_divide(c_0,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13020]) ).

cnf(c_0_13021_0,axiom,
    ( c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13021]) ).

cnf(c_0_13021_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13021]) ).

cnf(c_0_13021_2,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13021]) ).

cnf(c_0_13022_0,axiom,
    ( c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13022]) ).

cnf(c_0_13022_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13022]) ).

cnf(c_0_13022_2,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(c_uminus(c_Numeral_Onumber__of(X1,X2),X2),X2) = c_Numeral_Onumber__of(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13022]) ).

cnf(c_0_13023_0,axiom,
    ( X1 = c_emptyset
    | c_Union(X2,X3) != c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13023]) ).

cnf(c_0_13023_1,axiom,
    ( c_Union(X2,X3) != c_emptyset
    | X1 = c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13023]) ).

cnf(c_0_13023_2,axiom,
    ( ~ c_in(X1,X2,tc_set(X3))
    | c_Union(X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13023]) ).

cnf(c_0_13024_0,axiom,
    ( X1 = c_emptyset
    | c_Union(X2,X3) != c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13024]) ).

cnf(c_0_13024_1,axiom,
    ( c_Union(X2,X3) != c_emptyset
    | X1 = c_emptyset
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13024]) ).

cnf(c_0_13024_2,axiom,
    ( ~ c_in(X1,X2,tc_set(X3))
    | c_Union(X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13024]) ).

cnf(c_0_13025_0,axiom,
    ( X1 = c_UNIV
    | c_Inter(X2,X3) != c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13025]) ).

cnf(c_0_13025_1,axiom,
    ( c_Inter(X2,X3) != c_UNIV
    | X1 = c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13025]) ).

cnf(c_0_13025_2,axiom,
    ( ~ c_in(X1,X2,tc_set(X3))
    | c_Inter(X2,X3) != c_UNIV
    | X1 = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13025]) ).

cnf(c_0_13026_0,axiom,
    ( X1 = c_UNIV
    | c_Inter(X2,X3) != c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13026]) ).

cnf(c_0_13026_1,axiom,
    ( c_Inter(X2,X3) != c_UNIV
    | X1 = c_UNIV
    | ~ c_in(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13026]) ).

cnf(c_0_13026_2,axiom,
    ( ~ c_in(X1,X2,tc_set(X3))
    | c_Inter(X2,X3) != c_UNIV
    | X1 = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13026]) ).

cnf(c_0_13028_0,axiom,
    ( c_List_Oremdups(X1,X2) = X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13028]) ).

cnf(c_0_13028_1,axiom,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13028]) ).

cnf(c_0_13029_0,axiom,
    ( c_HOL_Oabs(X1,X2) = c_uminus(X1,X2)
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13029]) ).

cnf(c_0_13029_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_HOL_Oabs(X1,X2) = c_uminus(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13029]) ).

cnf(c_0_13029_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_HOL_Oabs(X1,X2) = c_uminus(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13029]) ).

cnf(c_0_13033_0,axiom,
    ( X1 = c_0
    | ~ c_less(c_HOL_Oabs(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13033]) ).

cnf(c_0_13033_1,axiom,
    ( ~ c_less(c_HOL_Oabs(X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13033]) ).

cnf(c_0_13037_0,axiom,
    ( X1 = c_emptyset
    | c_Finite__Set_Ocard(X1,X2) != c_0
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13037]) ).

cnf(c_0_13037_1,axiom,
    ( c_Finite__Set_Ocard(X1,X2) != c_0
    | X1 = c_emptyset
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13037]) ).

cnf(c_0_13037_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_Finite__Set_Ocard(X1,X2) != c_0
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13037]) ).

cnf(c_0_13041_0,axiom,
    ( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13041]) ).

cnf(c_0_13041_1,axiom,
    ( c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13041]) ).

cnf(c_0_13041_2,axiom,
    ( ~ class_Power_Orecpower(X1)
    | c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13041]) ).

cnf(c_0_13041_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Power_Orecpower(X1)
    | c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13041]) ).

cnf(c_0_13042_0,axiom,
    ( c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_uminus(c_1,X1)
    | c_Parity_Oeven(X2,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13042]) ).

cnf(c_0_13042_1,axiom,
    ( c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_uminus(c_1,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13042]) ).

cnf(c_0_13042_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_uminus(c_1,X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13042]) ).

cnf(c_0_13042_3,axiom,
    ( ~ class_Power_Orecpower(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_uminus(c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13042]) ).

cnf(c_0_13043_0,axiom,
    ( c_SetInterval_OatLeastAtMost(X1,X1,X2) = c_insert(X1,c_emptyset,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13043]) ).

cnf(c_0_13043_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_SetInterval_OatLeastAtMost(X1,X1,X2) = c_insert(X1,c_emptyset,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13043]) ).

cnf(c_0_13044_0,axiom,
    ( c_times(X1,c_0,X2) = c_times(X3,c_0,X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13044]) ).

cnf(c_0_13044_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_times(X1,c_0,X2) = c_times(X3,c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13044]) ).

cnf(c_0_13045_0,axiom,
    ( c_times(c_0,X1,X2) = c_times(c_0,X3,X2)
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13045]) ).

cnf(c_0_13045_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_times(c_0,X1,X2) = c_times(c_0,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13045]) ).

cnf(c_0_13046_0,axiom,
    ( c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13046]) ).

cnf(c_0_13046_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13046]) ).

cnf(c_0_13046_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13046]) ).

cnf(c_0_13046_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13046]) ).

cnf(c_0_13047_0,axiom,
    ( c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_1
    | ~ c_Parity_Oeven(X2,tc_nat)
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13047]) ).

cnf(c_0_13047_1,axiom,
    ( ~ c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_1
    | ~ class_Power_Orecpower(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13047]) ).

cnf(c_0_13047_2,axiom,
    ( ~ class_Power_Orecpower(X1)
    | ~ c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_1
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13047]) ).

cnf(c_0_13047_3,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Power_Orecpower(X1)
    | ~ c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13047]) ).

cnf(c_0_13048_0,axiom,
    ( c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_1
    | ~ c_Parity_Oeven(X2,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13048]) ).

cnf(c_0_13048_1,axiom,
    ( ~ c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13048]) ).

cnf(c_0_13048_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_1
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13048]) ).

cnf(c_0_13048_3,axiom,
    ( ~ class_Power_Orecpower(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ c_Parity_Oeven(X2,tc_nat)
    | c_Nat_Opower(c_uminus(c_1,X1),X2,X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13048]) ).

cnf(c_0_13053_0,axiom,
    ( c_List_Olist_OCons(c_List_Ohd(X1,X2),c_List_Otl(X1,X2),X2) = X1
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13053]) ).

cnf(c_0_13053_1,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_OCons(c_List_Ohd(X1,X2),c_List_Otl(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13053]) ).

cnf(c_0_13054_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_in(c_List_Olast(X1,X2),c_List_Oset(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13054]) ).

cnf(c_0_13054_1,axiom,
    ( c_in(c_List_Olast(X1,X2),c_List_Oset(X1,X2),X2)
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13054]) ).

cnf(c_0_13055_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_in(c_List_Ohd(X1,X2),c_List_Oset(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13055]) ).

cnf(c_0_13055_1,axiom,
    ( c_in(c_List_Ohd(X1,X2),c_List_Oset(X1,X2),X2)
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13055]) ).

cnf(c_0_13060_0,axiom,
    ( c_OrderedGroup_Opprt(X1,X2) = X1
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13060]) ).

cnf(c_0_13060_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_OrderedGroup_Opprt(X1,X2) = X1
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13060]) ).

cnf(c_0_13060_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_OrderedGroup_Opprt(X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13060]) ).

cnf(c_0_13061_0,axiom,
    ( c_OrderedGroup_Onprt(X1,X2) = X1
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13061]) ).

cnf(c_0_13061_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_OrderedGroup_Onprt(X1,X2) = X1
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13061]) ).

cnf(c_0_13061_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_OrderedGroup_Onprt(X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13061]) ).

cnf(c_0_13062_0,axiom,
    ( c_HOL_Oabs(X1,X2) = X1
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13062]) ).

cnf(c_0_13062_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_HOL_Oabs(X1,X2) = X1
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13062]) ).

cnf(c_0_13062_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_HOL_Oabs(X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13062]) ).

cnf(c_0_13063_0,axiom,
    ( c_plus(c_NatArith_Oof__nat(X1,X2),c_1,X2) = c_NatArith_Oof__nat(c_Suc(X1),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13063]) ).

cnf(c_0_13063_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2)
    | c_plus(c_NatArith_Oof__nat(X1,X2),c_1,X2) = c_NatArith_Oof__nat(c_Suc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13063]) ).

cnf(c_0_13064_0,axiom,
    ( c_OrderedGroup_Opprt(X1,X2) = c_0
    | ~ c_lessequals(X1,c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13064]) ).

cnf(c_0_13064_1,axiom,
    ( ~ c_lessequals(X1,c_0,X2)
    | c_OrderedGroup_Opprt(X1,X2) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13064]) ).

cnf(c_0_13064_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(X1,c_0,X2)
    | c_OrderedGroup_Opprt(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13064]) ).

cnf(c_0_13065_0,axiom,
    ( c_OrderedGroup_Onprt(X1,X2) = c_0
    | ~ c_lessequals(c_0,X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13065]) ).

cnf(c_0_13065_1,axiom,
    ( ~ c_lessequals(c_0,X1,X2)
    | c_OrderedGroup_Onprt(X1,X2) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13065]) ).

cnf(c_0_13065_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | ~ c_lessequals(c_0,X1,X2)
    | c_OrderedGroup_Onprt(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13065]) ).

cnf(c_0_13066_0,axiom,
    ( c_Finite__Set_Ocard(c_emptyset,X1) = c_0
    | ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_13066]) ).

cnf(c_0_13066_1,axiom,
    ( ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1))
    | c_Finite__Set_Ocard(c_emptyset,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13066]) ).

cnf(c_0_13067_0,axiom,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_1
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13067]) ).

cnf(c_0_13067_1,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13067]) ).

cnf(c_0_13067_2,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13067]) ).

cnf(c_0_13068_0,axiom,
    ( X1 = c_0
    | X2 = c_0
    | c_divide(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13068]) ).

cnf(c_0_13068_1,axiom,
    ( X2 = c_0
    | X1 = c_0
    | c_divide(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13068]) ).

cnf(c_0_13068_2,axiom,
    ( c_divide(X1,X2,X3) != c_0
    | X2 = c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13068]) ).

cnf(c_0_13068_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,X2,X3) != c_0
    | X2 = c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13068]) ).

cnf(c_0_13068_4,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,X2,X3) != c_0
    | X2 = c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13068]) ).

cnf(c_0_13069_0,axiom,
    ( X1 = X2
    | c_divide(X1,X2,X3) != c_1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13069]) ).

cnf(c_0_13069_1,axiom,
    ( c_divide(X1,X2,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13069]) ).

cnf(c_0_13069_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,X2,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13069]) ).

cnf(c_0_13069_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,X2,X3) != c_1
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13069]) ).

cnf(c_0_13070_0,axiom,
    ( X1 = X2
    | c_divide(X2,X1,X3) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13070]) ).

cnf(c_0_13070_1,axiom,
    ( c_divide(X2,X1,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13070]) ).

cnf(c_0_13070_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | c_divide(X2,X1,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13070]) ).

cnf(c_0_13070_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | c_divide(X2,X1,X3) != c_1
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13070]) ).

cnf(c_0_13071_0,axiom,
    ( X1 = X2
    | c_divide(X2,X1,X3) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13071]) ).

cnf(c_0_13071_1,axiom,
    ( c_divide(X2,X1,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13071]) ).

cnf(c_0_13071_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X3)
    | c_divide(X2,X1,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13071]) ).

cnf(c_0_13071_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Oordered__field(X3)
    | c_divide(X2,X1,X3) != c_1
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13071]) ).

cnf(c_0_13072_0,axiom,
    ( X1 = X2
    | c_divide(X1,X2,X3) != c_1
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13072]) ).

cnf(c_0_13072_1,axiom,
    ( c_divide(X1,X2,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13072]) ).

cnf(c_0_13072_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,X2,X3) != c_1
    | X1 = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13072]) ).

cnf(c_0_13072_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_divide(X1,X2,X3) != c_1
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13072]) ).

cnf(c_0_13076_0,axiom,
    ( X1 = c_0
    | c_Nat_Opower(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13076]) ).

cnf(c_0_13076_1,axiom,
    ( c_Nat_Opower(X1,X2,X3) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13076]) ).

cnf(c_0_13076_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X1,X2,X3) != c_0
    | X1 = c_0
    | ~ class_Power_Orecpower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13076]) ).

cnf(c_0_13076_3,axiom,
    ( ~ class_Power_Orecpower(X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_Nat_Opower(X1,X2,X3) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13076]) ).

cnf(c_0_13077_0,axiom,
    ( c_Union(X1,X2) = c_emptyset
    | c_in(c_Main_Oempty__Union__conv__1(X1,X2),X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13077]) ).

cnf(c_0_13077_1,axiom,
    ( c_in(c_Main_Oempty__Union__conv__1(X1,X2),X1,tc_set(X2))
    | c_Union(X1,X2) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13077]) ).

cnf(c_0_13078_0,axiom,
    ( c_Union(X1,X2) = c_emptyset
    | c_in(c_Main_OUnion__empty__conv__1(X1,X2),X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13078]) ).

cnf(c_0_13078_1,axiom,
    ( c_in(c_Main_OUnion__empty__conv__1(X1,X2),X1,tc_set(X2))
    | c_Union(X1,X2) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13078]) ).

cnf(c_0_13079_0,axiom,
    ( c_Inter(X1,X2) = c_UNIV
    | c_in(c_Main_OInter__UNIV__conv__2__1(X1,X2),X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13079]) ).

cnf(c_0_13079_1,axiom,
    ( c_in(c_Main_OInter__UNIV__conv__2__1(X1,X2),X1,tc_set(X2))
    | c_Inter(X1,X2) = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13079]) ).

cnf(c_0_13080_0,axiom,
    ( c_Inter(X1,X2) = c_UNIV
    | c_in(c_Main_OInter__UNIV__conv__1__1(X1,X2),X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13080]) ).

cnf(c_0_13080_1,axiom,
    ( c_in(c_Main_OInter__UNIV__conv__1__1(X1,X2),X1,tc_set(X2))
    | c_Inter(X1,X2) = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13080]) ).

cnf(c_0_13081_0,axiom,
    ( c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oint(X2) != c_Numeral_Onumber__of(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13081]) ).

cnf(c_0_13081_1,axiom,
    ( c_IntDef_Oint(X2) != c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | c_lessequals(c_0,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13081]) ).

cnf(c_0_13082_0,axiom,
    ( c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13082]) ).

cnf(c_0_13082_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13082]) ).

cnf(c_0_13082_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13082]) ).

cnf(c_0_13083_0,axiom,
    ( c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = X3
    | c_uminus(X3,X2) != c_Numeral_Onumber__of(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13083]) ).

cnf(c_0_13083_1,axiom,
    ( c_uminus(X3,X2) != c_Numeral_Onumber__of(X1,X2)
    | c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = X3
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13083]) ).

cnf(c_0_13083_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(X3,X2) != c_Numeral_Onumber__of(X1,X2)
    | c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = X3
    | ~ class_Numeral_Onumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13083]) ).

cnf(c_0_13083_3,axiom,
    ( ~ class_Numeral_Onumber(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(X3,X2) != c_Numeral_Onumber__of(X1,X2)
    | c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_13083]) ).

cnf(c_0_13084_0,axiom,
    ( X1 = c_uminus(c_Numeral_Onumber__of(X2,X3),X3)
    | c_Numeral_Onumber__of(X2,X3) != c_uminus(X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13084]) ).

cnf(c_0_13084_1,axiom,
    ( c_Numeral_Onumber__of(X2,X3) != c_uminus(X1,X3)
    | X1 = c_uminus(c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13084]) ).

cnf(c_0_13084_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_uminus(X1,X3)
    | X1 = c_uminus(c_Numeral_Onumber__of(X2,X3),X3)
    | ~ class_Numeral_Onumber(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13084]) ).

cnf(c_0_13084_3,axiom,
    ( ~ class_Numeral_Onumber(X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | c_Numeral_Onumber__of(X2,X3) != c_uminus(X1,X3)
    | X1 = c_uminus(c_Numeral_Onumber__of(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13084]) ).

cnf(c_0_13085_0,axiom,
    ( X1 = c_0
    | c_divide(c_1,X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13085]) ).

cnf(c_0_13085_1,axiom,
    ( c_divide(c_1,X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13085]) ).

cnf(c_0_13085_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(c_1,X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13085]) ).

cnf(c_0_13085_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(c_1,X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13085]) ).

cnf(c_0_13086_0,axiom,
    ( X1 = c_0
    | c_divide(c_1,X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13086]) ).

cnf(c_0_13086_1,axiom,
    ( c_divide(c_1,X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13086]) ).

cnf(c_0_13086_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(c_1,X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13086]) ).

cnf(c_0_13086_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(c_1,X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13086]) ).

cnf(c_0_13087_0,axiom,
    ( c_times(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13087]) ).

cnf(c_0_13087_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_times(X1,c_Numeral_Onumber__of(c_Numeral_OMin,X2),X2) = c_uminus(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13087]) ).

cnf(c_0_13088_0,axiom,
    ( c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13088]) ).

cnf(c_0_13088_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13088]) ).

cnf(c_0_13090_0,axiom,
    ( c_List_Oupt(X1,X2) = c_List_Olist_ONil
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13090]) ).

cnf(c_0_13090_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_List_Oupt(X1,X2) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13090]) ).

cnf(c_0_13092_0,axiom,
    ( c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13092]) ).

cnf(c_0_13092_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13092]) ).

cnf(c_0_13092_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(X1,c_0,X2) != c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13092]) ).

cnf(c_0_13093_0,axiom,
    ( c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13093]) ).

cnf(c_0_13093_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(X1,c_0,X2) != c_1
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13093]) ).

cnf(c_0_13093_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | c_divide(X1,c_0,X2) != c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13093]) ).

cnf(c_0_13094_0,axiom,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13094]) ).

cnf(c_0_13094_1,axiom,
    ( X2 = c_0
    | X1 = c_1
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13094]) ).

cnf(c_0_13094_2,axiom,
    ( c_times(X1,X2,X3) != X2
    | X2 = c_0
    | X1 = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13094]) ).

cnf(c_0_13094_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_times(X1,X2,X3) != X2
    | X2 = c_0
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13094]) ).

cnf(c_0_13095_0,axiom,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13095]) ).

cnf(c_0_13095_1,axiom,
    ( X2 = c_0
    | X1 = c_1
    | c_times(X1,X2,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13095]) ).

cnf(c_0_13095_2,axiom,
    ( c_times(X1,X2,X3) != X2
    | X2 = c_0
    | X1 = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13095]) ).

cnf(c_0_13095_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_times(X1,X2,X3) != X2
    | X2 = c_0
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13095]) ).

cnf(c_0_13096_0,axiom,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13096]) ).

cnf(c_0_13096_1,axiom,
    ( X2 = c_0
    | X1 = c_1
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13096]) ).

cnf(c_0_13096_2,axiom,
    ( c_times(X2,X1,X3) != X2
    | X2 = c_0
    | X1 = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13096]) ).

cnf(c_0_13096_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_times(X2,X1,X3) != X2
    | X2 = c_0
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13096]) ).

cnf(c_0_13097_0,axiom,
    ( X1 = c_1
    | X2 = c_0
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13097]) ).

cnf(c_0_13097_1,axiom,
    ( X2 = c_0
    | X1 = c_1
    | c_times(X2,X1,X3) != X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13097]) ).

cnf(c_0_13097_2,axiom,
    ( c_times(X2,X1,X3) != X2
    | X2 = c_0
    | X1 = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13097]) ).

cnf(c_0_13097_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_times(X2,X1,X3) != X2
    | X2 = c_0
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13097]) ).

cnf(c_0_13100_0,axiom,
    ( X1 = c_0
    | X2 = c_0
    | c_times(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13100]) ).

cnf(c_0_13100_1,axiom,
    ( X2 = c_0
    | X1 = c_0
    | c_times(X1,X2,X3) != c_0
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13100]) ).

cnf(c_0_13100_2,axiom,
    ( c_times(X1,X2,X3) != c_0
    | X2 = c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13100]) ).

cnf(c_0_13100_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | c_times(X1,X2,X3) != c_0
    | X2 = c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13100]) ).

cnf(c_0_13101_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13101]) ).

cnf(c_0_13101_1,axiom,
    ( c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13101]) ).

cnf(c_0_13101_2,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(c_0,c_Numeral_Onumber__of(X1,tc_nat),X2) = c_0
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13101]) ).

cnf(c_0_13103_0,axiom,
    ( X1 = X2
    | c_minus(X1,X2,X3) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13103]) ).

cnf(c_0_13103_1,axiom,
    ( c_minus(X1,X2,X3) != c_0
    | X1 = X2
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13103]) ).

cnf(c_0_13103_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_minus(X1,X2,X3) != c_0
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13103]) ).

cnf(c_0_13104_0,axiom,
    ( X1 = c_emptyset
    | ~ c_lessequals(X1,c_emptyset,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13104]) ).

cnf(c_0_13104_1,axiom,
    ( ~ c_lessequals(X1,c_emptyset,tc_set(X2))
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13104]) ).

cnf(c_0_13107_0,axiom,
    ( c_HOL_Oinverse(c_uminus(X1,X2),X2) = c_uminus(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13107]) ).

cnf(c_0_13107_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(c_uminus(X1,X2),X2) = c_uminus(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13107]) ).

cnf(c_0_13107_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(c_uminus(X1,X2),X2) = c_uminus(c_HOL_Oinverse(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13107]) ).

cnf(c_0_13108_0,axiom,
    ( c_HOL_Oinverse(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13108]) ).

cnf(c_0_13108_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | c_HOL_Oinverse(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(c_HOL_Oinverse(X1,X2),X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13108]) ).

cnf(c_0_13108_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | c_HOL_Oinverse(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(c_HOL_Oinverse(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13108]) ).

cnf(c_0_13109_0,axiom,
    ( c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_Numeral_Onumber__of(X1,X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13109]) ).

cnf(c_0_13109_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_Numeral_Onumber__of(X1,X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13109]) ).

cnf(c_0_13109_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_NatArith_Oof__nat(c_Numeral_Onumber__of(X1,tc_nat),X2) = c_Numeral_Onumber__of(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13109]) ).

cnf(c_0_13111_0,axiom,
    ( ~ c_less(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13111]) ).

cnf(c_0_13111_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_less(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13111]) ).

cnf(c_0_13115_0,axiom,
    ( c_IntDef_Oint(c_IntDef_Onat(X1)) = X1
    | ~ c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13115]) ).

cnf(c_0_13115_1,axiom,
    ( ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
    | c_IntDef_Oint(c_IntDef_Onat(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13115]) ).

cnf(c_0_13116_0,axiom,
    ( X1 = c_0
    | ~ c_lessequals(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13116]) ).

cnf(c_0_13116_1,axiom,
    ( ~ c_lessequals(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13116]) ).

cnf(c_0_13117_0,axiom,
    ( X1 = c_Suc(c_0)
    | ~ c_Divides_Oop_Advd(X1,c_Suc(c_0),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13117]) ).

cnf(c_0_13117_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_Suc(c_0),tc_nat)
    | X1 = c_Suc(c_0) ),
    inference(literals_permutation,[status(thm)],[c_0_13117]) ).

cnf(c_0_13118_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13118]) ).

cnf(c_0_13118_1,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13118]) ).

cnf(c_0_13118_2,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13118]) ).

cnf(c_0_13119_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13119]) ).

cnf(c_0_13119_1,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13119]) ).

cnf(c_0_13119_2,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) != c_0
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13119]) ).

cnf(c_0_13120_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13120]) ).

cnf(c_0_13120_1,axiom,
    ( c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13120]) ).

cnf(c_0_13122_0,axiom,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13122]) ).

cnf(c_0_13122_1,axiom,
    ( c_List_Oremdups(X1,X2) != X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13122]) ).

cnf(c_0_13123_0,axiom,
    ( X1 = c_0
    | ~ c_less(X1,c_Suc(c_0),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13123]) ).

cnf(c_0_13123_1,axiom,
    ( ~ c_less(X1,c_Suc(c_0),tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13123]) ).

cnf(c_0_13124_0,axiom,
    ( c_times(X1,c_HOL_Oinverse(X1,X2),X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13124]) ).

cnf(c_0_13124_1,axiom,
    ( X1 = c_0
    | c_times(X1,c_HOL_Oinverse(X1,X2),X2) = c_1
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13124]) ).

cnf(c_0_13124_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | X1 = c_0
    | c_times(X1,c_HOL_Oinverse(X1,X2),X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13124]) ).

cnf(c_0_13125_0,axiom,
    ( c_times(c_HOL_Oinverse(X1,X2),X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13125]) ).

cnf(c_0_13125_1,axiom,
    ( X1 = c_0
    | c_times(c_HOL_Oinverse(X1,X2),X1,X2) = c_1
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13125]) ).

cnf(c_0_13125_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | X1 = c_0
    | c_times(c_HOL_Oinverse(X1,X2),X1,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13125]) ).

cnf(c_0_13126_0,axiom,
    ( X1 = c_List_Olist_ONil
    | X2 = c_0
    | c_List_Otake(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13126]) ).

cnf(c_0_13126_1,axiom,
    ( X2 = c_0
    | X1 = c_List_Olist_ONil
    | c_List_Otake(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13126]) ).

cnf(c_0_13126_2,axiom,
    ( c_List_Otake(X2,X1,X3) != c_List_Olist_ONil
    | X2 = c_0
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13126]) ).

cnf(c_0_13127_0,axiom,
    ( X1 = c_1
    | c_times(X2,X1,tc_nat) != c_Suc(c_0) ),
    inference(literals_permutation,[status(thm)],[c_0_13127]) ).

cnf(c_0_13127_1,axiom,
    ( c_times(X2,X1,tc_nat) != c_Suc(c_0)
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13127]) ).

cnf(c_0_13128_0,axiom,
    ( X1 = c_1
    | c_times(X1,X2,tc_nat) != c_Suc(c_0) ),
    inference(literals_permutation,[status(thm)],[c_0_13128]) ).

cnf(c_0_13128_1,axiom,
    ( c_times(X1,X2,tc_nat) != c_Suc(c_0)
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13128]) ).

cnf(c_0_13129_0,axiom,
    ( X1 = c_1
    | c_times(X2,X1,tc_nat) != c_Suc(c_0) ),
    inference(literals_permutation,[status(thm)],[c_0_13129]) ).

cnf(c_0_13129_1,axiom,
    ( c_times(X2,X1,tc_nat) != c_Suc(c_0)
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13129]) ).

cnf(c_0_13130_0,axiom,
    ( X1 = c_1
    | c_times(X1,X2,tc_nat) != c_Suc(c_0) ),
    inference(literals_permutation,[status(thm)],[c_0_13130]) ).

cnf(c_0_13130_1,axiom,
    ( c_times(X1,X2,tc_nat) != c_Suc(c_0)
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13130]) ).

cnf(c_0_13131_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13131]) ).

cnf(c_0_13131_1,axiom,
    ( c_append(X2,X1,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13131]) ).

cnf(c_0_13132_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13132]) ).

cnf(c_0_13132_1,axiom,
    ( c_append(X1,X2,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13132]) ).

cnf(c_0_13133_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13133]) ).

cnf(c_0_13133_1,axiom,
    ( c_append(X2,X1,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13133]) ).

cnf(c_0_13134_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13134]) ).

cnf(c_0_13134_1,axiom,
    ( c_append(X1,X2,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13134]) ).

cnf(c_0_13136_0,axiom,
    ( ~ c_less(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13136]) ).

cnf(c_0_13136_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_less(c_1,c_0,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13136]) ).

cnf(c_0_13137_0,axiom,
    ( ~ c_lessequals(c_1,c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13137]) ).

cnf(c_0_13137_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_1,c_0,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13137]) ).

cnf(c_0_13138_0,axiom,
    ( X1 = c_0
    | c_less(c_0,c_HOL_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13138]) ).

cnf(c_0_13138_1,axiom,
    ( c_less(c_0,c_HOL_Oabs(X1,X2),X2)
    | X1 = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13138]) ).

cnf(c_0_13138_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_less(c_0,c_HOL_Oabs(X1,X2),X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13138]) ).

cnf(c_0_13139_0,axiom,
    ( c_plus(X1,c_uminus(X1,X2),X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13139]) ).

cnf(c_0_13139_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_plus(X1,c_uminus(X1,X2),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13139]) ).

cnf(c_0_13140_0,axiom,
    ( c_plus(c_uminus(X1,X2),X1,X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13140]) ).

cnf(c_0_13140_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_plus(c_uminus(X1,X2),X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13140]) ).

cnf(c_0_13141_0,axiom,
    ( X1 = c_emptyset
    | c_union(X2,X1,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13141]) ).

cnf(c_0_13141_1,axiom,
    ( c_union(X2,X1,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13141]) ).

cnf(c_0_13142_0,axiom,
    ( X1 = c_emptyset
    | c_union(X1,X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13142]) ).

cnf(c_0_13142_1,axiom,
    ( c_union(X1,X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13142]) ).

cnf(c_0_13143_0,axiom,
    ( X1 = c_UNIV
    | c_inter(X2,X1,X3) != c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13143]) ).

cnf(c_0_13143_1,axiom,
    ( c_inter(X2,X1,X3) != c_UNIV
    | X1 = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13143]) ).

cnf(c_0_13144_0,axiom,
    ( X1 = c_UNIV
    | c_inter(X1,X2,X3) != c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13144]) ).

cnf(c_0_13144_1,axiom,
    ( c_inter(X1,X2,X3) != c_UNIV
    | X1 = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13144]) ).

cnf(c_0_13145_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Orotate(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13145]) ).

cnf(c_0_13145_1,axiom,
    ( c_List_Orotate(X2,X1,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13145]) ).

cnf(c_0_13146_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13146]) ).

cnf(c_0_13146_1,axiom,
    ( c_append(X2,X1,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13146]) ).

cnf(c_0_13147_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13147]) ).

cnf(c_0_13147_1,axiom,
    ( c_append(X1,X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13147]) ).

cnf(c_0_13148_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13148]) ).

cnf(c_0_13148_1,axiom,
    ( c_append(X2,X1,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13148]) ).

cnf(c_0_13149_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13149]) ).

cnf(c_0_13149_1,axiom,
    ( c_append(X1,X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13149]) ).

cnf(c_0_13150_0,axiom,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13150]) ).

cnf(c_0_13150_1,axiom,
    ( c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13150]) ).

cnf(c_0_13151_0,axiom,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13151]) ).

cnf(c_0_13151_1,axiom,
    ( c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13151]) ).

cnf(c_0_13154_0,axiom,
    ( X1 = c_0
    | X2 = c_0
    | c_times(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13154]) ).

cnf(c_0_13154_1,axiom,
    ( X2 = c_0
    | X1 = c_0
    | c_times(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13154]) ).

cnf(c_0_13154_2,axiom,
    ( c_times(X1,X2,tc_nat) != c_0
    | X2 = c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13154]) ).

cnf(c_0_13155_0,axiom,
    ( c_Message_OinvKey(X1) = X1
    | ~ c_in(X1,c_Message_OsymKeys,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13155]) ).

cnf(c_0_13155_1,axiom,
    ( ~ c_in(X1,c_Message_OsymKeys,tc_nat)
    | c_Message_OinvKey(X1) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13155]) ).

cnf(c_0_13156_0,axiom,
    ( c_lessequals(c_0,c_OrderedGroup_Opprt(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13156]) ).

cnf(c_0_13156_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | c_lessequals(c_0,c_OrderedGroup_Opprt(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13156]) ).

cnf(c_0_13157_0,axiom,
    ( c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_0,X2)
    | ~ class_OrderedGroup_Olordered__ab__group(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13157]) ).

cnf(c_0_13157_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X2)
    | c_lessequals(c_OrderedGroup_Onprt(X1,X2),c_0,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13157]) ).

cnf(c_0_13158_0,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13158]) ).

cnf(c_0_13158_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_lessequals(c_0,c_HOL_Oabs(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13158]) ).

cnf(c_0_13159_0,axiom,
    ( c_lessequals(c_0,c_NatArith_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13159]) ).

cnf(c_0_13159_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | c_lessequals(c_0,c_NatArith_Oof__nat(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13159]) ).

cnf(c_0_13160_0,axiom,
    ( c_in(c_NatArith_Oof__nat(X1,X2),c_IntDef_ONats,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13160]) ).

cnf(c_0_13160_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X2)
    | c_in(c_NatArith_Oof__nat(X1,X2),c_IntDef_ONats,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13160]) ).

cnf(c_0_13168_0,axiom,
    ( c_IntDef_Onat(X1) = c_0
    | ~ c_lessequals(X1,c_0,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13168]) ).

cnf(c_0_13168_1,axiom,
    ( ~ c_lessequals(X1,c_0,tc_IntDef_Oint)
    | c_IntDef_Onat(X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13168]) ).

cnf(c_0_13169_0,axiom,
    ( X1 = c_0
    | c_plus(X2,X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13169]) ).

cnf(c_0_13169_1,axiom,
    ( c_plus(X2,X1,tc_nat) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13169]) ).

cnf(c_0_13170_0,axiom,
    ( X1 = c_0
    | c_plus(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13170]) ).

cnf(c_0_13170_1,axiom,
    ( c_plus(X1,X2,tc_nat) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13170]) ).

cnf(c_0_13174_0,axiom,
    ( c_IntDef_Oof__int(c_uminus(X1,tc_IntDef_Oint),X2) = c_uminus(c_IntDef_Oof__int(X1,X2),X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13174]) ).

cnf(c_0_13174_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_IntDef_Oof__int(c_uminus(X1,tc_IntDef_Oint),X2) = c_uminus(c_IntDef_Oof__int(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13174]) ).

cnf(c_0_13178_0,axiom,
    ( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13178]) ).

cnf(c_0_13178_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13178]) ).

cnf(c_0_13179_0,axiom,
    ( c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_1
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13179]) ).

cnf(c_0_13179_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13179]) ).

cnf(c_0_13180_0,axiom,
    ( c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13180]) ).

cnf(c_0_13180_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13180]) ).

cnf(c_0_13181_0,axiom,
    ( c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13181]) ).

cnf(c_0_13181_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13181]) ).

cnf(c_0_13182_0,axiom,
    ( c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13182]) ).

cnf(c_0_13182_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13182]) ).

cnf(c_0_13183_0,axiom,
    ( c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13183]) ).

cnf(c_0_13183_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13183]) ).

cnf(c_0_13184_0,axiom,
    ( X1 = c_0
    | ~ c_less(X1,c_1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13184]) ).

cnf(c_0_13184_1,axiom,
    ( ~ c_less(X1,c_1,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13184]) ).

cnf(c_0_13185_0,axiom,
    ( X1 = c_0
    | ~ c_lessequals(X1,c_0,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13185]) ).

cnf(c_0_13185_1,axiom,
    ( ~ c_lessequals(X1,c_0,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13185]) ).

cnf(c_0_13186_0,axiom,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13186]) ).

cnf(c_0_13186_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13186]) ).

cnf(c_0_13187_0,axiom,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13187]) ).

cnf(c_0_13187_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_0,X1,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13187]) ).

cnf(c_0_13188_0,axiom,
    ( X1 = c_emptyset
    | c_in(c_Main_Oall__not__in__conv__1(X1,X2),X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13188]) ).

cnf(c_0_13188_1,axiom,
    ( c_in(c_Main_Oall__not__in__conv__1(X1,X2),X1,X2)
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13188]) ).

cnf(c_0_13191_0,axiom,
    ( c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X1),tc_nat)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13191]) ).

cnf(c_0_13191_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Suc(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13191]) ).

cnf(c_0_13199_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orev(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13199]) ).

cnf(c_0_13199_1,axiom,
    ( ~ c_List_Odistinct(c_List_Orev(X1,X2),X2)
    | c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13199]) ).

cnf(c_0_13200_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate1(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13200]) ).

cnf(c_0_13200_1,axiom,
    ( ~ c_List_Odistinct(c_List_Orotate1(X1,X2),X2)
    | c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13200]) ).

cnf(c_0_13203_0,axiom,
    ( X1 = c_0
    | c_lessequals(X1,X2,tc_nat)
    | c_List_Oupt(X2,X1) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13203]) ).

cnf(c_0_13203_1,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | X1 = c_0
    | c_List_Oupt(X2,X1) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13203]) ).

cnf(c_0_13203_2,axiom,
    ( c_List_Oupt(X2,X1) != c_List_Olist_ONil
    | c_lessequals(X1,X2,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13203]) ).

cnf(c_0_13204_0,axiom,
    ( X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3))
    | c_Message_Omsg_OMPair(X1,X4) != c_Message_OHPair(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13204]) ).

cnf(c_0_13204_1,axiom,
    ( c_Message_Omsg_OMPair(X1,X4) != c_Message_OHPair(X2,X3)
    | X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13204]) ).

cnf(c_0_13205_0,axiom,
    ( X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3))
    | c_Message_OHPair(X2,X3) != c_Message_Omsg_OMPair(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13205]) ).

cnf(c_0_13205_1,axiom,
    ( c_Message_OHPair(X2,X3) != c_Message_Omsg_OMPair(X1,X4)
    | X1 = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13205]) ).

cnf(c_0_13209_0,axiom,
    ( c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13209]) ).

cnf(c_0_13209_1,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_IntDef_Oint(c_Numeral_Onumber__of(X1,tc_nat)) = c_Numeral_Onumber__of(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13209]) ).

cnf(c_0_13210_0,axiom,
    ( c_minus(c_0,X1,X2) = c_uminus(X1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13210]) ).

cnf(c_0_13210_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_minus(c_0,X1,X2) = c_uminus(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13210]) ).

cnf(c_0_13211_0,axiom,
    ( c_List_Oupt(X1,c_Suc(X2)) = c_List_Olist_ONil
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13211]) ).

cnf(c_0_13211_1,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_List_Oupt(X1,c_Suc(X2)) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13211]) ).

cnf(c_0_13212_0,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_0
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13212]) ).

cnf(c_0_13212_1,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_Finite__Set_Ocard(X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13212]) ).

cnf(c_0_13214_0,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13214]) ).

cnf(c_0_13214_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13214]) ).

cnf(c_0_13214_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13214]) ).

cnf(c_0_13217_0,axiom,
    ( c_divide(X1,X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13217]) ).

cnf(c_0_13217_1,axiom,
    ( X1 = c_0
    | c_divide(X1,X1,X2) = c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13217]) ).

cnf(c_0_13217_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | X1 = c_0
    | c_divide(X1,X1,X2) = c_1
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13217]) ).

cnf(c_0_13217_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | X1 = c_0
    | c_divide(X1,X1,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13217]) ).

cnf(c_0_13218_0,axiom,
    ( c_divide(X1,X1,X2) = c_1
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13218]) ).

cnf(c_0_13218_1,axiom,
    ( X1 = c_0
    | c_divide(X1,X1,X2) = c_1
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13218]) ).

cnf(c_0_13218_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X2)
    | X1 = c_0
    | c_divide(X1,X1,X2) = c_1
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13218]) ).

cnf(c_0_13218_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Oordered__field(X2)
    | X1 = c_0
    | c_divide(X1,X1,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13218]) ).

cnf(c_0_13223_0,axiom,
    ( c_Parity_Oeven(X1,tc_IntDef_Oint)
    | ~ c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13223]) ).

cnf(c_0_13223_1,axiom,
    ( ~ c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13223]) ).

cnf(c_0_13224_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13224]) ).

cnf(c_0_13224_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13224]) ).

cnf(c_0_13225_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13225]) ).

cnf(c_0_13225_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13225]) ).

cnf(c_0_13226_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13226]) ).

cnf(c_0_13226_1,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13226]) ).

cnf(c_0_13227_0,axiom,
    ( c_Numeral_Onumber__of(X1,tc_nat) = c_0
    | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13227]) ).

cnf(c_0_13227_1,axiom,
    ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Numeral_Onumber__of(X1,tc_nat) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13227]) ).

cnf(c_0_13228_0,axiom,
    ( c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13228]) ).

cnf(c_0_13228_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X1,X2)
    | c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13228]) ).

cnf(c_0_13229_0,axiom,
    ( c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13229]) ).

cnf(c_0_13229_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X1,X2)
    | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13229]) ).

cnf(c_0_13231_0,axiom,
    ( c_divide(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13231]) ).

cnf(c_0_13231_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13231]) ).

cnf(c_0_13231_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_0,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13231]) ).

cnf(c_0_13232_0,axiom,
    ( c_divide(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13232]) ).

cnf(c_0_13232_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13232]) ).

cnf(c_0_13232_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(c_0,X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13232]) ).

cnf(c_0_13233_0,axiom,
    ( c_uminus(c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_SetInterval_OatLeast(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13233]) ).

cnf(c_0_13233_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_uminus(c_SetInterval_OlessThan(X1,X2),tc_set(X2)) = c_SetInterval_OatLeast(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13233]) ).

cnf(c_0_13234_0,axiom,
    ( c_uminus(c_SetInterval_OgreaterThan(X1,X2),tc_set(X2)) = c_SetInterval_OatMost(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13234]) ).

cnf(c_0_13234_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_uminus(c_SetInterval_OgreaterThan(X1,X2),tc_set(X2)) = c_SetInterval_OatMost(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13234]) ).

cnf(c_0_13235_0,axiom,
    ( c_uminus(c_SetInterval_OatMost(X1,X2),tc_set(X2)) = c_SetInterval_OgreaterThan(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13235]) ).

cnf(c_0_13235_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_uminus(c_SetInterval_OatMost(X1,X2),tc_set(X2)) = c_SetInterval_OgreaterThan(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13235]) ).

cnf(c_0_13236_0,axiom,
    ( c_uminus(c_SetInterval_OatLeast(X1,X2),tc_set(X2)) = c_SetInterval_OlessThan(X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13236]) ).

cnf(c_0_13236_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_uminus(c_SetInterval_OatLeast(X1,X2),tc_set(X2)) = c_SetInterval_OlessThan(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13236]) ).

cnf(c_0_13237_0,axiom,
    ( c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2)
    | ~ class_Numeral_Onumber__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13237]) ).

cnf(c_0_13237_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X2)
    | c_uminus(c_Numeral_Onumber__of(X1,X2),X2) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13237]) ).

cnf(c_0_13238_0,axiom,
    ( c_Nat_Opower(c_0,c_Suc(X1),X2) = c_0
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13238]) ).

cnf(c_0_13238_1,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(c_0,c_Suc(X1),X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13238]) ).

cnf(c_0_13241_0,axiom,
    ( c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13241]) ).

cnf(c_0_13241_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13241]) ).

cnf(c_0_13241_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | c_divide(c_1,c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13241]) ).

cnf(c_0_13242_0,axiom,
    ( c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13242]) ).

cnf(c_0_13242_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | c_divide(c_1,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13242]) ).

cnf(c_0_13242_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1)
    | c_divide(c_1,c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13242]) ).

cnf(c_0_13243_0,axiom,
    ( c_divide(c_0,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13243]) ).

cnf(c_0_13243_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | c_divide(c_0,c_0,X1) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13243]) ).

cnf(c_0_13243_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | c_divide(c_0,c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13243]) ).

cnf(c_0_13244_0,axiom,
    ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13244]) ).

cnf(c_0_13244_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13244]) ).

cnf(c_0_13245_0,axiom,
    ( X1 = X2
    | c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_13245]) ).

cnf(c_0_13245_1,axiom,
    ( c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13245]) ).

cnf(c_0_13248_0,axiom,
    ( c_List_Odistinct(c_List_Orev(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13248]) ).

cnf(c_0_13248_1,axiom,
    ( ~ c_List_Odistinct(X1,X2)
    | c_List_Odistinct(c_List_Orev(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13248]) ).

cnf(c_0_13249_0,axiom,
    ( c_List_Odistinct(c_List_Orotate1(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13249]) ).

cnf(c_0_13249_1,axiom,
    ( ~ c_List_Odistinct(X1,X2)
    | c_List_Odistinct(c_List_Orotate1(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13249]) ).

cnf(c_0_13250_0,axiom,
    ( c_Orderings_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13250]) ).

cnf(c_0_13250_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Orderings_Omax(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13250]) ).

cnf(c_0_13251_0,axiom,
    ( c_Orderings_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13251]) ).

cnf(c_0_13251_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Orderings_Omin(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13251]) ).

cnf(c_0_13252_0,axiom,
    ( c_LOrder_Omeet(X1,X1,X2) = X1
    | ~ class_LOrder_Omeet__semilorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13252]) ).

cnf(c_0_13252_1,axiom,
    ( ~ class_LOrder_Omeet__semilorder(X2)
    | c_LOrder_Omeet(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13252]) ).

cnf(c_0_13253_0,axiom,
    ( c_LOrder_Ojoin(X1,X1,X2) = X1
    | ~ class_LOrder_Ojoin__semilorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13253]) ).

cnf(c_0_13253_1,axiom,
    ( ~ class_LOrder_Ojoin__semilorder(X2)
    | c_LOrder_Ojoin(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13253]) ).

cnf(c_0_13254_0,axiom,
    ( c_IntDef_Oint(c_IntDef_Onat(X1)) = c_0
    | c_lessequals(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13254]) ).

cnf(c_0_13254_1,axiom,
    ( c_lessequals(c_0,X1,tc_IntDef_Oint)
    | c_IntDef_Oint(c_IntDef_Onat(X1)) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13254]) ).

cnf(c_0_13255_0,axiom,
    ( c_minus(X1,X1,X2) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13255]) ).

cnf(c_0_13255_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_minus(X1,X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13255]) ).

cnf(c_0_13256_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13256]) ).

cnf(c_0_13256_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13256]) ).

cnf(c_0_13257_0,axiom,
    ( c_times(c_1,X1,X2) = X1
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13257]) ).

cnf(c_0_13257_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_times(c_1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13257]) ).

cnf(c_0_13258_0,axiom,
    ( c_times(X1,c_1,X2) = X1
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13258]) ).

cnf(c_0_13258_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_times(X1,c_1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13258]) ).

cnf(c_0_13259_0,axiom,
    ( c_divide(X1,c_1,X2) = X1
    | ~ class_Ring__and__Field_Ofield(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13259]) ).

cnf(c_0_13259_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_divide(X1,c_1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13259]) ).

cnf(c_0_13260_0,axiom,
    ( c_Nat_Opower(X1,c_1,X2) = X1
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13260]) ).

cnf(c_0_13260_1,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(X1,c_1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13260]) ).

cnf(c_0_13261_0,axiom,
    ( c_times(X1,c_1,X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13261]) ).

cnf(c_0_13261_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X2)
    | c_times(X1,c_1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13261]) ).

cnf(c_0_13262_0,axiom,
    ( c_times(c_1,X1,X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13262]) ).

cnf(c_0_13262_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X2)
    | c_times(c_1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13262]) ).

cnf(c_0_13263_0,axiom,
    ( c_minus(X1,c_0,X2) = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13263]) ).

cnf(c_0_13263_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_minus(X1,c_0,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13263]) ).

cnf(c_0_13264_0,axiom,
    ( c_plus(c_0,X1,X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13264]) ).

cnf(c_0_13264_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
    | c_plus(c_0,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13264]) ).

cnf(c_0_13265_0,axiom,
    ( c_plus(X1,c_0,X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13265]) ).

cnf(c_0_13265_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
    | c_plus(X1,c_0,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13265]) ).

cnf(c_0_13266_0,axiom,
    ( c_HOL_Oabs(c_uminus(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13266]) ).

cnf(c_0_13266_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_HOL_Oabs(c_uminus(X1,X2),X2) = c_HOL_Oabs(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13266]) ).

cnf(c_0_13267_0,axiom,
    ( c_HOL_Oabs(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13267]) ).

cnf(c_0_13267_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_HOL_Oabs(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13267]) ).

cnf(c_0_13270_0,axiom,
    ( X1 = X2
    | c_HOL_Oinverse(X1,X3) != c_HOL_Oinverse(X2,X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13270]) ).

cnf(c_0_13270_1,axiom,
    ( c_HOL_Oinverse(X1,X3) != c_HOL_Oinverse(X2,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Ofield(X3)
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13270]) ).

cnf(c_0_13270_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X3)
    | c_HOL_Oinverse(X1,X3) != c_HOL_Oinverse(X2,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Odivision__by__zero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13270]) ).

cnf(c_0_13270_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X3)
    | ~ class_Ring__and__Field_Ofield(X3)
    | c_HOL_Oinverse(X1,X3) != c_HOL_Oinverse(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13270]) ).

cnf(c_0_13272_0,axiom,
    ( c_times(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13272]) ).

cnf(c_0_13272_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X2)
    | c_times(X1,c_0,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13272]) ).

cnf(c_0_13273_0,axiom,
    ( c_times(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13273]) ).

cnf(c_0_13273_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X2)
    | c_times(c_0,X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13273]) ).

cnf(c_0_13274_0,axiom,
    ( c_times(X1,c_0,X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13274]) ).

cnf(c_0_13274_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_times(X1,c_0,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13274]) ).

cnf(c_0_13275_0,axiom,
    ( c_times(c_0,X1,X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13275]) ).

cnf(c_0_13275_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_times(c_0,X1,X2) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13275]) ).

cnf(c_0_13276_0,axiom,
    ( c_Nat_Opower(X1,c_0,X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13276]) ).

cnf(c_0_13276_1,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(X1,c_0,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13276]) ).

cnf(c_0_13277_0,axiom,
    ( c_Nat_Opower(c_1,X1,X2) = c_1
    | ~ class_Power_Orecpower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13277]) ).

cnf(c_0_13277_1,axiom,
    ( ~ class_Power_Orecpower(X2)
    | c_Nat_Opower(c_1,X1,X2) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13277]) ).

cnf(c_0_13286_0,axiom,
    ( c_lessequals(c_0,c_1,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13286]) ).

cnf(c_0_13286_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_0,c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13286]) ).

cnf(c_0_13287_0,axiom,
    ( c_less(c_0,c_1,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13287]) ).

cnf(c_0_13287_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_less(c_0,c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13287]) ).

cnf(c_0_13288_0,axiom,
    ( c_in(c_1,c_IntDef_ONats,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13288]) ).

cnf(c_0_13288_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | c_in(c_1,c_IntDef_ONats,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13288]) ).

cnf(c_0_13289_0,axiom,
    ( c_in(c_0,c_IntDef_ONats,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13289]) ).

cnf(c_0_13289_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | c_in(c_0,c_IntDef_ONats,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13289]) ).

cnf(c_0_13290_0,axiom,
    ( c_in(c_1,c_IntDef_OInts,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13290]) ).

cnf(c_0_13290_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | c_in(c_1,c_IntDef_OInts,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13290]) ).

cnf(c_0_13291_0,axiom,
    ( c_in(c_0,c_IntDef_OInts,X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13291]) ).

cnf(c_0_13291_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | c_in(c_0,c_IntDef_OInts,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13291]) ).

cnf(c_0_13292_0,axiom,
    ( c_IntDef_Oof__int(c_NatArith_Oof__nat(X1,tc_IntDef_Oint),X2) = c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13292]) ).

cnf(c_0_13292_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_IntDef_Oof__int(c_NatArith_Oof__nat(X1,tc_IntDef_Oint),X2) = c_NatArith_Oof__nat(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13292]) ).

cnf(c_0_13302_0,axiom,
    ( c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Parity_Oeven(X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13302]) ).

cnf(c_0_13302_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
    | c_Parity_Oeven(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13302]) ).

cnf(c_0_13305_0,axiom,
    ( c_HOL_Oinverse(c_HOL_Oinverse(X1,X2),X2) = X1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13305]) ).

cnf(c_0_13305_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(c_HOL_Oinverse(X1,X2),X2) = X1
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13305]) ).

cnf(c_0_13305_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(c_HOL_Oinverse(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13305]) ).

cnf(c_0_13307_0,axiom,
    ( c_div(X1,X1,tc_IntDef_Oint) = c_1
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13307]) ).

cnf(c_0_13307_1,axiom,
    ( X1 = c_0
    | c_div(X1,X1,tc_IntDef_Oint) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13307]) ).

cnf(c_0_13309_0,axiom,
    ( X1 = c_IntDef_Onat(c_Numeral_Onumber__of(X2,tc_IntDef_Oint))
    | c_IntDef_Oint(X1) != c_Numeral_Onumber__of(X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_13309]) ).

cnf(c_0_13309_1,axiom,
    ( c_IntDef_Oint(X1) != c_Numeral_Onumber__of(X2,tc_IntDef_Oint)
    | X1 = c_IntDef_Onat(c_Numeral_Onumber__of(X2,tc_IntDef_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_13309]) ).

cnf(c_0_13328_0,axiom,
    ( X1 = X2
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13328]) ).

cnf(c_0_13328_1,axiom,
    ( c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13328]) ).

cnf(c_0_13328_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13328]) ).

cnf(c_0_13329_0,axiom,
    ( X1 = X2
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13329]) ).

cnf(c_0_13329_1,axiom,
    ( c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13329]) ).

cnf(c_0_13329_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13329]) ).

cnf(c_0_13330_0,axiom,
    ( X1 = X2
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13330]) ).

cnf(c_0_13330_1,axiom,
    ( c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13330]) ).

cnf(c_0_13330_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13330]) ).

cnf(c_0_13331_0,axiom,
    ( X1 = X2
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13331]) ).

cnf(c_0_13331_1,axiom,
    ( c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13331]) ).

cnf(c_0_13331_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13331]) ).

cnf(c_0_13332_0,axiom,
    ( X1 = X2
    | c_uminus(X1,X3) != c_uminus(X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13332]) ).

cnf(c_0_13332_1,axiom,
    ( c_uminus(X1,X3) != c_uminus(X2,X3)
    | X1 = X2
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13332]) ).

cnf(c_0_13332_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_uminus(X1,X3) != c_uminus(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13332]) ).

cnf(c_0_13333_0,axiom,
    ( X1 = X2
    | c_NatArith_Oof__nat(X1,X3) != c_NatArith_Oof__nat(X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13333]) ).

cnf(c_0_13333_1,axiom,
    ( c_NatArith_Oof__nat(X1,X3) != c_NatArith_Oof__nat(X2,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13333]) ).

cnf(c_0_13333_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | c_NatArith_Oof__nat(X1,X3) != c_NatArith_Oof__nat(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13333]) ).

cnf(c_0_13334_0,axiom,
    ( X1 = X2
    | c_IntDef_Oof__int(X1,X3) != c_IntDef_Oof__int(X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13334]) ).

cnf(c_0_13334_1,axiom,
    ( c_IntDef_Oof__int(X1,X3) != c_IntDef_Oof__int(X2,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13334]) ).

cnf(c_0_13334_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_IntDef_Oof__int(X1,X3) != c_IntDef_Oof__int(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13334]) ).

cnf(c_0_13335_0,axiom,
    ( c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13335]) ).

cnf(c_0_13335_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) = c_Numeral_Onumber__of(c_Numeral_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13335]) ).

cnf(c_0_13345_0,axiom,
    ( X1 = c_0
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13345]) ).

cnf(c_0_13345_1,axiom,
    ( c_less(c_0,X1,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13345]) ).

cnf(c_0_13395_0,axiom,
    ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13395]) ).

cnf(c_0_13395_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13395]) ).

cnf(c_0_13395_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13395]) ).

cnf(c_0_13396_0,axiom,
    ( c_uminus(c_uminus(c_1,X1),X1) = c_1
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13396]) ).

cnf(c_0_13396_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | c_uminus(c_uminus(c_1,X1),X1) = c_1
    | ~ class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13396]) ).

cnf(c_0_13396_2,axiom,
    ( ~ class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_uminus(c_uminus(c_1,X1),X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13396]) ).

cnf(c_0_13397_0,axiom,
    ( c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13397]) ).

cnf(c_0_13397_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_1
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13397]) ).

cnf(c_0_13397_2,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13397]) ).

cnf(c_0_13398_0,axiom,
    ( X1 = c_uminus(c_1,X2)
    | c_uminus(X1,X2) != c_1
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13398]) ).

cnf(c_0_13398_1,axiom,
    ( c_uminus(X1,X2) != c_1
    | X1 = c_uminus(c_1,X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13398]) ).

cnf(c_0_13398_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(X1,X2) != c_1
    | X1 = c_uminus(c_1,X2)
    | ~ class_HOL_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13398]) ).

cnf(c_0_13398_3,axiom,
    ( ~ class_HOL_Oone(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(X1,X2) != c_1
    | X1 = c_uminus(c_1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13398]) ).

cnf(c_0_13400_0,axiom,
    ( ~ c_Parity_Oeven(c_Suc(X1),tc_nat)
    | ~ c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13400]) ).

cnf(c_0_13400_1,axiom,
    ( ~ c_Parity_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven(c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13400]) ).

cnf(c_0_13407_0,axiom,
    ( c_uminus(c_uminus(X1,X2),X2) = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13407]) ).

cnf(c_0_13407_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(c_uminus(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13407]) ).

cnf(c_0_13408_0,axiom,
    ( X1 = X2
    | c_Public_OpublicKey(X3,X1) != c_Public_OpublicKey(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13408]) ).

cnf(c_0_13408_1,axiom,
    ( c_Public_OpublicKey(X3,X1) != c_Public_OpublicKey(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13408]) ).

cnf(c_0_13409_0,axiom,
    ( X1 = X2
    | c_Public_OpublicKey(X1,X3) != c_Public_OpublicKey(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13409]) ).

cnf(c_0_13409_1,axiom,
    ( c_Public_OpublicKey(X1,X3) != c_Public_OpublicKey(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13409]) ).

cnf(c_0_13410_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X3,X1) != c_Message_OHPair(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13410]) ).

cnf(c_0_13410_1,axiom,
    ( c_Message_Omsg_OMPair(X3,X1) != c_Message_OHPair(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13410]) ).

cnf(c_0_13411_0,axiom,
    ( X1 = X2
    | c_Message_OHPair(X3,X2) != c_Message_Omsg_OMPair(X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13411]) ).

cnf(c_0_13411_1,axiom,
    ( c_Message_OHPair(X3,X2) != c_Message_Omsg_OMPair(X4,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13411]) ).

cnf(c_0_13412_0,axiom,
    ( X1 = X2
    | c_Message_OHPair(X3,X1) != c_Message_OHPair(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13412]) ).

cnf(c_0_13412_1,axiom,
    ( c_Message_OHPair(X3,X1) != c_Message_OHPair(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13412]) ).

cnf(c_0_13413_0,axiom,
    ( X1 = X2
    | c_Message_OHPair(X1,X3) != c_Message_OHPair(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13413]) ).

cnf(c_0_13413_1,axiom,
    ( c_Message_OHPair(X1,X3) != c_Message_OHPair(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13413]) ).

cnf(c_0_13414_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_ONotes(X3,X1) != c_Event_Oevent_ONotes(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13414]) ).

cnf(c_0_13414_1,axiom,
    ( c_Event_Oevent_ONotes(X3,X1) != c_Event_Oevent_ONotes(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13414]) ).

cnf(c_0_13415_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_ONotes(X1,X3) != c_Event_Oevent_ONotes(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13415]) ).

cnf(c_0_13415_1,axiom,
    ( c_Event_Oevent_ONotes(X1,X3) != c_Event_Oevent_ONotes(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13415]) ).

cnf(c_0_13416_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_OGets(X3,X1) != c_Event_Oevent_OGets(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13416]) ).

cnf(c_0_13416_1,axiom,
    ( c_Event_Oevent_OGets(X3,X1) != c_Event_Oevent_OGets(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13416]) ).

cnf(c_0_13417_0,axiom,
    ( X1 = X2
    | c_Event_Oevent_OGets(X1,X3) != c_Event_Oevent_OGets(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13417]) ).

cnf(c_0_13417_1,axiom,
    ( c_Event_Oevent_OGets(X1,X3) != c_Event_Oevent_OGets(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13417]) ).

cnf(c_0_13418_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OCrypt(X3,X1) != c_Message_Omsg_OCrypt(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13418]) ).

cnf(c_0_13418_1,axiom,
    ( c_Message_Omsg_OCrypt(X3,X1) != c_Message_Omsg_OCrypt(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13418]) ).

cnf(c_0_13419_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OCrypt(X1,X3) != c_Message_Omsg_OCrypt(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13419]) ).

cnf(c_0_13419_1,axiom,
    ( c_Message_Omsg_OCrypt(X1,X3) != c_Message_Omsg_OCrypt(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13419]) ).

cnf(c_0_13420_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X3,X1) != c_Message_Omsg_OMPair(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13420]) ).

cnf(c_0_13420_1,axiom,
    ( c_Message_Omsg_OMPair(X3,X1) != c_Message_Omsg_OMPair(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13420]) ).

cnf(c_0_13421_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OMPair(X1,X3) != c_Message_Omsg_OMPair(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13421]) ).

cnf(c_0_13421_1,axiom,
    ( c_Message_Omsg_OMPair(X1,X3) != c_Message_Omsg_OMPair(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13421]) ).

cnf(c_0_13422_0,axiom,
    ( X1 = X2
    | c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13422]) ).

cnf(c_0_13422_1,axiom,
    ( c_List_Orev(X1,X3) != c_List_Orev(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13422]) ).

cnf(c_0_13423_0,axiom,
    ( X1 = X2
    | c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13423]) ).

cnf(c_0_13423_1,axiom,
    ( c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13423]) ).

cnf(c_0_13424_0,axiom,
    ( X1 = X2
    | c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_13424]) ).

cnf(c_0_13424_1,axiom,
    ( c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13424]) ).

cnf(c_0_13425_0,axiom,
    ( X1 = X2
    | c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_13425]) ).

cnf(c_0_13425_1,axiom,
    ( c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13425]) ).

cnf(c_0_13430_0,axiom,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13430]) ).

cnf(c_0_13430_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13430]) ).

cnf(c_0_13430_2,axiom,
    ( ~ class_Finite__Set_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_sum(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13430]) ).

cnf(c_0_13431_0,axiom,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13431]) ).

cnf(c_0_13431_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13431]) ).

cnf(c_0_13431_2,axiom,
    ( ~ class_Finite__Set_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_prod(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13431]) ).

cnf(c_0_13432_0,axiom,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13432]) ).

cnf(c_0_13432_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13432]) ).

cnf(c_0_13432_2,axiom,
    ( ~ class_Finite__Set_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_13432]) ).

cnf(c_0_13433_0,axiom,
    ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13433]) ).

cnf(c_0_13433_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13433]) ).

cnf(c_0_13438_0,axiom,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    inference(literals_permutation,[status(thm)],[c_0_13438]) ).

cnf(c_0_13438_1,axiom,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13438]) ).

cnf(c_0_13439_0,axiom,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    inference(literals_permutation,[status(thm)],[c_0_13439]) ).

cnf(c_0_13439_1,axiom,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13439]) ).

cnf(c_0_13440_0,axiom,
    ( c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) = c_1
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13440]) ).

cnf(c_0_13440_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13440]) ).

cnf(c_0_13441_0,axiom,
    ( c_IntDef_Oof__int(c_IntDef_Oint(X1),X2) = c_NatArith_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13441]) ).

cnf(c_0_13441_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X2)
    | c_IntDef_Oof__int(c_IntDef_Oint(X1),X2) = c_NatArith_Oof__nat(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13441]) ).

cnf(c_0_13455_0,axiom,
    ( X1 = c_0
    | c_HOL_Oinverse(X1,X2) != c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13455]) ).

cnf(c_0_13455_1,axiom,
    ( c_HOL_Oinverse(X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13455]) ).

cnf(c_0_13455_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13455]) ).

cnf(c_0_13455_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13455]) ).

cnf(c_0_13456_0,axiom,
    ( X1 = c_1
    | c_HOL_Oinverse(X1,X2) != c_1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13456]) ).

cnf(c_0_13456_1,axiom,
    ( c_HOL_Oinverse(X1,X2) != c_1
    | X1 = c_1
    | ~ class_Ring__and__Field_Ofield(X2)
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13456]) ).

cnf(c_0_13456_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(X1,X2) != c_1
    | X1 = c_1
    | ~ class_Ring__and__Field_Odivision__by__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13456]) ).

cnf(c_0_13456_3,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X2)
    | ~ class_Ring__and__Field_Ofield(X2)
    | c_HOL_Oinverse(X1,X2) != c_1
    | X1 = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13456]) ).

cnf(c_0_13457_0,axiom,
    ( X1 = c_0
    | c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) != c_IntDef_Oint(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13457]) ).

cnf(c_0_13457_1,axiom,
    ( c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) != c_IntDef_Oint(X1)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13457]) ).

cnf(c_0_13458_0,axiom,
    ( X1 = c_0
    | c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint) != c_IntDef_Oint(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13458]) ).

cnf(c_0_13458_1,axiom,
    ( c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint) != c_IntDef_Oint(X2)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13458]) ).

cnf(c_0_13459_0,axiom,
    ( c_Union(X1,X2) = c_emptyset
    | c_Main_Oempty__Union__conv__1(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13459]) ).

cnf(c_0_13459_1,axiom,
    ( c_Main_Oempty__Union__conv__1(X1,X2) != c_emptyset
    | c_Union(X1,X2) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13459]) ).

cnf(c_0_13460_0,axiom,
    ( c_Union(X1,X2) = c_emptyset
    | c_Main_OUnion__empty__conv__1(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13460]) ).

cnf(c_0_13460_1,axiom,
    ( c_Main_OUnion__empty__conv__1(X1,X2) != c_emptyset
    | c_Union(X1,X2) = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13460]) ).

cnf(c_0_13461_0,axiom,
    ( c_Inter(X1,X2) = c_UNIV
    | c_Main_OInter__UNIV__conv__2__1(X1,X2) != c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13461]) ).

cnf(c_0_13461_1,axiom,
    ( c_Main_OInter__UNIV__conv__2__1(X1,X2) != c_UNIV
    | c_Inter(X1,X2) = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13461]) ).

cnf(c_0_13462_0,axiom,
    ( c_Inter(X1,X2) = c_UNIV
    | c_Main_OInter__UNIV__conv__1__1(X1,X2) != c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13462]) ).

cnf(c_0_13462_1,axiom,
    ( c_Main_OInter__UNIV__conv__1__1(X1,X2) != c_UNIV
    | c_Inter(X1,X2) = c_UNIV ),
    inference(literals_permutation,[status(thm)],[c_0_13462]) ).

cnf(c_0_13463_0,axiom,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_Main_Oconcat__eq__Nil__conv__1(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13463]) ).

cnf(c_0_13463_1,axiom,
    ( c_Main_Oconcat__eq__Nil__conv__1(X1,X2) != c_List_Olist_ONil
    | c_List_Oconcat(X1,X2) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13463]) ).

cnf(c_0_13464_0,axiom,
    ( c_List_Oconcat(X1,X2) = c_List_Olist_ONil
    | c_Main_ONil__eq__concat__conv__1(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13464]) ).

cnf(c_0_13464_1,axiom,
    ( c_Main_ONil__eq__concat__conv__1(X1,X2) != c_List_Olist_ONil
    | c_List_Oconcat(X1,X2) = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13464]) ).

cnf(c_0_13466_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13466]) ).

cnf(c_0_13466_1,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13466]) ).

cnf(c_0_13468_0,axiom,
    ( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13468]) ).

cnf(c_0_13468_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13468]) ).

cnf(c_0_13469_0,axiom,
    ( c_Parity_Oeven(c_Suc(X1),tc_nat)
    | c_Parity_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13469]) ).

cnf(c_0_13469_1,axiom,
    ( c_Parity_Oeven(X1,tc_nat)
    | c_Parity_Oeven(c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_13469]) ).

cnf(c_0_13470_0,axiom,
    ( X1 = c_0
    | c_uminus(X1,X2) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13470]) ).

cnf(c_0_13470_1,axiom,
    ( c_uminus(X1,X2) != c_0
    | X1 = c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13470]) ).

cnf(c_0_13470_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13470]) ).

cnf(c_0_13471_0,axiom,
    ( c_0 = X1
    | c_uminus(X1,X2) != c_0
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13471]) ).

cnf(c_0_13471_1,axiom,
    ( c_uminus(X1,X2) != c_0
    | c_0 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13471]) ).

cnf(c_0_13471_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_uminus(X1,X2) != c_0
    | c_0 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13471]) ).

cnf(c_0_13472_0,axiom,
    ( X1 = c_0
    | c_HOL_Oabs(X1,X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13472]) ).

cnf(c_0_13472_1,axiom,
    ( c_HOL_Oabs(X1,X2) != c_0
    | X1 = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13472]) ).

cnf(c_0_13472_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_HOL_Oabs(X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13472]) ).

cnf(c_0_13473_0,axiom,
    ( X1 = c_0
    | c_HOL_Oabs(X1,X2) != c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13473]) ).

cnf(c_0_13473_1,axiom,
    ( c_HOL_Oabs(X1,X2) != c_0
    | X1 = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13473]) ).

cnf(c_0_13473_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | c_HOL_Oabs(X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13473]) ).

cnf(c_0_13474_0,axiom,
    ( X1 = c_0
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13474]) ).

cnf(c_0_13474_1,axiom,
    ( c_NatArith_Oof__nat(X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13474]) ).

cnf(c_0_13474_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13474]) ).

cnf(c_0_13475_0,axiom,
    ( c_0 = X1
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13475]) ).

cnf(c_0_13475_1,axiom,
    ( c_NatArith_Oof__nat(X1,X2) != c_0
    | c_0 = X1
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13475]) ).

cnf(c_0_13475_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | c_NatArith_Oof__nat(X1,X2) != c_0
    | c_0 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13475]) ).

cnf(c_0_13476_0,axiom,
    ( X1 = c_0
    | c_IntDef_Oof__int(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13476]) ).

cnf(c_0_13476_1,axiom,
    ( c_IntDef_Oof__int(X1,X2) != c_0
    | X1 = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13476]) ).

cnf(c_0_13476_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oof__int(X1,X2) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13476]) ).

cnf(c_0_13477_0,axiom,
    ( c_0 = X1
    | c_IntDef_Oof__int(X1,X2) != c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13477]) ).

cnf(c_0_13477_1,axiom,
    ( c_IntDef_Oof__int(X1,X2) != c_0
    | c_0 = X1
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13477]) ).

cnf(c_0_13477_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_IntDef_Oof__int(X1,X2) != c_0
    | c_0 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_13477]) ).

cnf(c_0_13492_0,axiom,
    ( ~ c_IntDef_Oneg(c_1,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13492]) ).

cnf(c_0_13492_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_IntDef_Oneg(c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13492]) ).

cnf(c_0_13493_0,axiom,
    ( ~ c_IntDef_Oneg(c_0,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13493]) ).

cnf(c_0_13493_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_IntDef_Oneg(c_0,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13493]) ).

cnf(c_0_13494_0,axiom,
    ( ~ c_IntDef_Oiszero(c_1,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13494]) ).

cnf(c_0_13494_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ c_IntDef_Oiszero(c_1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13494]) ).

cnf(c_0_13495_0,axiom,
    ( c_HOL_Oinverse(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13495]) ).

cnf(c_0_13495_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | c_HOL_Oinverse(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13495]) ).

cnf(c_0_13495_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | c_HOL_Oinverse(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13495]) ).

cnf(c_0_13496_0,axiom,
    ( c_HOL_Oinverse(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13496]) ).

cnf(c_0_13496_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | c_HOL_Oinverse(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13496]) ).

cnf(c_0_13496_2,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | c_HOL_Oinverse(c_1,X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13496]) ).

cnf(c_0_13498_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13498]) ).

cnf(c_0_13498_1,axiom,
    ( c_List_Oset(X1,X2) != c_emptyset
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13498]) ).

cnf(c_0_13499_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13499]) ).

cnf(c_0_13499_1,axiom,
    ( c_List_Oset(X1,X2) != c_emptyset
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13499]) ).

cnf(c_0_13500_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Orotate1(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13500]) ).

cnf(c_0_13500_1,axiom,
    ( c_List_Orotate1(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13500]) ).

cnf(c_0_13501_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13501]) ).

cnf(c_0_13501_1,axiom,
    ( c_List_Orev(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13501]) ).

cnf(c_0_13502_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13502]) ).

cnf(c_0_13502_1,axiom,
    ( c_List_Oremdups(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13502]) ).

cnf(c_0_13503_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13503]) ).

cnf(c_0_13503_1,axiom,
    ( c_List_Oremdups(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13503]) ).

cnf(c_0_13504_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13504]) ).

cnf(c_0_13504_1,axiom,
    ( c_List_Orev(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_13504]) ).

cnf(c_0_13505_0,axiom,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Oo2s(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_13505]) ).

cnf(c_0_13505_1,axiom,
    ( c_Datatype_Oo2s(X1,X2) != c_emptyset
    | X1 = c_Datatype_Ooption_ONone ),
    inference(literals_permutation,[status(thm)],[c_0_13505]) ).

cnf(c_0_13510_0,axiom,
    ( c_HOL_Oabs(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13510]) ).

cnf(c_0_13510_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_HOL_Oabs(c_1,X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13510]) ).

cnf(c_0_13511_0,axiom,
    ( c_OrderedGroup_Opprt(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13511]) ).

cnf(c_0_13511_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | c_OrderedGroup_Opprt(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13511]) ).

cnf(c_0_13512_0,axiom,
    ( c_OrderedGroup_Onprt(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13512]) ).

cnf(c_0_13512_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | c_OrderedGroup_Onprt(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13512]) ).

cnf(c_0_13513_0,axiom,
    ( c_uminus(c_0,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13513]) ).

cnf(c_0_13513_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | c_uminus(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13513]) ).

cnf(c_0_13514_0,axiom,
    ( c_uminus(c_0,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13514]) ).

cnf(c_0_13514_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | c_uminus(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13514]) ).

cnf(c_0_13515_0,axiom,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13515]) ).

cnf(c_0_13515_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | c_HOL_Oabs(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13515]) ).

cnf(c_0_13516_0,axiom,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13516]) ).

cnf(c_0_13516_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | c_HOL_Oabs(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13516]) ).

cnf(c_0_13517_0,axiom,
    ( c_Numeral_Onumber__of(c_Numeral_OPls,X1) = c_0
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13517]) ).

cnf(c_0_13517_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | c_Numeral_Onumber__of(c_Numeral_OPls,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13517]) ).

cnf(c_0_13518_0,axiom,
    ( c_NatArith_Oof__nat(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13518]) ).

cnf(c_0_13518_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_NatArith_Oof__nat(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13518]) ).

cnf(c_0_13519_0,axiom,
    ( c_NatArith_Oof__nat(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13519]) ).

cnf(c_0_13519_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | c_NatArith_Oof__nat(c_1,X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13519]) ).

cnf(c_0_13520_0,axiom,
    ( c_NatArith_Oof__nat(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13520]) ).

cnf(c_0_13520_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_NatArith_Oof__nat(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13520]) ).

cnf(c_0_13521_0,axiom,
    ( c_IntDef_Oof__int(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13521]) ).

cnf(c_0_13521_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_IntDef_Oof__int(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13521]) ).

cnf(c_0_13522_0,axiom,
    ( c_IntDef_Oof__int(c_1,X1) = c_1
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13522]) ).

cnf(c_0_13522_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | c_IntDef_Oof__int(c_1,X1) = c_1 ),
    inference(literals_permutation,[status(thm)],[c_0_13522]) ).

cnf(c_0_13523_0,axiom,
    ( c_IntDef_Oof__int(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13523]) ).

cnf(c_0_13523_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | c_IntDef_Oof__int(c_0,X1) = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_13523]) ).

cnf(c_0_13537_0,axiom,
    ( class_Finite__Set_Ofinite(tc_set(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13537]) ).

cnf(c_0_13537_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_set(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_13537]) ).

cnf(c_0_13538_0,axiom,
    ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13538]) ).

cnf(c_0_13538_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_13538]) ).

cnf(c_0_13543_0,axiom,
    ( X1 = X2
    | c_Public_OshrK(X1) != c_Public_OshrK(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13543]) ).

cnf(c_0_13543_1,axiom,
    ( c_Public_OshrK(X1) != c_Public_OshrK(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13543]) ).

cnf(c_0_13544_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OHash(X1) != c_Message_Omsg_OHash(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13544]) ).

cnf(c_0_13544_1,axiom,
    ( c_Message_Omsg_OHash(X1) != c_Message_Omsg_OHash(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13544]) ).

cnf(c_0_13545_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OKey(X1) != c_Message_Omsg_OKey(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13545]) ).

cnf(c_0_13545_1,axiom,
    ( c_Message_Omsg_OKey(X1) != c_Message_Omsg_OKey(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13545]) ).

cnf(c_0_13546_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_ONonce(X1) != c_Message_Omsg_ONonce(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13546]) ).

cnf(c_0_13546_1,axiom,
    ( c_Message_Omsg_ONonce(X1) != c_Message_Omsg_ONonce(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13546]) ).

cnf(c_0_13547_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_ONumber(X1) != c_Message_Omsg_ONumber(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13547]) ).

cnf(c_0_13547_1,axiom,
    ( c_Message_Omsg_ONumber(X1) != c_Message_Omsg_ONumber(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13547]) ).

cnf(c_0_13548_0,axiom,
    ( X1 = X2
    | c_Message_Omsg_OAgent(X1) != c_Message_Omsg_OAgent(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13548]) ).

cnf(c_0_13548_1,axiom,
    ( c_Message_Omsg_OAgent(X1) != c_Message_Omsg_OAgent(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13548]) ).

cnf(c_0_13549_0,axiom,
    ( X1 = X2
    | c_Message_OinvKey(X1) != c_Message_OinvKey(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13549]) ).

cnf(c_0_13549_1,axiom,
    ( c_Message_OinvKey(X1) != c_Message_OinvKey(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13549]) ).

cnf(c_0_13550_0,axiom,
    ( X1 = X2
    | c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OFriend(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13550]) ).

cnf(c_0_13550_1,axiom,
    ( c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OFriend(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13550]) ).

cnf(c_0_13551_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13551]) ).

cnf(c_0_13551_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13551]) ).

cnf(c_0_13552_0,axiom,
    ( X1 = X2
    | c_IntDef_Oint(X1) != c_IntDef_Oint(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_13552]) ).

cnf(c_0_13552_1,axiom,
    ( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_13552]) ).

cnf(c_0_13593_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13593]) ).

cnf(c_0_13593_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13593]) ).

cnf(c_0_13594_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13594]) ).

cnf(c_0_13594_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13594]) ).

cnf(c_0_13595_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13595]) ).

cnf(c_0_13595_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13595]) ).

cnf(c_0_13596_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13596]) ).

cnf(c_0_13596_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13596]) ).

cnf(c_0_13597_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13597]) ).

cnf(c_0_13597_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13597]) ).

cnf(c_0_13598_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13598]) ).

cnf(c_0_13598_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13598]) ).

cnf(c_0_13599_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13599]) ).

cnf(c_0_13599_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13599]) ).

cnf(c_0_13600_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13600]) ).

cnf(c_0_13600_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13600]) ).

cnf(c_0_13601_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13601]) ).

cnf(c_0_13601_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13601]) ).

cnf(c_0_13602_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13602]) ).

cnf(c_0_13602_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13602]) ).

cnf(c_0_13603_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13603]) ).

cnf(c_0_13603_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13603]) ).

cnf(c_0_13604_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13604]) ).

cnf(c_0_13604_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13604]) ).

cnf(c_0_13605_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13605]) ).

cnf(c_0_13605_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13605]) ).

cnf(c_0_13606_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13606]) ).

cnf(c_0_13606_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13606]) ).

cnf(c_0_13607_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13607]) ).

cnf(c_0_13607_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13607]) ).

cnf(c_0_13608_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13608]) ).

cnf(c_0_13608_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13608]) ).

cnf(c_0_13609_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13609]) ).

cnf(c_0_13609_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13609]) ).

cnf(c_0_13610_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13610]) ).

cnf(c_0_13610_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13610]) ).

cnf(c_0_13611_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13611]) ).

cnf(c_0_13611_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13611]) ).

cnf(c_0_13612_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13612]) ).

cnf(c_0_13612_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13612]) ).

cnf(c_0_13613_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13613]) ).

cnf(c_0_13613_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13613]) ).

cnf(c_0_13614_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13614]) ).

cnf(c_0_13614_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13614]) ).

cnf(c_0_13615_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13615]) ).

cnf(c_0_13615_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13615]) ).

cnf(c_0_13616_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13616]) ).

cnf(c_0_13616_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13616]) ).

cnf(c_0_13617_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13617]) ).

cnf(c_0_13617_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13617]) ).

cnf(c_0_13618_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13618]) ).

cnf(c_0_13618_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13618]) ).

cnf(c_0_13619_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13619]) ).

cnf(c_0_13619_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13619]) ).

cnf(c_0_13620_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13620]) ).

cnf(c_0_13620_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13620]) ).

cnf(c_0_13621_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13621]) ).

cnf(c_0_13621_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13621]) ).

cnf(c_0_13622_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13622]) ).

cnf(c_0_13622_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13622]) ).

cnf(c_0_13623_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13623]) ).

cnf(c_0_13623_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13623]) ).

cnf(c_0_13624_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13624]) ).

cnf(c_0_13624_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13624]) ).

cnf(c_0_13625_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13625]) ).

cnf(c_0_13625_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13625]) ).

cnf(c_0_13626_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13626]) ).

cnf(c_0_13626_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13626]) ).

cnf(c_0_13627_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13627]) ).

cnf(c_0_13627_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13627]) ).

cnf(c_0_13628_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13628]) ).

cnf(c_0_13628_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13628]) ).

cnf(c_0_13629_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13629]) ).

cnf(c_0_13629_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13629]) ).

cnf(c_0_13630_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13630]) ).

cnf(c_0_13630_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13630]) ).

cnf(c_0_13631_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13631]) ).

cnf(c_0_13631_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13631]) ).

cnf(c_0_13632_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13632]) ).

cnf(c_0_13632_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13632]) ).

cnf(c_0_13633_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13633]) ).

cnf(c_0_13633_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13633]) ).

cnf(c_0_13634_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13634]) ).

cnf(c_0_13634_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13634]) ).

cnf(c_0_13635_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13635]) ).

cnf(c_0_13635_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13635]) ).

cnf(c_0_13636_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13636]) ).

cnf(c_0_13636_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13636]) ).

cnf(c_0_13637_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13637]) ).

cnf(c_0_13637_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13637]) ).

cnf(c_0_13638_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13638]) ).

cnf(c_0_13638_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13638]) ).

cnf(c_0_13639_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13639]) ).

cnf(c_0_13639_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13639]) ).

cnf(c_0_13640_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13640]) ).

cnf(c_0_13640_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13640]) ).

cnf(c_0_13641_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13641]) ).

cnf(c_0_13641_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13641]) ).

cnf(c_0_13642_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13642]) ).

cnf(c_0_13642_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13642]) ).

cnf(c_0_13643_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13643]) ).

cnf(c_0_13643_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13643]) ).

cnf(c_0_13644_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13644]) ).

cnf(c_0_13644_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13644]) ).

cnf(c_0_13645_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13645]) ).

cnf(c_0_13645_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13645]) ).

cnf(c_0_13646_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13646]) ).

cnf(c_0_13646_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13646]) ).

cnf(c_0_13647_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13647]) ).

cnf(c_0_13647_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13647]) ).

cnf(c_0_13648_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13648]) ).

cnf(c_0_13648_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13648]) ).

cnf(c_0_13649_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13649]) ).

cnf(c_0_13649_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13649]) ).

cnf(c_0_13650_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13650]) ).

cnf(c_0_13650_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13650]) ).

cnf(c_0_13651_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13651]) ).

cnf(c_0_13651_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13651]) ).

cnf(c_0_13652_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13652]) ).

cnf(c_0_13652_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13652]) ).

cnf(c_0_13653_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13653]) ).

cnf(c_0_13653_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13653]) ).

cnf(c_0_13654_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13654]) ).

cnf(c_0_13654_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13654]) ).

cnf(c_0_13655_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13655]) ).

cnf(c_0_13655_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13655]) ).

cnf(c_0_13656_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13656]) ).

cnf(c_0_13656_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13656]) ).

cnf(c_0_13657_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13657]) ).

cnf(c_0_13657_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13657]) ).

cnf(c_0_13658_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13658]) ).

cnf(c_0_13658_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13658]) ).

cnf(c_0_13659_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13659]) ).

cnf(c_0_13659_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13659]) ).

cnf(c_0_13660_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13660]) ).

cnf(c_0_13660_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13660]) ).

cnf(c_0_13661_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13661]) ).

cnf(c_0_13661_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13661]) ).

cnf(c_0_13662_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13662]) ).

cnf(c_0_13662_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13662]) ).

cnf(c_0_13663_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13663]) ).

cnf(c_0_13663_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13663]) ).

cnf(c_0_13664_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13664]) ).

cnf(c_0_13664_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13664]) ).

cnf(c_0_13665_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13665]) ).

cnf(c_0_13665_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13665]) ).

cnf(c_0_13666_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13666]) ).

cnf(c_0_13666_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13666]) ).

cnf(c_0_13667_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13667]) ).

cnf(c_0_13667_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13667]) ).

cnf(c_0_13668_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13668]) ).

cnf(c_0_13668_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13668]) ).

cnf(c_0_13669_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13669]) ).

cnf(c_0_13669_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13669]) ).

cnf(c_0_13670_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13670]) ).

cnf(c_0_13670_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13670]) ).

cnf(c_0_13671_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13671]) ).

cnf(c_0_13671_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13671]) ).

cnf(c_0_13672_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13672]) ).

cnf(c_0_13672_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13672]) ).

cnf(c_0_13673_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13673]) ).

cnf(c_0_13673_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13673]) ).

cnf(c_0_13674_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13674]) ).

cnf(c_0_13674_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13674]) ).

cnf(c_0_13675_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13675]) ).

cnf(c_0_13675_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13675]) ).

cnf(c_0_13676_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13676]) ).

cnf(c_0_13676_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13676]) ).

cnf(c_0_13677_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13677]) ).

cnf(c_0_13677_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13677]) ).

cnf(c_0_13678_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13678]) ).

cnf(c_0_13678_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13678]) ).

cnf(c_0_13679_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13679]) ).

cnf(c_0_13679_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13679]) ).

cnf(c_0_13680_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13680]) ).

cnf(c_0_13680_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13680]) ).

cnf(c_0_13681_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13681]) ).

cnf(c_0_13681_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13681]) ).

cnf(c_0_13682_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13682]) ).

cnf(c_0_13682_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13682]) ).

cnf(c_0_13683_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13683]) ).

cnf(c_0_13683_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13683]) ).

cnf(c_0_13684_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13684]) ).

cnf(c_0_13684_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13684]) ).

cnf(c_0_13685_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13685]) ).

cnf(c_0_13685_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13685]) ).

cnf(c_0_13686_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13686]) ).

cnf(c_0_13686_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13686]) ).

cnf(c_0_13687_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13687]) ).

cnf(c_0_13687_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13687]) ).

cnf(c_0_13688_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13688]) ).

cnf(c_0_13688_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13688]) ).

cnf(c_0_13689_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13689]) ).

cnf(c_0_13689_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13689]) ).

cnf(c_0_13690_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13690]) ).

cnf(c_0_13690_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13690]) ).

cnf(c_0_13691_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13691]) ).

cnf(c_0_13691_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13691]) ).

cnf(c_0_13692_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13692]) ).

cnf(c_0_13692_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13692]) ).

cnf(c_0_13693_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13693]) ).

cnf(c_0_13693_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13693]) ).

cnf(c_0_13694_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13694]) ).

cnf(c_0_13694_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13694]) ).

cnf(c_0_13695_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13695]) ).

cnf(c_0_13695_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13695]) ).

cnf(c_0_13696_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13696]) ).

cnf(c_0_13696_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13696]) ).

cnf(c_0_13697_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13697]) ).

cnf(c_0_13697_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13697]) ).

cnf(c_0_13698_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13698]) ).

cnf(c_0_13698_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13698]) ).

cnf(c_0_13699_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13699]) ).

cnf(c_0_13699_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13699]) ).

cnf(c_0_13700_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13700]) ).

cnf(c_0_13700_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13700]) ).

cnf(c_0_13701_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13701]) ).

cnf(c_0_13701_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13701]) ).

cnf(c_0_13702_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13702]) ).

cnf(c_0_13702_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13702]) ).

cnf(c_0_13703_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13703]) ).

cnf(c_0_13703_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13703]) ).

cnf(c_0_13704_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13704]) ).

cnf(c_0_13704_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13704]) ).

cnf(c_0_13705_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13705]) ).

cnf(c_0_13705_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13705]) ).

cnf(c_0_13706_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13706]) ).

cnf(c_0_13706_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13706]) ).

cnf(c_0_13707_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13707]) ).

cnf(c_0_13707_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13707]) ).

cnf(c_0_13708_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13708]) ).

cnf(c_0_13708_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13708]) ).

cnf(c_0_13709_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13709]) ).

cnf(c_0_13709_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13709]) ).

cnf(c_0_13710_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13710]) ).

cnf(c_0_13710_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13710]) ).

cnf(c_0_13711_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13711]) ).

cnf(c_0_13711_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13711]) ).

cnf(c_0_13712_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13712]) ).

cnf(c_0_13712_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13712]) ).

cnf(c_0_13713_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13713]) ).

cnf(c_0_13713_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13713]) ).

cnf(c_0_13714_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13714]) ).

cnf(c_0_13714_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13714]) ).

cnf(c_0_13715_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13715]) ).

cnf(c_0_13715_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13715]) ).

cnf(c_0_13716_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13716]) ).

cnf(c_0_13716_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13716]) ).

cnf(c_0_13717_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13717]) ).

cnf(c_0_13717_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13717]) ).

cnf(c_0_13718_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13718]) ).

cnf(c_0_13718_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13718]) ).

cnf(c_0_13719_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13719]) ).

cnf(c_0_13719_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13719]) ).

cnf(c_0_13720_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13720]) ).

cnf(c_0_13720_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13720]) ).

cnf(c_0_13721_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13721]) ).

cnf(c_0_13721_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13721]) ).

cnf(c_0_13722_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13722]) ).

cnf(c_0_13722_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13722]) ).

cnf(c_0_13723_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13723]) ).

cnf(c_0_13723_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13723]) ).

cnf(c_0_13724_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13724]) ).

cnf(c_0_13724_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13724]) ).

cnf(c_0_13725_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13725]) ).

cnf(c_0_13725_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13725]) ).

cnf(c_0_13726_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13726]) ).

cnf(c_0_13726_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13726]) ).

cnf(c_0_13727_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13727]) ).

cnf(c_0_13727_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13727]) ).

cnf(c_0_13728_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13728]) ).

cnf(c_0_13728_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13728]) ).

cnf(c_0_13729_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13729]) ).

cnf(c_0_13729_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13729]) ).

cnf(c_0_13730_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13730]) ).

cnf(c_0_13730_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13730]) ).

cnf(c_0_13731_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13731]) ).

cnf(c_0_13731_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13731]) ).

cnf(c_0_13732_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13732]) ).

cnf(c_0_13732_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13732]) ).

cnf(c_0_13733_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13733]) ).

cnf(c_0_13733_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13733]) ).

cnf(c_0_13734_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13734]) ).

cnf(c_0_13734_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13734]) ).

cnf(c_0_13735_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13735]) ).

cnf(c_0_13735_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13735]) ).

cnf(c_0_13736_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13736]) ).

cnf(c_0_13736_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13736]) ).

cnf(c_0_13737_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13737]) ).

cnf(c_0_13737_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13737]) ).

cnf(c_0_13738_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13738]) ).

cnf(c_0_13738_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13738]) ).

cnf(c_0_13739_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13739]) ).

cnf(c_0_13739_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13739]) ).

cnf(c_0_13740_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13740]) ).

cnf(c_0_13740_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13740]) ).

cnf(c_0_13741_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13741]) ).

cnf(c_0_13741_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13741]) ).

cnf(c_0_13742_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13742]) ).

cnf(c_0_13742_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13742]) ).

cnf(c_0_13743_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13743]) ).

cnf(c_0_13743_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13743]) ).

cnf(c_0_13744_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13744]) ).

cnf(c_0_13744_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13744]) ).

cnf(c_0_13745_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13745]) ).

cnf(c_0_13745_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13745]) ).

cnf(c_0_13746_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13746]) ).

cnf(c_0_13746_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13746]) ).

cnf(c_0_13747_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13747]) ).

cnf(c_0_13747_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13747]) ).

cnf(c_0_13748_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13748]) ).

cnf(c_0_13748_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13748]) ).

cnf(c_0_13749_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13749]) ).

cnf(c_0_13749_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13749]) ).

cnf(c_0_13750_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13750]) ).

cnf(c_0_13750_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13750]) ).

cnf(c_0_13751_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13751]) ).

cnf(c_0_13751_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13751]) ).

cnf(c_0_13752_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13752]) ).

cnf(c_0_13752_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13752]) ).

cnf(c_0_13753_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13753]) ).

cnf(c_0_13753_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13753]) ).

cnf(c_0_13754_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13754]) ).

cnf(c_0_13754_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13754]) ).

cnf(c_0_13755_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13755]) ).

cnf(c_0_13755_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13755]) ).

cnf(c_0_13756_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13756]) ).

cnf(c_0_13756_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13756]) ).

cnf(c_0_13757_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13757]) ).

cnf(c_0_13757_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13757]) ).

cnf(c_0_13758_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13758]) ).

cnf(c_0_13758_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13758]) ).

cnf(c_0_13759_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13759]) ).

cnf(c_0_13759_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13759]) ).

cnf(c_0_13760_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13760]) ).

cnf(c_0_13760_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13760]) ).

cnf(c_0_13761_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13761]) ).

cnf(c_0_13761_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13761]) ).

cnf(c_0_13762_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13762]) ).

cnf(c_0_13762_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13762]) ).

cnf(c_0_13763_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13763]) ).

cnf(c_0_13763_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13763]) ).

cnf(c_0_13764_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13764]) ).

cnf(c_0_13764_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13764]) ).

cnf(c_0_13765_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13765]) ).

cnf(c_0_13765_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13765]) ).

cnf(c_0_13766_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13766]) ).

cnf(c_0_13766_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13766]) ).

cnf(c_0_13767_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13767]) ).

cnf(c_0_13767_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13767]) ).

cnf(c_0_13768_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13768]) ).

cnf(c_0_13768_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13768]) ).

cnf(c_0_13769_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13769]) ).

cnf(c_0_13769_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13769]) ).

cnf(c_0_13770_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13770]) ).

cnf(c_0_13770_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13770]) ).

cnf(c_0_13771_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13771]) ).

cnf(c_0_13771_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13771]) ).

cnf(c_0_13772_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13772]) ).

cnf(c_0_13772_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13772]) ).

cnf(c_0_13773_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13773]) ).

cnf(c_0_13773_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13773]) ).

cnf(c_0_13774_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13774]) ).

cnf(c_0_13774_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13774]) ).

cnf(c_0_13775_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13775]) ).

cnf(c_0_13775_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13775]) ).

cnf(c_0_13776_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13776]) ).

cnf(c_0_13776_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13776]) ).

cnf(c_0_13777_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13777]) ).

cnf(c_0_13777_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13777]) ).

cnf(c_0_13778_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13778]) ).

cnf(c_0_13778_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13778]) ).

cnf(c_0_13779_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13779]) ).

cnf(c_0_13779_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13779]) ).

cnf(c_0_13780_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13780]) ).

cnf(c_0_13780_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13780]) ).

cnf(c_0_13781_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13781]) ).

cnf(c_0_13781_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13781]) ).

cnf(c_0_13782_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13782]) ).

cnf(c_0_13782_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13782]) ).

cnf(c_0_13783_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13783]) ).

cnf(c_0_13783_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13783]) ).

cnf(c_0_13784_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13784]) ).

cnf(c_0_13784_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13784]) ).

cnf(c_0_13785_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13785]) ).

cnf(c_0_13785_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13785]) ).

cnf(c_0_13786_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13786]) ).

cnf(c_0_13786_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13786]) ).

cnf(c_0_13787_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13787]) ).

cnf(c_0_13787_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13787]) ).

cnf(c_0_13788_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13788]) ).

cnf(c_0_13788_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13788]) ).

cnf(c_0_13789_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13789]) ).

cnf(c_0_13789_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13789]) ).

cnf(c_0_13790_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13790]) ).

cnf(c_0_13790_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13790]) ).

cnf(c_0_13791_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13791]) ).

cnf(c_0_13791_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13791]) ).

cnf(c_0_13792_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13792]) ).

cnf(c_0_13792_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13792]) ).

cnf(c_0_13793_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13793]) ).

cnf(c_0_13793_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13793]) ).

cnf(c_0_13794_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13794]) ).

cnf(c_0_13794_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13794]) ).

cnf(c_0_13795_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13795]) ).

cnf(c_0_13795_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13795]) ).

cnf(c_0_13796_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13796]) ).

cnf(c_0_13796_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13796]) ).

cnf(c_0_13797_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13797]) ).

cnf(c_0_13797_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13797]) ).

cnf(c_0_13798_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13798]) ).

cnf(c_0_13798_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13798]) ).

cnf(c_0_13799_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13799]) ).

cnf(c_0_13799_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13799]) ).

cnf(c_0_13800_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13800]) ).

cnf(c_0_13800_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13800]) ).

cnf(c_0_13801_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13801]) ).

cnf(c_0_13801_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13801]) ).

cnf(c_0_13802_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13802]) ).

cnf(c_0_13802_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13802]) ).

cnf(c_0_13803_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13803]) ).

cnf(c_0_13803_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13803]) ).

cnf(c_0_13804_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13804]) ).

cnf(c_0_13804_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13804]) ).

cnf(c_0_13805_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13805]) ).

cnf(c_0_13805_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13805]) ).

cnf(c_0_13806_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13806]) ).

cnf(c_0_13806_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13806]) ).

cnf(c_0_13807_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13807]) ).

cnf(c_0_13807_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13807]) ).

cnf(c_0_13808_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13808]) ).

cnf(c_0_13808_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13808]) ).

cnf(c_0_13809_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13809]) ).

cnf(c_0_13809_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13809]) ).

cnf(c_0_13810_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13810]) ).

cnf(c_0_13810_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13810]) ).

cnf(c_0_13811_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13811]) ).

cnf(c_0_13811_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13811]) ).

cnf(c_0_13812_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13812]) ).

cnf(c_0_13812_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13812]) ).

cnf(c_0_13813_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13813]) ).

cnf(c_0_13813_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13813]) ).

cnf(c_0_13814_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13814]) ).

cnf(c_0_13814_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13814]) ).

cnf(c_0_13815_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13815]) ).

cnf(c_0_13815_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13815]) ).

cnf(c_0_13816_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13816]) ).

cnf(c_0_13816_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13816]) ).

cnf(c_0_13817_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13817]) ).

cnf(c_0_13817_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13817]) ).

cnf(c_0_13818_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13818]) ).

cnf(c_0_13818_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13818]) ).

cnf(c_0_13819_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13819]) ).

cnf(c_0_13819_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13819]) ).

cnf(c_0_13820_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13820]) ).

cnf(c_0_13820_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13820]) ).

cnf(c_0_13821_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13821]) ).

cnf(c_0_13821_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13821]) ).

cnf(c_0_13822_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13822]) ).

cnf(c_0_13822_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13822]) ).

cnf(c_0_13823_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13823]) ).

cnf(c_0_13823_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13823]) ).

cnf(c_0_13824_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13824]) ).

cnf(c_0_13824_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13824]) ).

cnf(c_0_13825_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13825]) ).

cnf(c_0_13825_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13825]) ).

cnf(c_0_13826_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13826]) ).

cnf(c_0_13826_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13826]) ).

cnf(c_0_13827_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13827]) ).

cnf(c_0_13827_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13827]) ).

cnf(c_0_13828_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13828]) ).

cnf(c_0_13828_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13828]) ).

cnf(c_0_13829_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13829]) ).

cnf(c_0_13829_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13829]) ).

cnf(c_0_13830_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13830]) ).

cnf(c_0_13830_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13830]) ).

cnf(c_0_13831_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13831]) ).

cnf(c_0_13831_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13831]) ).

cnf(c_0_13832_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13832]) ).

cnf(c_0_13832_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13832]) ).

cnf(c_0_13833_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13833]) ).

cnf(c_0_13833_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13833]) ).

cnf(c_0_13834_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13834]) ).

cnf(c_0_13834_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13834]) ).

cnf(c_0_13835_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13835]) ).

cnf(c_0_13835_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13835]) ).

cnf(c_0_13836_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13836]) ).

cnf(c_0_13836_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13836]) ).

cnf(c_0_13837_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13837]) ).

cnf(c_0_13837_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13837]) ).

cnf(c_0_13838_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13838]) ).

cnf(c_0_13838_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13838]) ).

cnf(c_0_13839_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13839]) ).

cnf(c_0_13839_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13839]) ).

cnf(c_0_13840_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13840]) ).

cnf(c_0_13840_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13840]) ).

cnf(c_0_13841_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13841]) ).

cnf(c_0_13841_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13841]) ).

cnf(c_0_13842_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13842]) ).

cnf(c_0_13842_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13842]) ).

cnf(c_0_13843_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13843]) ).

cnf(c_0_13843_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13843]) ).

cnf(c_0_13844_0,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13844]) ).

cnf(c_0_13844_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13844]) ).

cnf(c_0_13845_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13845]) ).

cnf(c_0_13845_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13845]) ).

cnf(c_0_13846_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13846]) ).

cnf(c_0_13846_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13846]) ).

cnf(c_0_13847_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13847]) ).

cnf(c_0_13847_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13847]) ).

cnf(c_0_13848_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13848]) ).

cnf(c_0_13848_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13848]) ).

cnf(c_0_13849_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13849]) ).

cnf(c_0_13849_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13849]) ).

cnf(c_0_13850_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13850]) ).

cnf(c_0_13850_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13850]) ).

cnf(c_0_13851_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13851]) ).

cnf(c_0_13851_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13851]) ).

cnf(c_0_13852_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13852]) ).

cnf(c_0_13852_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13852]) ).

cnf(c_0_13853_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13853]) ).

cnf(c_0_13853_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13853]) ).

cnf(c_0_13854_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13854]) ).

cnf(c_0_13854_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13854]) ).

cnf(c_0_13855_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13855]) ).

cnf(c_0_13855_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13855]) ).

cnf(c_0_13856_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13856]) ).

cnf(c_0_13856_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13856]) ).

cnf(c_0_13857_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13857]) ).

cnf(c_0_13857_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13857]) ).

cnf(c_0_13858_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13858]) ).

cnf(c_0_13858_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13858]) ).

cnf(c_0_13859_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13859]) ).

cnf(c_0_13859_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13859]) ).

cnf(c_0_13860_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13860]) ).

cnf(c_0_13860_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13860]) ).

cnf(c_0_13861_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13861]) ).

cnf(c_0_13861_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13861]) ).

cnf(c_0_13862_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13862]) ).

cnf(c_0_13862_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13862]) ).

cnf(c_0_13863_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13863]) ).

cnf(c_0_13863_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13863]) ).

cnf(c_0_13864_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13864]) ).

cnf(c_0_13864_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13864]) ).

cnf(c_0_13865_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13865]) ).

cnf(c_0_13865_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13865]) ).

cnf(c_0_13866_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13866]) ).

cnf(c_0_13866_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13866]) ).

cnf(c_0_13867_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13867]) ).

cnf(c_0_13867_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13867]) ).

cnf(c_0_13868_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13868]) ).

cnf(c_0_13868_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13868]) ).

cnf(c_0_13869_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13869]) ).

cnf(c_0_13869_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13869]) ).

cnf(c_0_13870_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13870]) ).

cnf(c_0_13870_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13870]) ).

cnf(c_0_13871_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13871]) ).

cnf(c_0_13871_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13871]) ).

cnf(c_0_13872_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13872]) ).

cnf(c_0_13872_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13872]) ).

cnf(c_0_13873_0,axiom,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13873]) ).

cnf(c_0_13873_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13873]) ).

cnf(c_0_13874_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13874]) ).

cnf(c_0_13874_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13874]) ).

cnf(c_0_13875_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13875]) ).

cnf(c_0_13875_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13875]) ).

cnf(c_0_13876_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13876]) ).

cnf(c_0_13876_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13876]) ).

cnf(c_0_13877_0,axiom,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13877]) ).

cnf(c_0_13877_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13877]) ).

cnf(c_0_13878_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13878]) ).

cnf(c_0_13878_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13878]) ).

cnf(c_0_13879_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13879]) ).

cnf(c_0_13879_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13879]) ).

cnf(c_0_13880_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13880]) ).

cnf(c_0_13880_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13880]) ).

cnf(c_0_13881_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13881]) ).

cnf(c_0_13881_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13881]) ).

cnf(c_0_13882_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13882]) ).

cnf(c_0_13882_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13882]) ).

cnf(c_0_13883_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13883]) ).

cnf(c_0_13883_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13883]) ).

cnf(c_0_13884_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13884]) ).

cnf(c_0_13884_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13884]) ).

cnf(c_0_13885_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13885]) ).

cnf(c_0_13885_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13885]) ).

cnf(c_0_13886_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13886]) ).

cnf(c_0_13886_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13886]) ).

cnf(c_0_13887_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13887]) ).

cnf(c_0_13887_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13887]) ).

cnf(c_0_13888_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13888]) ).

cnf(c_0_13888_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13888]) ).

cnf(c_0_13889_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13889]) ).

cnf(c_0_13889_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13889]) ).

cnf(c_0_13890_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13890]) ).

cnf(c_0_13890_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13890]) ).

cnf(c_0_13891_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13891]) ).

cnf(c_0_13891_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13891]) ).

cnf(c_0_13892_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13892]) ).

cnf(c_0_13892_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13892]) ).

cnf(c_0_13893_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13893]) ).

cnf(c_0_13893_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13893]) ).

cnf(c_0_13894_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13894]) ).

cnf(c_0_13894_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13894]) ).

cnf(c_0_13895_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13895]) ).

cnf(c_0_13895_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13895]) ).

cnf(c_0_13896_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13896]) ).

cnf(c_0_13896_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13896]) ).

cnf(c_0_13897_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13897]) ).

cnf(c_0_13897_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13897]) ).

cnf(c_0_13898_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13898]) ).

cnf(c_0_13898_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13898]) ).

cnf(c_0_13899_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13899]) ).

cnf(c_0_13899_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13899]) ).

cnf(c_0_13900_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13900]) ).

cnf(c_0_13900_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13900]) ).

cnf(c_0_13901_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13901]) ).

cnf(c_0_13901_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13901]) ).

cnf(c_0_13902_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13902]) ).

cnf(c_0_13902_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13902]) ).

cnf(c_0_13903_0,axiom,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13903]) ).

cnf(c_0_13903_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13903]) ).

cnf(c_0_13904_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13904]) ).

cnf(c_0_13904_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13904]) ).

cnf(c_0_13905_0,axiom,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13905]) ).

cnf(c_0_13905_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13905]) ).

cnf(c_0_13906_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13906]) ).

cnf(c_0_13906_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13906]) ).

cnf(c_0_13907_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13907]) ).

cnf(c_0_13907_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13907]) ).

cnf(c_0_13908_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13908]) ).

cnf(c_0_13908_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13908]) ).

cnf(c_0_13909_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13909]) ).

cnf(c_0_13909_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13909]) ).

cnf(c_0_13910_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13910]) ).

cnf(c_0_13910_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13910]) ).

cnf(c_0_13911_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13911]) ).

cnf(c_0_13911_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13911]) ).

cnf(c_0_13912_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13912]) ).

cnf(c_0_13912_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13912]) ).

cnf(c_0_13913_0,axiom,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13913]) ).

cnf(c_0_13913_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13913]) ).

cnf(c_0_13914_0,axiom,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13914]) ).

cnf(c_0_13914_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13914]) ).

cnf(c_0_13915_0,axiom,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13915]) ).

cnf(c_0_13915_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13915]) ).

cnf(c_0_13916_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13916]) ).

cnf(c_0_13916_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13916]) ).

cnf(c_0_13917_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13917]) ).

cnf(c_0_13917_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13917]) ).

cnf(c_0_13918_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13918]) ).

cnf(c_0_13918_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13918]) ).

cnf(c_0_13919_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13919]) ).

cnf(c_0_13919_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13919]) ).

cnf(c_0_13920_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13920]) ).

cnf(c_0_13920_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13920]) ).

cnf(c_0_13921_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13921]) ).

cnf(c_0_13921_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13921]) ).

cnf(c_0_13922_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13922]) ).

cnf(c_0_13922_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13922]) ).

cnf(c_0_13923_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13923]) ).

cnf(c_0_13923_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13923]) ).

cnf(c_0_13924_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13924]) ).

cnf(c_0_13924_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13924]) ).

cnf(c_0_13925_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13925]) ).

cnf(c_0_13925_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13925]) ).

cnf(c_0_13926_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13926]) ).

cnf(c_0_13926_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13926]) ).

cnf(c_0_13927_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13927]) ).

cnf(c_0_13927_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13927]) ).

cnf(c_0_13928_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13928]) ).

cnf(c_0_13928_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13928]) ).

cnf(c_0_13929_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13929]) ).

cnf(c_0_13929_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13929]) ).

cnf(c_0_13930_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13930]) ).

cnf(c_0_13930_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13930]) ).

cnf(c_0_13931_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13931]) ).

cnf(c_0_13931_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13931]) ).

cnf(c_0_13932_0,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13932]) ).

cnf(c_0_13932_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13932]) ).

cnf(c_0_13933_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13933]) ).

cnf(c_0_13933_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13933]) ).

cnf(c_0_13934_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13934]) ).

cnf(c_0_13934_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13934]) ).

cnf(c_0_13935_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13935]) ).

cnf(c_0_13935_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13935]) ).

cnf(c_0_13936_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13936]) ).

cnf(c_0_13936_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13936]) ).

cnf(c_0_13937_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13937]) ).

cnf(c_0_13937_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13937]) ).

cnf(c_0_13938_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13938]) ).

cnf(c_0_13938_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13938]) ).

cnf(c_0_13939_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13939]) ).

cnf(c_0_13939_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13939]) ).

cnf(c_0_13940_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13940]) ).

cnf(c_0_13940_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13940]) ).

cnf(c_0_13941_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13941]) ).

cnf(c_0_13941_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13941]) ).

cnf(c_0_13942_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13942]) ).

cnf(c_0_13942_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13942]) ).

cnf(c_0_13943_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13943]) ).

cnf(c_0_13943_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13943]) ).

cnf(c_0_13944_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13944]) ).

cnf(c_0_13944_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13944]) ).

cnf(c_0_13945_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13945]) ).

cnf(c_0_13945_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13945]) ).

cnf(c_0_13946_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13946]) ).

cnf(c_0_13946_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13946]) ).

cnf(c_0_13947_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13947]) ).

cnf(c_0_13947_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13947]) ).

cnf(c_0_13948_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13948]) ).

cnf(c_0_13948_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13948]) ).

cnf(c_0_13949_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13949]) ).

cnf(c_0_13949_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13949]) ).

cnf(c_0_13950_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13950]) ).

cnf(c_0_13950_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13950]) ).

cnf(c_0_13951_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13951]) ).

cnf(c_0_13951_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13951]) ).

cnf(c_0_13952_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13952]) ).

cnf(c_0_13952_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13952]) ).

cnf(c_0_13953_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13953]) ).

cnf(c_0_13953_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13953]) ).

cnf(c_0_13954_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13954]) ).

cnf(c_0_13954_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13954]) ).

cnf(c_0_13955_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13955]) ).

cnf(c_0_13955_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13955]) ).

cnf(c_0_13956_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13956]) ).

cnf(c_0_13956_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13956]) ).

cnf(c_0_13957_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13957]) ).

cnf(c_0_13957_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13957]) ).

cnf(c_0_13958_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13958]) ).

cnf(c_0_13958_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13958]) ).

cnf(c_0_13959_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13959]) ).

cnf(c_0_13959_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13959]) ).

cnf(c_0_13960_0,axiom,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13960]) ).

cnf(c_0_13960_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13960]) ).

cnf(c_0_13961_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13961]) ).

cnf(c_0_13961_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13961]) ).

cnf(c_0_13962_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13962]) ).

cnf(c_0_13962_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13962]) ).

cnf(c_0_13963_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13963]) ).

cnf(c_0_13963_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13963]) ).

cnf(c_0_13964_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13964]) ).

cnf(c_0_13964_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13964]) ).

cnf(c_0_13965_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13965]) ).

cnf(c_0_13965_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13965]) ).

cnf(c_0_13966_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13966]) ).

cnf(c_0_13966_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13966]) ).

cnf(c_0_13967_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13967]) ).

cnf(c_0_13967_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13967]) ).

cnf(c_0_13968_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13968]) ).

cnf(c_0_13968_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13968]) ).

cnf(c_0_13969_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13969]) ).

cnf(c_0_13969_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13969]) ).

cnf(c_0_13970_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13970]) ).

cnf(c_0_13970_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13970]) ).

cnf(c_0_13971_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13971]) ).

cnf(c_0_13971_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13971]) ).

cnf(c_0_13972_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13972]) ).

cnf(c_0_13972_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13972]) ).

cnf(c_0_13973_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13973]) ).

cnf(c_0_13973_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13973]) ).

cnf(c_0_13974_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13974]) ).

cnf(c_0_13974_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13974]) ).

cnf(c_0_13975_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13975]) ).

cnf(c_0_13975_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13975]) ).

cnf(c_0_13976_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13976]) ).

cnf(c_0_13976_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13976]) ).

cnf(c_0_13977_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13977]) ).

cnf(c_0_13977_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13977]) ).

cnf(c_0_13978_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13978]) ).

cnf(c_0_13978_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13978]) ).

cnf(c_0_13979_0,axiom,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13979]) ).

cnf(c_0_13979_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13979]) ).

cnf(c_0_13980_0,axiom,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13980]) ).

cnf(c_0_13980_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13980]) ).

cnf(c_0_13981_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13981]) ).

cnf(c_0_13981_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13981]) ).

cnf(c_0_13982_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13982]) ).

cnf(c_0_13982_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13982]) ).

cnf(c_0_13983_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13983]) ).

cnf(c_0_13983_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13983]) ).

cnf(c_0_13984_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13984]) ).

cnf(c_0_13984_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13984]) ).

cnf(c_0_13985_0,axiom,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13985]) ).

cnf(c_0_13985_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13985]) ).

cnf(c_0_13986_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13986]) ).

cnf(c_0_13986_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13986]) ).

cnf(c_0_13987_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13987]) ).

cnf(c_0_13987_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13987]) ).

cnf(c_0_13988_0,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13988]) ).

cnf(c_0_13988_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13988]) ).

cnf(c_0_13989_0,axiom,
    ( class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13989]) ).

cnf(c_0_13989_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13989]) ).

cnf(c_0_13990_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13990]) ).

cnf(c_0_13990_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13990]) ).

cnf(c_0_13991_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13991]) ).

cnf(c_0_13991_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13991]) ).

cnf(c_0_13992_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13992]) ).

cnf(c_0_13992_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13992]) ).

cnf(c_0_13993_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13993]) ).

cnf(c_0_13993_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13993]) ).

cnf(c_0_13994_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13994]) ).

cnf(c_0_13994_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13994]) ).

cnf(c_0_13995_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13995]) ).

cnf(c_0_13995_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13995]) ).

cnf(c_0_13996_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13996]) ).

cnf(c_0_13996_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13996]) ).

cnf(c_0_13997_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13997]) ).

cnf(c_0_13997_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13997]) ).

cnf(c_0_13998_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13998]) ).

cnf(c_0_13998_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13998]) ).

cnf(c_0_13999_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13999]) ).

cnf(c_0_13999_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_13999]) ).

cnf(c_0_14000_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14000]) ).

cnf(c_0_14000_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14000]) ).

cnf(c_0_14001_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14001]) ).

cnf(c_0_14001_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14001]) ).

cnf(c_0_14002_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14002]) ).

cnf(c_0_14002_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14002]) ).

cnf(c_0_14003_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14003]) ).

cnf(c_0_14003_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14003]) ).

cnf(c_0_14004_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14004]) ).

cnf(c_0_14004_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14004]) ).

cnf(c_0_14005_0,axiom,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14005]) ).

cnf(c_0_14005_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14005]) ).

cnf(c_0_14006_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14006]) ).

cnf(c_0_14006_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14006]) ).

cnf(c_0_14007_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14007]) ).

cnf(c_0_14007_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14007]) ).

cnf(c_0_14008_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14008]) ).

cnf(c_0_14008_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14008]) ).

cnf(c_0_14009_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14009]) ).

cnf(c_0_14009_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14009]) ).

cnf(c_0_14010_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14010]) ).

cnf(c_0_14010_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14010]) ).

cnf(c_0_14011_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14011]) ).

cnf(c_0_14011_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14011]) ).

cnf(c_0_14012_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14012]) ).

cnf(c_0_14012_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14012]) ).

cnf(c_0_14013_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14013]) ).

cnf(c_0_14013_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14013]) ).

cnf(c_0_14014_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14014]) ).

cnf(c_0_14014_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14014]) ).

cnf(c_0_14015_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14015]) ).

cnf(c_0_14015_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14015]) ).

cnf(c_0_14016_0,axiom,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14016]) ).

cnf(c_0_14016_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Oinverse(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14016]) ).

cnf(c_0_14017_0,axiom,
    ( class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14017]) ).

cnf(c_0_14017_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14017]) ).

cnf(c_0_14018_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14018]) ).

cnf(c_0_14018_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14018]) ).

cnf(c_0_14019_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14019]) ).

cnf(c_0_14019_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14019]) ).

cnf(c_0_14020_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14020]) ).

cnf(c_0_14020_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14020]) ).

cnf(c_0_14021_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14021]) ).

cnf(c_0_14021_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14021]) ).

cnf(c_0_14022_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14022]) ).

cnf(c_0_14022_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14022]) ).

cnf(c_0_14023_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14023]) ).

cnf(c_0_14023_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14023]) ).

cnf(c_0_14024_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14024]) ).

cnf(c_0_14024_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14024]) ).

cnf(c_0_14025_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14025]) ).

cnf(c_0_14025_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14025]) ).

cnf(c_0_14026_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14026]) ).

cnf(c_0_14026_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14026]) ).

cnf(c_0_14027_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14027]) ).

cnf(c_0_14027_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14027]) ).

cnf(c_0_14028_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14028]) ).

cnf(c_0_14028_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14028]) ).

cnf(c_0_14029_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14029]) ).

cnf(c_0_14029_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14029]) ).

cnf(c_0_14030_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14030]) ).

cnf(c_0_14030_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14030]) ).

cnf(c_0_14031_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14031]) ).

cnf(c_0_14031_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14031]) ).

cnf(c_0_14032_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14032]) ).

cnf(c_0_14032_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14032]) ).

cnf(c_0_14033_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14033]) ).

cnf(c_0_14033_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14033]) ).

cnf(c_0_14034_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14034]) ).

cnf(c_0_14034_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14034]) ).

cnf(c_0_14035_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14035]) ).

cnf(c_0_14035_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14035]) ).

cnf(c_0_14036_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14036]) ).

cnf(c_0_14036_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14036]) ).

cnf(c_0_14037_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14037]) ).

cnf(c_0_14037_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14037]) ).

cnf(c_0_14038_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14038]) ).

cnf(c_0_14038_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14038]) ).

cnf(c_0_14039_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14039]) ).

cnf(c_0_14039_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14039]) ).

cnf(c_0_14040_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14040]) ).

cnf(c_0_14040_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14040]) ).

cnf(c_0_14041_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14041]) ).

cnf(c_0_14041_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14041]) ).

cnf(c_0_14042_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14042]) ).

cnf(c_0_14042_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14042]) ).

cnf(c_0_14043_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14043]) ).

cnf(c_0_14043_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14043]) ).

cnf(c_0_14044_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14044]) ).

cnf(c_0_14044_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14044]) ).

cnf(c_0_14045_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14045]) ).

cnf(c_0_14045_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14045]) ).

cnf(c_0_14046_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14046]) ).

cnf(c_0_14046_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14046]) ).

cnf(c_0_14047_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14047]) ).

cnf(c_0_14047_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14047]) ).

cnf(c_0_14048_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14048]) ).

cnf(c_0_14048_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14048]) ).

cnf(c_0_14049_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14049]) ).

cnf(c_0_14049_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14049]) ).

cnf(c_0_14050_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14050]) ).

cnf(c_0_14050_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14050]) ).

cnf(c_0_14051_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14051]) ).

cnf(c_0_14051_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14051]) ).

cnf(c_0_14052_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14052]) ).

cnf(c_0_14052_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14052]) ).

cnf(c_0_14053_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14053]) ).

cnf(c_0_14053_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14053]) ).

cnf(c_0_14054_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14054]) ).

cnf(c_0_14054_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14054]) ).

cnf(c_0_14055_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14055]) ).

cnf(c_0_14055_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14055]) ).

cnf(c_0_14056_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14056]) ).

cnf(c_0_14056_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14056]) ).

cnf(c_0_14057_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14057]) ).

cnf(c_0_14057_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14057]) ).

cnf(c_0_14058_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14058]) ).

cnf(c_0_14058_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14058]) ).

cnf(c_0_14059_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14059]) ).

cnf(c_0_14059_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14059]) ).

cnf(c_0_14060_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14060]) ).

cnf(c_0_14060_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14060]) ).

cnf(c_0_14061_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14061]) ).

cnf(c_0_14061_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14061]) ).

cnf(c_0_14062_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14062]) ).

cnf(c_0_14062_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14062]) ).

cnf(c_0_14063_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14063]) ).

cnf(c_0_14063_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14063]) ).

cnf(c_0_14064_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14064]) ).

cnf(c_0_14064_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14064]) ).

cnf(c_0_14065_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14065]) ).

cnf(c_0_14065_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14065]) ).

cnf(c_0_14066_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14066]) ).

cnf(c_0_14066_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14066]) ).

cnf(c_0_14067_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14067]) ).

cnf(c_0_14067_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14067]) ).

cnf(c_0_14068_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14068]) ).

cnf(c_0_14068_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14068]) ).

cnf(c_0_14069_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14069]) ).

cnf(c_0_14069_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14069]) ).

cnf(c_0_14070_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14070]) ).

cnf(c_0_14070_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14070]) ).

cnf(c_0_14071_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14071]) ).

cnf(c_0_14071_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14071]) ).

cnf(c_0_14072_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14072]) ).

cnf(c_0_14072_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14072]) ).

cnf(c_0_14073_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14073]) ).

cnf(c_0_14073_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14073]) ).

cnf(c_0_14074_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14074]) ).

cnf(c_0_14074_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14074]) ).

cnf(c_0_14075_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14075]) ).

cnf(c_0_14075_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14075]) ).

cnf(c_0_14076_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14076]) ).

cnf(c_0_14076_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14076]) ).

cnf(c_0_14077_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14077]) ).

cnf(c_0_14077_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14077]) ).

cnf(c_0_14078_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14078]) ).

cnf(c_0_14078_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14078]) ).

cnf(c_0_14079_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14079]) ).

cnf(c_0_14079_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14079]) ).

cnf(c_0_14080_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14080]) ).

cnf(c_0_14080_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14080]) ).

cnf(c_0_14081_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14081]) ).

cnf(c_0_14081_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14081]) ).

cnf(c_0_14082_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14082]) ).

cnf(c_0_14082_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14082]) ).

cnf(c_0_14083_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14083]) ).

cnf(c_0_14083_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14083]) ).

cnf(c_0_14084_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14084]) ).

cnf(c_0_14084_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14084]) ).

cnf(c_0_14085_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14085]) ).

cnf(c_0_14085_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14085]) ).

cnf(c_0_14086_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14086]) ).

cnf(c_0_14086_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14086]) ).

cnf(c_0_14087_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14087]) ).

cnf(c_0_14087_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14087]) ).

cnf(c_0_14088_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14088]) ).

cnf(c_0_14088_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14088]) ).

cnf(c_0_14089_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14089]) ).

cnf(c_0_14089_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14089]) ).

cnf(c_0_14090_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14090]) ).

cnf(c_0_14090_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14090]) ).

cnf(c_0_14091_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14091]) ).

cnf(c_0_14091_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14091]) ).

cnf(c_0_14092_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14092]) ).

cnf(c_0_14092_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14092]) ).

cnf(c_0_14093_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14093]) ).

cnf(c_0_14093_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14093]) ).

cnf(c_0_14094_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14094]) ).

cnf(c_0_14094_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14094]) ).

cnf(c_0_14095_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14095]) ).

cnf(c_0_14095_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14095]) ).

cnf(c_0_14096_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14096]) ).

cnf(c_0_14096_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14096]) ).

cnf(c_0_14097_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14097]) ).

cnf(c_0_14097_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14097]) ).

cnf(c_0_14098_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14098]) ).

cnf(c_0_14098_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14098]) ).

cnf(c_0_14099_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14099]) ).

cnf(c_0_14099_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14099]) ).

cnf(c_0_14100_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14100]) ).

cnf(c_0_14100_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14100]) ).

cnf(c_0_14101_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14101]) ).

cnf(c_0_14101_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14101]) ).

cnf(c_0_14102_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14102]) ).

cnf(c_0_14102_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14102]) ).

cnf(c_0_14103_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14103]) ).

cnf(c_0_14103_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14103]) ).

cnf(c_0_14104_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14104]) ).

cnf(c_0_14104_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14104]) ).

cnf(c_0_14105_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14105]) ).

cnf(c_0_14105_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14105]) ).

cnf(c_0_14106_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14106]) ).

cnf(c_0_14106_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14106]) ).

cnf(c_0_14107_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14107]) ).

cnf(c_0_14107_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14107]) ).

cnf(c_0_14108_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14108]) ).

cnf(c_0_14108_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14108]) ).

cnf(c_0_14109_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14109]) ).

cnf(c_0_14109_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14109]) ).

cnf(c_0_14110_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14110]) ).

cnf(c_0_14110_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14110]) ).

cnf(c_0_14111_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14111]) ).

cnf(c_0_14111_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14111]) ).

cnf(c_0_14112_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14112]) ).

cnf(c_0_14112_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14112]) ).

cnf(c_0_14113_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14113]) ).

cnf(c_0_14113_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14113]) ).

cnf(c_0_14114_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14114]) ).

cnf(c_0_14114_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14114]) ).

cnf(c_0_14115_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14115]) ).

cnf(c_0_14115_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14115]) ).

cnf(c_0_14116_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14116]) ).

cnf(c_0_14116_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14116]) ).

cnf(c_0_14117_0,axiom,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14117]) ).

cnf(c_0_14117_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14117]) ).

cnf(c_0_14118_0,axiom,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14118]) ).

cnf(c_0_14118_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Oinverse(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14118]) ).

cnf(c_0_14119_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14119]) ).

cnf(c_0_14119_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14119]) ).

cnf(c_0_14120_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14120]) ).

cnf(c_0_14120_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14120]) ).

cnf(c_0_14121_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14121]) ).

cnf(c_0_14121_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14121]) ).

cnf(c_0_14122_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14122]) ).

cnf(c_0_14122_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14122]) ).

cnf(c_0_14123_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14123]) ).

cnf(c_0_14123_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14123]) ).

cnf(c_0_14124_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14124]) ).

cnf(c_0_14124_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14124]) ).

cnf(c_0_14125_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14125]) ).

cnf(c_0_14125_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14125]) ).

cnf(c_0_14126_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14126]) ).

cnf(c_0_14126_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14126]) ).

cnf(c_0_14127_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14127]) ).

cnf(c_0_14127_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14127]) ).

cnf(c_0_14128_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14128]) ).

cnf(c_0_14128_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14128]) ).

cnf(c_0_14129_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14129]) ).

cnf(c_0_14129_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14129]) ).

cnf(c_0_14130_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14130]) ).

cnf(c_0_14130_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14130]) ).

cnf(c_0_14131_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14131]) ).

cnf(c_0_14131_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14131]) ).

cnf(c_0_14132_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14132]) ).

cnf(c_0_14132_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14132]) ).

cnf(c_0_14133_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14133]) ).

cnf(c_0_14133_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14133]) ).

cnf(c_0_14134_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14134]) ).

cnf(c_0_14134_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14134]) ).

cnf(c_0_14135_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14135]) ).

cnf(c_0_14135_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14135]) ).

cnf(c_0_14136_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14136]) ).

cnf(c_0_14136_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14136]) ).

cnf(c_0_14137_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14137]) ).

cnf(c_0_14137_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14137]) ).

cnf(c_0_14138_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14138]) ).

cnf(c_0_14138_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14138]) ).

cnf(c_0_14139_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14139]) ).

cnf(c_0_14139_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14139]) ).

cnf(c_0_14140_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14140]) ).

cnf(c_0_14140_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14140]) ).

cnf(c_0_14141_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14141]) ).

cnf(c_0_14141_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14141]) ).

cnf(c_0_14142_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14142]) ).

cnf(c_0_14142_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14142]) ).

cnf(c_0_14143_0,axiom,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14143]) ).

cnf(c_0_14143_1,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | class_HOL_Oinverse(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14143]) ).

cnf(c_0_14144_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14144]) ).

cnf(c_0_14144_1,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14144]) ).

cnf(c_0_14145_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14145]) ).

cnf(c_0_14145_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14145]) ).

cnf(c_0_14146_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14146]) ).

cnf(c_0_14146_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14146]) ).

cnf(c_0_14147_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14147]) ).

cnf(c_0_14147_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14147]) ).

cnf(c_0_14148_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14148]) ).

cnf(c_0_14148_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14148]) ).

cnf(c_0_14149_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14149]) ).

cnf(c_0_14149_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14149]) ).

cnf(c_0_14150_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14150]) ).

cnf(c_0_14150_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14150]) ).

cnf(c_0_14151_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14151]) ).

cnf(c_0_14151_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14151]) ).

cnf(c_0_14152_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14152]) ).

cnf(c_0_14152_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14152]) ).

cnf(c_0_14153_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14153]) ).

cnf(c_0_14153_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14153]) ).

cnf(c_0_14154_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14154]) ).

cnf(c_0_14154_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14154]) ).

cnf(c_0_14155_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14155]) ).

cnf(c_0_14155_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14155]) ).

cnf(c_0_14156_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14156]) ).

cnf(c_0_14156_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14156]) ).

cnf(c_0_14157_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14157]) ).

cnf(c_0_14157_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14157]) ).

cnf(c_0_14158_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14158]) ).

cnf(c_0_14158_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14158]) ).

cnf(c_0_14159_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14159]) ).

cnf(c_0_14159_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14159]) ).

cnf(c_0_14160_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14160]) ).

cnf(c_0_14160_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14160]) ).

cnf(c_0_14161_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14161]) ).

cnf(c_0_14161_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14161]) ).

cnf(c_0_14162_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14162]) ).

cnf(c_0_14162_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14162]) ).

cnf(c_0_14163_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14163]) ).

cnf(c_0_14163_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14163]) ).

cnf(c_0_14164_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14164]) ).

cnf(c_0_14164_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14164]) ).

cnf(c_0_14165_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14165]) ).

cnf(c_0_14165_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14165]) ).

cnf(c_0_14166_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14166]) ).

cnf(c_0_14166_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14166]) ).

cnf(c_0_14167_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14167]) ).

cnf(c_0_14167_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14167]) ).

cnf(c_0_14168_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14168]) ).

cnf(c_0_14168_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14168]) ).

cnf(c_0_14169_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14169]) ).

cnf(c_0_14169_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14169]) ).

cnf(c_0_14170_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14170]) ).

cnf(c_0_14170_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14170]) ).

cnf(c_0_14171_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14171]) ).

cnf(c_0_14171_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14171]) ).

cnf(c_0_14172_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14172]) ).

cnf(c_0_14172_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14172]) ).

cnf(c_0_14173_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14173]) ).

cnf(c_0_14173_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14173]) ).

cnf(c_0_14174_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14174]) ).

cnf(c_0_14174_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14174]) ).

cnf(c_0_14175_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14175]) ).

cnf(c_0_14175_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14175]) ).

cnf(c_0_14176_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14176]) ).

cnf(c_0_14176_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14176]) ).

cnf(c_0_14177_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14177]) ).

cnf(c_0_14177_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14177]) ).

cnf(c_0_14178_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14178]) ).

cnf(c_0_14178_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14178]) ).

cnf(c_0_14179_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14179]) ).

cnf(c_0_14179_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14179]) ).

cnf(c_0_14180_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14180]) ).

cnf(c_0_14180_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14180]) ).

cnf(c_0_14181_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14181]) ).

cnf(c_0_14181_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14181]) ).

cnf(c_0_14182_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14182]) ).

cnf(c_0_14182_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14182]) ).

cnf(c_0_14183_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14183]) ).

cnf(c_0_14183_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14183]) ).

cnf(c_0_14184_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14184]) ).

cnf(c_0_14184_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14184]) ).

cnf(c_0_14185_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14185]) ).

cnf(c_0_14185_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14185]) ).

cnf(c_0_14186_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14186]) ).

cnf(c_0_14186_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14186]) ).

cnf(c_0_14187_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14187]) ).

cnf(c_0_14187_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14187]) ).

cnf(c_0_14188_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14188]) ).

cnf(c_0_14188_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14188]) ).

cnf(c_0_14189_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14189]) ).

cnf(c_0_14189_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14189]) ).

cnf(c_0_14190_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14190]) ).

cnf(c_0_14190_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14190]) ).

cnf(c_0_14191_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14191]) ).

cnf(c_0_14191_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14191]) ).

cnf(c_0_14192_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14192]) ).

cnf(c_0_14192_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14192]) ).

cnf(c_0_14193_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14193]) ).

cnf(c_0_14193_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14193]) ).

cnf(c_0_14194_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14194]) ).

cnf(c_0_14194_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14194]) ).

cnf(c_0_14195_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14195]) ).

cnf(c_0_14195_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14195]) ).

cnf(c_0_14196_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14196]) ).

cnf(c_0_14196_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14196]) ).

cnf(c_0_14197_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14197]) ).

cnf(c_0_14197_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14197]) ).

cnf(c_0_14198_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14198]) ).

cnf(c_0_14198_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14198]) ).

cnf(c_0_14199_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14199]) ).

cnf(c_0_14199_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14199]) ).

cnf(c_0_14200_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14200]) ).

cnf(c_0_14200_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14200]) ).

cnf(c_0_14201_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14201]) ).

cnf(c_0_14201_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14201]) ).

cnf(c_0_14202_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14202]) ).

cnf(c_0_14202_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14202]) ).

cnf(c_0_14203_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14203]) ).

cnf(c_0_14203_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14203]) ).

cnf(c_0_14204_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14204]) ).

cnf(c_0_14204_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14204]) ).

cnf(c_0_14205_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14205]) ).

cnf(c_0_14205_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14205]) ).

cnf(c_0_14206_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14206]) ).

cnf(c_0_14206_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14206]) ).

cnf(c_0_14207_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14207]) ).

cnf(c_0_14207_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14207]) ).

cnf(c_0_14208_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14208]) ).

cnf(c_0_14208_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14208]) ).

cnf(c_0_14209_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14209]) ).

cnf(c_0_14209_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14209]) ).

cnf(c_0_14210_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14210]) ).

cnf(c_0_14210_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14210]) ).

cnf(c_0_14211_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14211]) ).

cnf(c_0_14211_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14211]) ).

cnf(c_0_14212_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14212]) ).

cnf(c_0_14212_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14212]) ).

cnf(c_0_14213_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14213]) ).

cnf(c_0_14213_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14213]) ).

cnf(c_0_14214_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14214]) ).

cnf(c_0_14214_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14214]) ).

cnf(c_0_14215_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14215]) ).

cnf(c_0_14215_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14215]) ).

cnf(c_0_14216_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14216]) ).

cnf(c_0_14216_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14216]) ).

cnf(c_0_14217_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14217]) ).

cnf(c_0_14217_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14217]) ).

cnf(c_0_14218_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14218]) ).

cnf(c_0_14218_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14218]) ).

cnf(c_0_14219_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14219]) ).

cnf(c_0_14219_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14219]) ).

cnf(c_0_14220_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14220]) ).

cnf(c_0_14220_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14220]) ).

cnf(c_0_14221_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14221]) ).

cnf(c_0_14221_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14221]) ).

cnf(c_0_14222_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14222]) ).

cnf(c_0_14222_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14222]) ).

cnf(c_0_14223_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14223]) ).

cnf(c_0_14223_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14223]) ).

cnf(c_0_14224_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14224]) ).

cnf(c_0_14224_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14224]) ).

cnf(c_0_14225_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14225]) ).

cnf(c_0_14225_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14225]) ).

cnf(c_0_14226_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14226]) ).

cnf(c_0_14226_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14226]) ).

cnf(c_0_14227_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14227]) ).

cnf(c_0_14227_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14227]) ).

cnf(c_0_14228_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14228]) ).

cnf(c_0_14228_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14228]) ).

cnf(c_0_14229_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14229]) ).

cnf(c_0_14229_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14229]) ).

cnf(c_0_14230_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14230]) ).

cnf(c_0_14230_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14230]) ).

cnf(c_0_14231_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14231]) ).

cnf(c_0_14231_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14231]) ).

cnf(c_0_14232_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14232]) ).

cnf(c_0_14232_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14232]) ).

cnf(c_0_14233_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14233]) ).

cnf(c_0_14233_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14233]) ).

cnf(c_0_14234_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14234]) ).

cnf(c_0_14234_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14234]) ).

cnf(c_0_14235_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14235]) ).

cnf(c_0_14235_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14235]) ).

cnf(c_0_14236_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14236]) ).

cnf(c_0_14236_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14236]) ).

cnf(c_0_14237_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14237]) ).

cnf(c_0_14237_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14237]) ).

cnf(c_0_14238_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14238]) ).

cnf(c_0_14238_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14238]) ).

cnf(c_0_14239_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14239]) ).

cnf(c_0_14239_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14239]) ).

cnf(c_0_14240_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14240]) ).

cnf(c_0_14240_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14240]) ).

cnf(c_0_14241_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14241]) ).

cnf(c_0_14241_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14241]) ).

cnf(c_0_14242_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14242]) ).

cnf(c_0_14242_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14242]) ).

cnf(c_0_14243_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14243]) ).

cnf(c_0_14243_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14243]) ).

cnf(c_0_14244_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14244]) ).

cnf(c_0_14244_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14244]) ).

cnf(c_0_14245_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14245]) ).

cnf(c_0_14245_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14245]) ).

cnf(c_0_14246_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14246]) ).

cnf(c_0_14246_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14246]) ).

cnf(c_0_14247_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14247]) ).

cnf(c_0_14247_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14247]) ).

cnf(c_0_14248_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14248]) ).

cnf(c_0_14248_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14248]) ).

cnf(c_0_14249_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14249]) ).

cnf(c_0_14249_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14249]) ).

cnf(c_0_14250_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14250]) ).

cnf(c_0_14250_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14250]) ).

cnf(c_0_14251_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14251]) ).

cnf(c_0_14251_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14251]) ).

cnf(c_0_14252_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14252]) ).

cnf(c_0_14252_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14252]) ).

cnf(c_0_14253_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14253]) ).

cnf(c_0_14253_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14253]) ).

cnf(c_0_14254_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14254]) ).

cnf(c_0_14254_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14254]) ).

cnf(c_0_14255_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14255]) ).

cnf(c_0_14255_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14255]) ).

cnf(c_0_14256_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14256]) ).

cnf(c_0_14256_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14256]) ).

cnf(c_0_14257_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14257]) ).

cnf(c_0_14257_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14257]) ).

cnf(c_0_14258_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14258]) ).

cnf(c_0_14258_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14258]) ).

cnf(c_0_14259_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14259]) ).

cnf(c_0_14259_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14259]) ).

cnf(c_0_14260_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14260]) ).

cnf(c_0_14260_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14260]) ).

cnf(c_0_14261_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14261]) ).

cnf(c_0_14261_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14261]) ).

cnf(c_0_14262_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14262]) ).

cnf(c_0_14262_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14262]) ).

cnf(c_0_14263_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14263]) ).

cnf(c_0_14263_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14263]) ).

cnf(c_0_14264_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14264]) ).

cnf(c_0_14264_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14264]) ).

cnf(c_0_14265_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14265]) ).

cnf(c_0_14265_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14265]) ).

cnf(c_0_14266_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14266]) ).

cnf(c_0_14266_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14266]) ).

cnf(c_0_14267_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14267]) ).

cnf(c_0_14267_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14267]) ).

cnf(c_0_14268_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14268]) ).

cnf(c_0_14268_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__abs__if(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14268]) ).

cnf(c_0_14269_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14269]) ).

cnf(c_0_14269_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__abs__if(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14269]) ).

cnf(c_0_14270_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14270]) ).

cnf(c_0_14270_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__abs__if(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14270]) ).

cnf(c_0_14271_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14271]) ).

cnf(c_0_14271_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14271]) ).

cnf(c_0_14272_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14272]) ).

cnf(c_0_14272_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14272]) ).

cnf(c_0_14273_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14273]) ).

cnf(c_0_14273_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14273]) ).

cnf(c_0_14274_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14274]) ).

cnf(c_0_14274_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14274]) ).

cnf(c_0_14275_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14275]) ).

cnf(c_0_14275_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14275]) ).

cnf(c_0_14276_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14276]) ).

cnf(c_0_14276_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14276]) ).

cnf(c_0_14277_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14277]) ).

cnf(c_0_14277_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14277]) ).

cnf(c_0_14278_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14278]) ).

cnf(c_0_14278_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14278]) ).

cnf(c_0_14279_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14279]) ).

cnf(c_0_14279_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14279]) ).

cnf(c_0_14280_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14280]) ).

cnf(c_0_14280_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14280]) ).

cnf(c_0_14281_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14281]) ).

cnf(c_0_14281_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14281]) ).

cnf(c_0_14282_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14282]) ).

cnf(c_0_14282_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14282]) ).

cnf(c_0_14283_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14283]) ).

cnf(c_0_14283_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14283]) ).

cnf(c_0_14284_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14284]) ).

cnf(c_0_14284_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14284]) ).

cnf(c_0_14285_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14285]) ).

cnf(c_0_14285_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14285]) ).

cnf(c_0_14286_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14286]) ).

cnf(c_0_14286_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14286]) ).

cnf(c_0_14287_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14287]) ).

cnf(c_0_14287_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14287]) ).

cnf(c_0_14288_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14288]) ).

cnf(c_0_14288_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14288]) ).

cnf(c_0_14289_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14289]) ).

cnf(c_0_14289_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14289]) ).

cnf(c_0_14290_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14290]) ).

cnf(c_0_14290_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14290]) ).

cnf(c_0_14291_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14291]) ).

cnf(c_0_14291_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14291]) ).

cnf(c_0_14292_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14292]) ).

cnf(c_0_14292_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14292]) ).

cnf(c_0_14293_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14293]) ).

cnf(c_0_14293_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14293]) ).

cnf(c_0_14294_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14294]) ).

cnf(c_0_14294_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14294]) ).

cnf(c_0_14295_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14295]) ).

cnf(c_0_14295_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14295]) ).

cnf(c_0_14296_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14296]) ).

cnf(c_0_14296_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14296]) ).

cnf(c_0_14297_0,axiom,
    ( class_Nat_Opower(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14297]) ).

cnf(c_0_14297_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Nat_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14297]) ).

cnf(c_0_14298_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14298]) ).

cnf(c_0_14298_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14298]) ).

cnf(c_0_14299_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14299]) ).

cnf(c_0_14299_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14299]) ).

cnf(c_0_14300_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14300]) ).

cnf(c_0_14300_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14300]) ).

cnf(c_0_14301_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14301]) ).

cnf(c_0_14301_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14301]) ).

cnf(c_0_14302_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14302]) ).

cnf(c_0_14302_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14302]) ).

cnf(c_0_14303_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14303]) ).

cnf(c_0_14303_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14303]) ).

cnf(c_0_14304_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14304]) ).

cnf(c_0_14304_1,axiom,
    ( ~ class_OrderedGroup_Osemigroup__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14304]) ).

cnf(c_0_14305_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14305]) ).

cnf(c_0_14305_1,axiom,
    ( ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14305]) ).

cnf(c_0_14306_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14306]) ).

cnf(c_0_14306_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14306]) ).

cnf(c_0_14307_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14307]) ).

cnf(c_0_14307_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14307]) ).

cnf(c_0_14308_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14308]) ).

cnf(c_0_14308_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14308]) ).

cnf(c_0_14309_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14309]) ).

cnf(c_0_14309_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14309]) ).

cnf(c_0_14310_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14310]) ).

cnf(c_0_14310_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14310]) ).

cnf(c_0_14311_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14311]) ).

cnf(c_0_14311_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14311]) ).

cnf(c_0_14312_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14312]) ).

cnf(c_0_14312_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14312]) ).

cnf(c_0_14313_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14313]) ).

cnf(c_0_14313_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14313]) ).

cnf(c_0_14314_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14314]) ).

cnf(c_0_14314_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14314]) ).

cnf(c_0_14315_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14315]) ).

cnf(c_0_14315_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14315]) ).

cnf(c_0_14316_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14316]) ).

cnf(c_0_14316_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14316]) ).

cnf(c_0_14317_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14317]) ).

cnf(c_0_14317_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14317]) ).

cnf(c_0_14318_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14318]) ).

cnf(c_0_14318_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14318]) ).

cnf(c_0_14319_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14319]) ).

cnf(c_0_14319_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14319]) ).

cnf(c_0_14320_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14320]) ).

cnf(c_0_14320_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14320]) ).

cnf(c_0_14321_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14321]) ).

cnf(c_0_14321_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14321]) ).

cnf(c_0_14322_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14322]) ).

cnf(c_0_14322_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14322]) ).

cnf(c_0_14323_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14323]) ).

cnf(c_0_14323_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14323]) ).

cnf(c_0_14324_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14324]) ).

cnf(c_0_14324_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14324]) ).

cnf(c_0_14325_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14325]) ).

cnf(c_0_14325_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14325]) ).

cnf(c_0_14326_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14326]) ).

cnf(c_0_14326_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14326]) ).

cnf(c_0_14327_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14327]) ).

cnf(c_0_14327_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14327]) ).

cnf(c_0_14328_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14328]) ).

cnf(c_0_14328_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14328]) ).

cnf(c_0_14329_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14329]) ).

cnf(c_0_14329_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14329]) ).

cnf(c_0_14330_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14330]) ).

cnf(c_0_14330_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14330]) ).

cnf(c_0_14331_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14331]) ).

cnf(c_0_14331_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14331]) ).

cnf(c_0_14332_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14332]) ).

cnf(c_0_14332_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14332]) ).

cnf(c_0_14333_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14333]) ).

cnf(c_0_14333_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14333]) ).

cnf(c_0_14334_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14334]) ).

cnf(c_0_14334_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14334]) ).

cnf(c_0_14335_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14335]) ).

cnf(c_0_14335_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14335]) ).

cnf(c_0_14336_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14336]) ).

cnf(c_0_14336_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14336]) ).

cnf(c_0_14337_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14337]) ).

cnf(c_0_14337_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14337]) ).

cnf(c_0_14338_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14338]) ).

cnf(c_0_14338_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14338]) ).

cnf(c_0_14339_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14339]) ).

cnf(c_0_14339_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14339]) ).

cnf(c_0_14340_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14340]) ).

cnf(c_0_14340_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14340]) ).

cnf(c_0_14341_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14341]) ).

cnf(c_0_14341_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14341]) ).

cnf(c_0_14342_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14342]) ).

cnf(c_0_14342_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14342]) ).

cnf(c_0_14343_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14343]) ).

cnf(c_0_14343_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14343]) ).

cnf(c_0_14344_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14344]) ).

cnf(c_0_14344_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14344]) ).

cnf(c_0_14345_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14345]) ).

cnf(c_0_14345_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14345]) ).

cnf(c_0_14346_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14346]) ).

cnf(c_0_14346_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14346]) ).

cnf(c_0_14347_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14347]) ).

cnf(c_0_14347_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14347]) ).

cnf(c_0_14348_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14348]) ).

cnf(c_0_14348_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14348]) ).

cnf(c_0_14349_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14349]) ).

cnf(c_0_14349_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14349]) ).

cnf(c_0_14350_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14350]) ).

cnf(c_0_14350_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14350]) ).

cnf(c_0_14351_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14351]) ).

cnf(c_0_14351_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14351]) ).

cnf(c_0_14352_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14352]) ).

cnf(c_0_14352_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14352]) ).

cnf(c_0_14353_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14353]) ).

cnf(c_0_14353_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14353]) ).

cnf(c_0_14354_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14354]) ).

cnf(c_0_14354_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14354]) ).

cnf(c_0_14355_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14355]) ).

cnf(c_0_14355_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14355]) ).

cnf(c_0_14356_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14356]) ).

cnf(c_0_14356_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14356]) ).

cnf(c_0_14357_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14357]) ).

cnf(c_0_14357_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14357]) ).

cnf(c_0_14358_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14358]) ).

cnf(c_0_14358_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14358]) ).

cnf(c_0_14359_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14359]) ).

cnf(c_0_14359_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14359]) ).

cnf(c_0_14360_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14360]) ).

cnf(c_0_14360_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14360]) ).

cnf(c_0_14361_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14361]) ).

cnf(c_0_14361_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14361]) ).

cnf(c_0_14362_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14362]) ).

cnf(c_0_14362_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14362]) ).

cnf(c_0_14363_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14363]) ).

cnf(c_0_14363_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14363]) ).

cnf(c_0_14364_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14364]) ).

cnf(c_0_14364_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14364]) ).

cnf(c_0_14365_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14365]) ).

cnf(c_0_14365_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14365]) ).

cnf(c_0_14366_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14366]) ).

cnf(c_0_14366_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14366]) ).

cnf(c_0_14367_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14367]) ).

cnf(c_0_14367_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14367]) ).

cnf(c_0_14368_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14368]) ).

cnf(c_0_14368_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14368]) ).

cnf(c_0_14369_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14369]) ).

cnf(c_0_14369_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14369]) ).

cnf(c_0_14370_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14370]) ).

cnf(c_0_14370_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14370]) ).

cnf(c_0_14371_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14371]) ).

cnf(c_0_14371_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14371]) ).

cnf(c_0_14372_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14372]) ).

cnf(c_0_14372_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14372]) ).

cnf(c_0_14373_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14373]) ).

cnf(c_0_14373_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14373]) ).

cnf(c_0_14374_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14374]) ).

cnf(c_0_14374_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14374]) ).

cnf(c_0_14375_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14375]) ).

cnf(c_0_14375_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14375]) ).

cnf(c_0_14376_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14376]) ).

cnf(c_0_14376_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14376]) ).

cnf(c_0_14377_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14377]) ).

cnf(c_0_14377_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14377]) ).

cnf(c_0_14378_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14378]) ).

cnf(c_0_14378_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14378]) ).

cnf(c_0_14379_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14379]) ).

cnf(c_0_14379_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14379]) ).

cnf(c_0_14380_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14380]) ).

cnf(c_0_14380_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14380]) ).

cnf(c_0_14381_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14381]) ).

cnf(c_0_14381_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14381]) ).

cnf(c_0_14382_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14382]) ).

cnf(c_0_14382_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14382]) ).

cnf(c_0_14383_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14383]) ).

cnf(c_0_14383_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14383]) ).

cnf(c_0_14384_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14384]) ).

cnf(c_0_14384_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14384]) ).

cnf(c_0_14385_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14385]) ).

cnf(c_0_14385_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14385]) ).

cnf(c_0_14386_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14386]) ).

cnf(c_0_14386_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14386]) ).

cnf(c_0_14387_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14387]) ).

cnf(c_0_14387_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14387]) ).

cnf(c_0_14388_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14388]) ).

cnf(c_0_14388_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14388]) ).

cnf(c_0_14389_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14389]) ).

cnf(c_0_14389_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14389]) ).

cnf(c_0_14390_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14390]) ).

cnf(c_0_14390_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14390]) ).

cnf(c_0_14391_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14391]) ).

cnf(c_0_14391_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14391]) ).

cnf(c_0_14392_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14392]) ).

cnf(c_0_14392_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14392]) ).

cnf(c_0_14393_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14393]) ).

cnf(c_0_14393_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14393]) ).

cnf(c_0_14394_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14394]) ).

cnf(c_0_14394_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14394]) ).

cnf(c_0_14395_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14395]) ).

cnf(c_0_14395_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14395]) ).

cnf(c_0_14396_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14396]) ).

cnf(c_0_14396_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14396]) ).

cnf(c_0_14397_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14397]) ).

cnf(c_0_14397_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14397]) ).

cnf(c_0_14398_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14398]) ).

cnf(c_0_14398_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14398]) ).

cnf(c_0_14399_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14399]) ).

cnf(c_0_14399_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14399]) ).

cnf(c_0_14400_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14400]) ).

cnf(c_0_14400_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14400]) ).

cnf(c_0_14401_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14401]) ).

cnf(c_0_14401_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14401]) ).

cnf(c_0_14402_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14402]) ).

cnf(c_0_14402_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14402]) ).

cnf(c_0_14403_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14403]) ).

cnf(c_0_14403_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14403]) ).

cnf(c_0_14404_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14404]) ).

cnf(c_0_14404_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14404]) ).

cnf(c_0_14405_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14405]) ).

cnf(c_0_14405_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14405]) ).

cnf(c_0_14406_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14406]) ).

cnf(c_0_14406_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14406]) ).

cnf(c_0_14407_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14407]) ).

cnf(c_0_14407_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14407]) ).

cnf(c_0_14408_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14408]) ).

cnf(c_0_14408_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14408]) ).

cnf(c_0_14409_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14409]) ).

cnf(c_0_14409_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14409]) ).

cnf(c_0_14410_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14410]) ).

cnf(c_0_14410_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14410]) ).

cnf(c_0_14411_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14411]) ).

cnf(c_0_14411_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14411]) ).

cnf(c_0_14412_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14412]) ).

cnf(c_0_14412_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14412]) ).

cnf(c_0_14413_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14413]) ).

cnf(c_0_14413_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14413]) ).

cnf(c_0_14414_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14414]) ).

cnf(c_0_14414_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14414]) ).

cnf(c_0_14415_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14415]) ).

cnf(c_0_14415_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14415]) ).

cnf(c_0_14416_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14416]) ).

cnf(c_0_14416_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14416]) ).

cnf(c_0_14417_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14417]) ).

cnf(c_0_14417_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14417]) ).

cnf(c_0_14418_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14418]) ).

cnf(c_0_14418_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14418]) ).

cnf(c_0_14419_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14419]) ).

cnf(c_0_14419_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14419]) ).

cnf(c_0_14420_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14420]) ).

cnf(c_0_14420_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14420]) ).

cnf(c_0_14421_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14421]) ).

cnf(c_0_14421_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14421]) ).

cnf(c_0_14422_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14422]) ).

cnf(c_0_14422_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14422]) ).

cnf(c_0_14423_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14423]) ).

cnf(c_0_14423_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14423]) ).

cnf(c_0_14424_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14424]) ).

cnf(c_0_14424_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14424]) ).

cnf(c_0_14425_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14425]) ).

cnf(c_0_14425_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14425]) ).

cnf(c_0_14426_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14426]) ).

cnf(c_0_14426_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14426]) ).

cnf(c_0_14427_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14427]) ).

cnf(c_0_14427_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14427]) ).

cnf(c_0_14428_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14428]) ).

cnf(c_0_14428_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14428]) ).

cnf(c_0_14429_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14429]) ).

cnf(c_0_14429_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14429]) ).

cnf(c_0_14430_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14430]) ).

cnf(c_0_14430_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14430]) ).

cnf(c_0_14431_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14431]) ).

cnf(c_0_14431_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14431]) ).

cnf(c_0_14432_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14432]) ).

cnf(c_0_14432_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14432]) ).

cnf(c_0_14433_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14433]) ).

cnf(c_0_14433_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14433]) ).

cnf(c_0_14434_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14434]) ).

cnf(c_0_14434_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14434]) ).

cnf(c_0_14435_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14435]) ).

cnf(c_0_14435_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14435]) ).

cnf(c_0_14436_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14436]) ).

cnf(c_0_14436_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14436]) ).

cnf(c_0_14437_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14437]) ).

cnf(c_0_14437_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14437]) ).

cnf(c_0_14438_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14438]) ).

cnf(c_0_14438_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14438]) ).

cnf(c_0_14439_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14439]) ).

cnf(c_0_14439_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14439]) ).

cnf(c_0_14440_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14440]) ).

cnf(c_0_14440_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14440]) ).

cnf(c_0_14441_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14441]) ).

cnf(c_0_14441_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14441]) ).

cnf(c_0_14442_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14442]) ).

cnf(c_0_14442_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14442]) ).

cnf(c_0_14443_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14443]) ).

cnf(c_0_14443_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14443]) ).

cnf(c_0_14444_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14444]) ).

cnf(c_0_14444_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14444]) ).

cnf(c_0_14445_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14445]) ).

cnf(c_0_14445_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14445]) ).

cnf(c_0_14446_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14446]) ).

cnf(c_0_14446_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14446]) ).

cnf(c_0_14447_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14447]) ).

cnf(c_0_14447_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14447]) ).

cnf(c_0_14448_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14448]) ).

cnf(c_0_14448_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14448]) ).

cnf(c_0_14449_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14449]) ).

cnf(c_0_14449_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14449]) ).

cnf(c_0_14450_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14450]) ).

cnf(c_0_14450_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14450]) ).

cnf(c_0_14451_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14451]) ).

cnf(c_0_14451_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14451]) ).

cnf(c_0_14452_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14452]) ).

cnf(c_0_14452_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14452]) ).

cnf(c_0_14453_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14453]) ).

cnf(c_0_14453_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14453]) ).

cnf(c_0_14454_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14454]) ).

cnf(c_0_14454_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14454]) ).

cnf(c_0_14455_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14455]) ).

cnf(c_0_14455_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14455]) ).

cnf(c_0_14456_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14456]) ).

cnf(c_0_14456_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14456]) ).

cnf(c_0_14457_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14457]) ).

cnf(c_0_14457_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14457]) ).

cnf(c_0_14458_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14458]) ).

cnf(c_0_14458_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14458]) ).

cnf(c_0_14459_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14459]) ).

cnf(c_0_14459_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14459]) ).

cnf(c_0_14460_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14460]) ).

cnf(c_0_14460_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14460]) ).

cnf(c_0_14461_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14461]) ).

cnf(c_0_14461_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14461]) ).

cnf(c_0_14462_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14462]) ).

cnf(c_0_14462_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14462]) ).

cnf(c_0_14463_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14463]) ).

cnf(c_0_14463_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14463]) ).

cnf(c_0_14464_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14464]) ).

cnf(c_0_14464_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14464]) ).

cnf(c_0_14465_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14465]) ).

cnf(c_0_14465_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14465]) ).

cnf(c_0_14466_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14466]) ).

cnf(c_0_14466_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14466]) ).

cnf(c_0_14467_0,axiom,
    ( class_Numeral_Onumber(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14467]) ).

cnf(c_0_14467_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Numeral_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14467]) ).

cnf(c_0_14468_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14468]) ).

cnf(c_0_14468_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14468]) ).

cnf(c_0_14469_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14469]) ).

cnf(c_0_14469_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14469]) ).

cnf(c_0_14470_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14470]) ).

cnf(c_0_14470_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14470]) ).

cnf(c_0_14471_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14471]) ).

cnf(c_0_14471_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14471]) ).

cnf(c_0_14472_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14472]) ).

cnf(c_0_14472_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14472]) ).

cnf(c_0_14473_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14473]) ).

cnf(c_0_14473_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14473]) ).

cnf(c_0_14474_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14474]) ).

cnf(c_0_14474_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14474]) ).

cnf(c_0_14475_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14475]) ).

cnf(c_0_14475_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14475]) ).

cnf(c_0_14476_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14476]) ).

cnf(c_0_14476_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14476]) ).

cnf(c_0_14477_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14477]) ).

cnf(c_0_14477_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14477]) ).

cnf(c_0_14478_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14478]) ).

cnf(c_0_14478_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14478]) ).

cnf(c_0_14479_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14479]) ).

cnf(c_0_14479_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14479]) ).

cnf(c_0_14480_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14480]) ).

cnf(c_0_14480_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14480]) ).

cnf(c_0_14481_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14481]) ).

cnf(c_0_14481_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14481]) ).

cnf(c_0_14482_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14482]) ).

cnf(c_0_14482_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14482]) ).

cnf(c_0_14483_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14483]) ).

cnf(c_0_14483_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14483]) ).

cnf(c_0_14484_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14484]) ).

cnf(c_0_14484_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14484]) ).

cnf(c_0_14485_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14485]) ).

cnf(c_0_14485_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14485]) ).

cnf(c_0_14486_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14486]) ).

cnf(c_0_14486_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14486]) ).

cnf(c_0_14487_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14487]) ).

cnf(c_0_14487_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14487]) ).

cnf(c_0_14488_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14488]) ).

cnf(c_0_14488_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14488]) ).

cnf(c_0_14489_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14489]) ).

cnf(c_0_14489_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14489]) ).

cnf(c_0_14490_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14490]) ).

cnf(c_0_14490_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14490]) ).

cnf(c_0_14491_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14491]) ).

cnf(c_0_14491_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14491]) ).

cnf(c_0_14492_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14492]) ).

cnf(c_0_14492_1,axiom,
    ( ~ class_LOrder_Omeet__semilorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14492]) ).

cnf(c_0_14493_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14493]) ).

cnf(c_0_14493_1,axiom,
    ( ~ class_LOrder_Omeet__semilorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14493]) ).

cnf(c_0_14494_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14494]) ).

cnf(c_0_14494_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14494]) ).

cnf(c_0_14495_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14495]) ).

cnf(c_0_14495_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14495]) ).

cnf(c_0_14496_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14496]) ).

cnf(c_0_14496_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14496]) ).

cnf(c_0_14497_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14497]) ).

cnf(c_0_14497_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14497]) ).

cnf(c_0_14498_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14498]) ).

cnf(c_0_14498_1,axiom,
    ( ~ class_LOrder_Ojoin__semilorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14498]) ).

cnf(c_0_14499_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14499]) ).

cnf(c_0_14499_1,axiom,
    ( ~ class_LOrder_Ojoin__semilorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14499]) ).

cnf(c_0_14540_0,axiom,
    ( X1 = c_0
    | c_IntDef_Oint(X1) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_14540]) ).

cnf(c_0_14540_1,axiom,
    ( c_IntDef_Oint(X1) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_14540]) ).

cnf(c_0_14541_0,axiom,
    ( c_1 != c_0
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14541]) ).

cnf(c_0_14541_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | c_1 != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_14541]) ).

cnf(c_0_14542_0,axiom,
    ( c_1 != c_0
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_14542]) ).

cnf(c_0_14542_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | c_1 != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_14542]) ).

cnf(c_0_11895_0,axiom,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olexord(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(literals_permutation,[status(thm)],[c_0_11895]) ).

cnf(c_0_11896_0,axiom,
    ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(literals_permutation,[status(thm)],[c_0_11896]) ).

cnf(c_0_11897_0,axiom,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(literals_permutation,[status(thm)],[c_0_11897]) ).

cnf(c_0_12059_0,axiom,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_ONumb(X5,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12059]) ).

cnf(c_0_12060_0,axiom,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OLeaf(X5,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12060]) ).

cnf(c_0_12061_0,axiom,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OAtom(X5,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12061]) ).

cnf(c_0_12062_0,axiom,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12062]) ).

cnf(c_0_12063_0,axiom,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12063]) ).

cnf(c_0_12064_0,axiom,
    c_Datatype__Universe_OAtom(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12064]) ).

cnf(c_0_12477_0,axiom,
    ~ c_less(c_plus(X1,X2,tc_nat),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12477]) ).

cnf(c_0_12478_0,axiom,
    ~ c_less(c_plus(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12478]) ).

cnf(c_0_12693_0,axiom,
    ~ c_List_Onull(c_List_Olist_OCons(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12693]) ).

cnf(c_0_12756_0,axiom,
    ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12756]) ).

cnf(c_0_12789_0,axiom,
    ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X1,X2)),c_Message_OsymKeys,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12789]) ).

cnf(c_0_12799_0,axiom,
    c_Sum__Type_OInr(X1,X2,X3) != c_Sum__Type_OInl(X4,X3,X2),
    inference(literals_permutation,[status(thm)],[c_0_12799]) ).

cnf(c_0_12800_0,axiom,
    c_Sum__Type_OInl(X1,X2,X3) != c_Sum__Type_OInr(X4,X3,X2),
    inference(literals_permutation,[status(thm)],[c_0_12800]) ).

cnf(c_0_12801_0,axiom,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12801]) ).

cnf(c_0_12802_0,axiom,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12802]) ).

cnf(c_0_12803_0,axiom,
    c_Datatype__Universe_OIn1(X1,X2,X3) != c_Datatype__Universe_OIn0(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12803]) ).

cnf(c_0_12804_0,axiom,
    c_Datatype__Universe_OIn0(X1,X2,X3) != c_Datatype__Universe_OIn1(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12804]) ).

cnf(c_0_12924_0,axiom,
    ~ c_less(c_IntDef_Oint(X1),c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12924]) ).

cnf(c_0_12973_0,axiom,
    ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12973]) ).

cnf(c_0_12997_0,axiom,
    ~ c_in(c_Message_Omsg_OCrypt(X1,X2),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12997]) ).

cnf(c_0_13014_0,axiom,
    ~ c_in(c_Public_OpublicKey(X1,X2),c_Message_OsymKeys,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13014]) ).

cnf(c_0_13015_0,axiom,
    ~ c_in(c_Message_Omsg_ONonce(X1),c_Message_Oparts(c_Event_OinitState(X2)),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13015]) ).

cnf(c_0_13056_0,axiom,
    c_Event_Oevent_ONotes(X1,X2) != c_Event_Oevent_OSays(X3,X4,X5),
    inference(literals_permutation,[status(thm)],[c_0_13056]) ).

cnf(c_0_13057_0,axiom,
    c_Event_Oevent_OSays(X1,X2,X3) != c_Event_Oevent_ONotes(X4,X5),
    inference(literals_permutation,[status(thm)],[c_0_13057]) ).

cnf(c_0_13058_0,axiom,
    c_Event_Oevent_OGets(X1,X2) != c_Event_Oevent_OSays(X3,X4,X5),
    inference(literals_permutation,[status(thm)],[c_0_13058]) ).

cnf(c_0_13059_0,axiom,
    c_Event_Oevent_OSays(X1,X2,X3) != c_Event_Oevent_OGets(X4,X5),
    inference(literals_permutation,[status(thm)],[c_0_13059]) ).

cnf(c_0_13091_0,axiom,
    ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13091]) ).

cnf(c_0_13110_0,axiom,
    ~ c_less(X1,c_emptyset,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13110]) ).

cnf(c_0_13121_0,axiom,
    ~ c_less(c_IntDef_Oint(X1),c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13121]) ).

cnf(c_0_13135_0,axiom,
    ~ c_in(X1,c_Message_Oparts(c_emptyset),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13135]) ).

cnf(c_0_13152_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(literals_permutation,[status(thm)],[c_0_13152]) ).

cnf(c_0_13153_0,axiom,
    c_List_Olist_OCons(X2,X1,X3) != X1,
    inference(literals_permutation,[status(thm)],[c_0_13153]) ).

cnf(c_0_13161_0,axiom,
    c_insert(X1,X2,X3) != c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13161]) ).

cnf(c_0_13162_0,axiom,
    c_insert(X1,X2,X3) != c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13162]) ).

cnf(c_0_13163_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13163]) ).

cnf(c_0_13164_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13164]) ).

cnf(c_0_13165_0,axiom,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_13165]) ).

cnf(c_0_13175_0,axiom,
    ~ c_in(X1,c_emptyset,X2),
    inference(literals_permutation,[status(thm)],[c_0_13175]) ).

cnf(c_0_13176_0,axiom,
    ~ c_List_Oop_Amem(X1,c_List_Olist_ONil,X2),
    inference(literals_permutation,[status(thm)],[c_0_13176]) ).

cnf(c_0_13177_0,axiom,
    ~ c_less(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13177]) ).

cnf(c_0_13192_0,axiom,
    ~ c_less(X1,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13192]) ).

cnf(c_0_13197_0,axiom,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    inference(literals_permutation,[status(thm)],[c_0_13197]) ).

cnf(c_0_13198_0,axiom,
    ~ c_less(c_0,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13198]) ).

cnf(c_0_13221_0,axiom,
    c_Public_OpublicKey(X1,X2) != c_Message_OinvKey(c_Public_OpublicKey(X3,X4)),
    inference(literals_permutation,[status(thm)],[c_0_13221]) ).

cnf(c_0_13222_0,axiom,
    c_Message_OinvKey(c_Public_OpublicKey(X1,X2)) != c_Public_OpublicKey(X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_13222]) ).

cnf(c_0_13326_0,axiom,
    c_Message_OinvKey(c_Public_OpublicKey(X1,X2)) != c_Public_OshrK(X3),
    inference(literals_permutation,[status(thm)],[c_0_13326]) ).

cnf(c_0_13327_0,axiom,
    c_Public_OshrK(X1) != c_Message_OinvKey(c_Public_OpublicKey(X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_13327]) ).

cnf(c_0_13406_0,axiom,
    c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,X1)) != c_Public_OshrK(X2),
    inference(literals_permutation,[status(thm)],[c_0_13406]) ).

cnf(c_0_13434_0,axiom,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OCrypt(X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_13434]) ).

cnf(c_0_13435_0,axiom,
    c_Message_Omsg_OCrypt(X1,X2) != c_Message_OHPair(X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_13435]) ).

cnf(c_0_13436_0,axiom,
    c_Event_Oevent_ONotes(X1,X2) != c_Event_Oevent_OGets(X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_13436]) ).

cnf(c_0_13437_0,axiom,
    c_Event_Oevent_OGets(X1,X2) != c_Event_Oevent_ONotes(X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_13437]) ).

cnf(c_0_13479_0,axiom,
    ~ c_IntDef_Oneg(c_IntDef_Oint(X1),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13479]) ).

cnf(c_0_13480_0,axiom,
    c_Public_OpublicKey(X1,X2) != c_Public_OshrK(X3),
    inference(literals_permutation,[status(thm)],[c_0_13480]) ).

cnf(c_0_13481_0,axiom,
    c_Public_OshrK(X1) != c_Public_OpublicKey(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_13481]) ).

cnf(c_0_13482_0,axiom,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_ONumber(X3),
    inference(literals_permutation,[status(thm)],[c_0_13482]) ).

cnf(c_0_13483_0,axiom,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_ONonce(X3),
    inference(literals_permutation,[status(thm)],[c_0_13483]) ).

cnf(c_0_13484_0,axiom,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OKey(X3),
    inference(literals_permutation,[status(thm)],[c_0_13484]) ).

cnf(c_0_13485_0,axiom,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OHash(X3),
    inference(literals_permutation,[status(thm)],[c_0_13485]) ).

cnf(c_0_13486_0,axiom,
    c_Message_OHPair(X1,X2) != c_Message_Omsg_OAgent(X3),
    inference(literals_permutation,[status(thm)],[c_0_13486]) ).

cnf(c_0_13487_0,axiom,
    c_Message_Omsg_OHash(X1) != c_Message_OHPair(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_13487]) ).

cnf(c_0_13488_0,axiom,
    c_Message_Omsg_OKey(X1) != c_Message_OHPair(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_13488]) ).

cnf(c_0_13489_0,axiom,
    c_Message_Omsg_ONumber(X1) != c_Message_OHPair(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_13489]) ).

cnf(c_0_13490_0,axiom,
    c_Message_Omsg_ONonce(X1) != c_Message_OHPair(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_13490]) ).

cnf(c_0_13491_0,axiom,
    c_Message_Omsg_OAgent(X1) != c_Message_OHPair(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_13491]) ).

cnf(c_0_13508_0,axiom,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    inference(literals_permutation,[status(thm)],[c_0_13508]) ).

cnf(c_0_13509_0,axiom,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    inference(literals_permutation,[status(thm)],[c_0_13509]) ).

cnf(c_0_13536_0,axiom,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13536]) ).

cnf(c_0_14543_0,axiom,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OSpy,
    inference(literals_permutation,[status(thm)],[c_0_14543]) ).

cnf(c_0_14544_0,axiom,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OSpy,
    inference(literals_permutation,[status(thm)],[c_0_14544]) ).

cnf(c_0_14545_0,axiom,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OServer,
    inference(literals_permutation,[status(thm)],[c_0_14545]) ).

cnf(c_0_14546_0,axiom,
    c_Message_Oagent_OFriend(X1) != c_Message_Oagent_OServer,
    inference(literals_permutation,[status(thm)],[c_0_14546]) ).

cnf(c_0_14547_0,axiom,
    c_Suc(X1) != c_0,
    inference(literals_permutation,[status(thm)],[c_0_14547]) ).

cnf(c_0_14548_0,axiom,
    c_Suc(X1) != c_0,
    inference(literals_permutation,[status(thm)],[c_0_14548]) ).

cnf(c_0_14675_0,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    inference(literals_permutation,[status(thm)],[c_0_14675]) ).

cnf(c_0_14676_0,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    inference(literals_permutation,[status(thm)],[c_0_14676]) ).

cnf(c_0_14677_0,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(literals_permutation,[status(thm)],[c_0_14677]) ).

cnf(c_0_14678_0,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(literals_permutation,[status(thm)],[c_0_14678]) ).

cnf(c_0_14679_0,axiom,
    c_UNIV != c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_14679]) ).

cnf(c_0_14680_0,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    inference(literals_permutation,[status(thm)],[c_0_14680]) ).

cnf(c_0_14681_0,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    inference(literals_permutation,[status(thm)],[c_0_14681]) ).

cnf(c_0_14682_0,axiom,
    c_1 != c_0,
    inference(literals_permutation,[status(thm)],[c_0_14682]) ).

cnf(c_0_14683_0,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    inference(literals_permutation,[status(thm)],[c_0_14683]) ).

cnf(c_0_14684_0,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    inference(literals_permutation,[status(thm)],[c_0_14684]) ).

cnf(c_0_11748_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble8,X17) = X9,
    inference(literals_permutation,[status(thm)],[c_0_11748]) ).

cnf(c_0_11749_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble7,X17) = X8,
    inference(literals_permutation,[status(thm)],[c_0_11749]) ).

cnf(c_0_11750_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble6,X17) = X7,
    inference(literals_permutation,[status(thm)],[c_0_11750]) ).

cnf(c_0_11751_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble5,X17) = X6,
    inference(literals_permutation,[status(thm)],[c_0_11751]) ).

cnf(c_0_11752_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble4,X17) = X5,
    inference(literals_permutation,[status(thm)],[c_0_11752]) ).

cnf(c_0_11753_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble3,X17) = X4,
    inference(literals_permutation,[status(thm)],[c_0_11753]) ).

cnf(c_0_11754_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble2,X17) = X3,
    inference(literals_permutation,[status(thm)],[c_0_11754]) ).

cnf(c_0_11755_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble1,X17) = X2,
    inference(literals_permutation,[status(thm)],[c_0_11755]) ).

cnf(c_0_11756_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble0,X17) = X1,
    inference(literals_permutation,[status(thm)],[c_0_11756]) ).

cnf(c_0_11757_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleF,X17) = X16,
    inference(literals_permutation,[status(thm)],[c_0_11757]) ).

cnf(c_0_11758_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleE,X17) = X15,
    inference(literals_permutation,[status(thm)],[c_0_11758]) ).

cnf(c_0_11759_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleD,X17) = X14,
    inference(literals_permutation,[status(thm)],[c_0_11759]) ).

cnf(c_0_11760_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleC,X17) = X13,
    inference(literals_permutation,[status(thm)],[c_0_11760]) ).

cnf(c_0_11761_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleB,X17) = X12,
    inference(literals_permutation,[status(thm)],[c_0_11761]) ).

cnf(c_0_11762_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleA,X17) = X11,
    inference(literals_permutation,[status(thm)],[c_0_11762]) ).

cnf(c_0_11763_0,axiom,
    c_List_Onibble_Onibble__rec(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble9,X17) = X10,
    inference(literals_permutation,[status(thm)],[c_0_11763]) ).

cnf(c_0_11764_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble8,X17) = X9,
    inference(literals_permutation,[status(thm)],[c_0_11764]) ).

cnf(c_0_11765_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble7,X17) = X8,
    inference(literals_permutation,[status(thm)],[c_0_11765]) ).

cnf(c_0_11766_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble6,X17) = X7,
    inference(literals_permutation,[status(thm)],[c_0_11766]) ).

cnf(c_0_11767_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble5,X17) = X6,
    inference(literals_permutation,[status(thm)],[c_0_11767]) ).

cnf(c_0_11768_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble4,X17) = X5,
    inference(literals_permutation,[status(thm)],[c_0_11768]) ).

cnf(c_0_11769_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble3,X17) = X4,
    inference(literals_permutation,[status(thm)],[c_0_11769]) ).

cnf(c_0_11770_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble2,X17) = X3,
    inference(literals_permutation,[status(thm)],[c_0_11770]) ).

cnf(c_0_11771_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble1,X17) = X2,
    inference(literals_permutation,[status(thm)],[c_0_11771]) ).

cnf(c_0_11772_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble0,X17) = X1,
    inference(literals_permutation,[status(thm)],[c_0_11772]) ).

cnf(c_0_11773_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleF,X17) = X16,
    inference(literals_permutation,[status(thm)],[c_0_11773]) ).

cnf(c_0_11774_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleE,X17) = X15,
    inference(literals_permutation,[status(thm)],[c_0_11774]) ).

cnf(c_0_11775_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleD,X17) = X14,
    inference(literals_permutation,[status(thm)],[c_0_11775]) ).

cnf(c_0_11776_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleC,X17) = X13,
    inference(literals_permutation,[status(thm)],[c_0_11776]) ).

cnf(c_0_11777_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleB,X17) = X12,
    inference(literals_permutation,[status(thm)],[c_0_11777]) ).

cnf(c_0_11778_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibbleA,X17) = X11,
    inference(literals_permutation,[status(thm)],[c_0_11778]) ).

cnf(c_0_11779_0,axiom,
    c_List_Onibble_Onibble__case(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,c_List_Onibble_ONibble9,X17) = X10,
    inference(literals_permutation,[status(thm)],[c_0_11779]) ).

cnf(c_0_11818_0,axiom,
    c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X1,X2,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(literals_permutation,[status(thm)],[c_0_11818]) ).

cnf(c_0_11839_0,axiom,
    c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X1,X2,X4,X5),c_Datatype__Universe_Ontrunc(X1,X3,X4,X5),X4,X5) = c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OScons(X2,X3,X4,X5),X4,X5),
    inference(literals_permutation,[status(thm)],[c_0_11839]) ).

cnf(c_0_11854_0,axiom,
    c_Datatype__Universe_Ousum(c_Relation_ODomain(X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Relation_ODomain(X2,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X3,X4) = c_Relation_ODomain(c_Datatype__Universe_Odsum(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),
    inference(literals_permutation,[status(thm)],[c_0_11854]) ).

cnf(c_0_11855_0,axiom,
    c_Datatype__Universe_Ouprod(c_Relation_ODomain(X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Relation_ODomain(X2,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X3,X4) = c_Relation_ODomain(c_Datatype__Universe_Odprod(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),
    inference(literals_permutation,[status(thm)],[c_0_11855]) ).

cnf(c_0_11862_0,axiom,
    c_Relation_Orel__comp(X1,c_Nat_Opower(X1,X2,tc_set(tc_prod(X3,X3))),X3,X3,X3) = c_Nat_Opower(X1,c_Suc(X2),tc_set(tc_prod(X3,X3))),
    inference(literals_permutation,[status(thm)],[c_0_11862]) ).

cnf(c_0_11866_0,axiom,
    c_List_Olist_OCons(c_Pair(X1,X4,X3,X6),c_List_Ozip(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X4,X5,X6),X3,X6),
    inference(literals_permutation,[status(thm)],[c_0_11866]) ).

cnf(c_0_11874_0,axiom,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_11874]) ).

cnf(c_0_11875_0,axiom,
    c_Relation_Orel__comp(X1,c_Relation_OId,X2,X3,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_11875]) ).

cnf(c_0_11876_0,axiom,
    c_Relation_Orel__comp(c_Relation_OId,X1,X2,X2,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_11876]) ).

cnf(c_0_11878_0,axiom,
    c_GCD_Ogcd(c_Pair(X1,c_plus(X2,X1,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_11878]) ).

cnf(c_0_11879_0,axiom,
    c_GCD_Ogcd(c_Pair(X1,c_plus(X1,X2,tc_nat),tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_11879]) ).

cnf(c_0_11880_0,axiom,
    c_GCD_Ogcd(c_Pair(c_plus(X1,X2,tc_nat),X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_11880]) ).

cnf(c_0_11881_0,axiom,
    c_List_Oreplicate(c_Orderings_Omin(X1,X4,tc_nat),c_Pair(X2,X5,X3,X6),tc_prod(X3,X6)) = c_List_Ozip(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X5,X6),X3,X6),
    inference(literals_permutation,[status(thm)],[c_0_11881]) ).

cnf(c_0_11887_0,axiom,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_11887]) ).

cnf(c_0_11888_0,axiom,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_11888]) ).

cnf(c_0_11905_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X1)),c_Datatype__Universe_OIn1(X2,X3,X4),X3,X4) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X1),X2,X3,X4),X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_11905]) ).

cnf(c_0_11906_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X1)),c_Datatype__Universe_OIn0(X2,X3,X4),X3,X4) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X1),X2,X3,X4),X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_11906]) ).

cnf(c_0_11910_0,axiom,
    c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_11910]) ).

cnf(c_0_11913_0,axiom,
    c_insert(c_Message_OHPair(X1,X2),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oparts(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_11913]) ).

cnf(c_0_11914_0,axiom,
    c_insert(c_Message_OHPair(X1,X2),c_insert(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),c_Message_Oanalz(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_11914]) ).

cnf(c_0_11916_0,axiom,
    c_insert(c_Message_Omsg_OMPair(X1,X2),c_Message_Oparts(c_insert(X1,c_insert(X2,X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_11916]) ).

cnf(c_0_11917_0,axiom,
    c_insert(c_Message_Omsg_OMPair(X1,X2),c_Message_Oanalz(c_insert(X1,c_insert(X2,X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_11917]) ).

cnf(c_0_11918_0,axiom,
    c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X4,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    inference(literals_permutation,[status(thm)],[c_0_11918]) ).

cnf(c_0_11920_0,axiom,
    c_append(c_List_Otake(X1,X2,X4),c_List_Otake(c_minus(X1,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4) = c_List_Otake(X1,c_append(X2,X3,X4),X4),
    inference(literals_permutation,[status(thm)],[c_0_11920]) ).

cnf(c_0_11921_0,axiom,
    c_append(c_List_Odrop(X1,X2,X4),c_List_Odrop(c_minus(X1,c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4) = c_List_Odrop(X1,c_append(X2,X3,X4),X4),
    inference(literals_permutation,[status(thm)],[c_0_11921]) ).

cnf(c_0_11943_0,axiom,
    c_List_Olist__update(c_append(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize(X1,tc_List_Olist(X4)),X5,X4) = c_append(X1,c_List_Olist_OCons(X5,X3,X4),X4),
    inference(literals_permutation,[status(thm)],[c_0_11943]) ).

cnf(c_0_11946_0,axiom,
    c_Pair(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) = c_IntDiv_OnegateSnd(c_Pair(X1,X2,tc_IntDef_Oint,tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_11946]) ).

cnf(c_0_11955_0,axiom,
    c_IntDiv_OposDivAlg(c_Pair(c_0,X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_11955]) ).

cnf(c_0_11956_0,axiom,
    c_GCD_Ogcd(c_Pair(X1,c_times(X1,X2,tc_nat),tc_nat,tc_nat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_11956]) ).

cnf(c_0_11965_0,axiom,
    c_Nat_Osize(c_List_Ozip(X1,X2,X3,X4),tc_List_Olist(tc_prod(X3,X4))) = c_Orderings_Omin(c_Nat_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize(X2,tc_List_Olist(X4)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_11965]) ).

cnf(c_0_11974_0,axiom,
    c_div(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_11974]) ).

cnf(c_0_11978_0,axiom,
    c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
    inference(literals_permutation,[status(thm)],[c_0_11978]) ).

cnf(c_0_11979_0,axiom,
    c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X1))),c_Numeral_Onumber__of(X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_11979]) ).

cnf(c_0_11980_0,axiom,
    c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X1,tc_nat),c_Numeral_Onumber__of(X2,tc_nat),tc_nat) = c_div(c_Suc(c_Suc(c_Suc(X1))),c_Numeral_Onumber__of(X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_11980]) ).

cnf(c_0_11981_0,axiom,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X1,X2,X3),X4,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X3,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X4),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_11981]) ).

cnf(c_0_11991_0,axiom,
    c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
    inference(literals_permutation,[status(thm)],[c_0_11991]) ).

cnf(c_0_12012_0,axiom,
    c_snd(c_Pair(X1,X2,X3,X4),X3,X4) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12012]) ).

cnf(c_0_12013_0,axiom,
    c_fst(c_Pair(X1,X2,X3,X4),X3,X4) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12013]) ).

cnf(c_0_12014_0,axiom,
    c_Divides_Oop_Amod(X1,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12014]) ).

cnf(c_0_12015_0,axiom,
    c_div(X1,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X1,c_Suc(c_Suc(c_Suc(X2))),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12015]) ).

cnf(c_0_12025_0,axiom,
    c_Nat_Osize(c_List_Olist__update(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize(X1,tc_List_Olist(X4)),
    inference(literals_permutation,[status(thm)],[c_0_12025]) ).

cnf(c_0_12026_0,axiom,
    c_Nat_Osize(c_Pair(X1,X2,X3,X4),tc_prod(X3,X4)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12026]) ).

cnf(c_0_12037_0,axiom,
    c_GCD_Ogcd(c_Pair(c_Suc(c_0),X1,tc_nat,tc_nat)) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_12037]) ).

cnf(c_0_12038_0,axiom,
    c_GCD_Ogcd(c_Pair(X1,c_Suc(c_0),tc_nat,tc_nat)) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_12038]) ).

cnf(c_0_12040_0,axiom,
    c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12040]) ).

cnf(c_0_12041_0,axiom,
    c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12041]) ).

cnf(c_0_12042_0,axiom,
    c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12042]) ).

cnf(c_0_12071_0,axiom,
    c_Pair(c_Main_Osurj__pair__1(X1,X2,X3),c_Main_Osurj__pair__2(X1,X2,X3),X2,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12071]) ).

cnf(c_0_12072_0,axiom,
    c_Pair(c_fst(X1,X2,X3),c_snd(X1,X2,X3),X2,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12072]) ).

cnf(c_0_12079_0,axiom,
    c_Relation_OImage(c_List_Olistrel(X1,X2),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X2)),tc_List_Olist(X2),tc_List_Olist(X2)) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X2)),
    inference(literals_permutation,[status(thm)],[c_0_12079]) ).

cnf(c_0_12083_0,axiom,
    c_insert(c_Message_Omsg_OCrypt(X1,X2),c_Message_Oparts(c_insert(X2,X3,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_12083]) ).

cnf(c_0_12102_0,axiom,
    c_insert(X1,c_minus(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)),X3) = c_insert(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12102]) ).

cnf(c_0_12103_0,axiom,
    c_List_Orev(c_append(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil,X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_12103]) ).

cnf(c_0_12104_0,axiom,
    c_inter(c_insert(X1,X2,X3),c_insert(X1,X4,X3),X3) = c_insert(X1,c_inter(X2,X4,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12104]) ).

cnf(c_0_12105_0,axiom,
    c_IntDef_Onat(c_plus(c_minus(X2,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12105]) ).

cnf(c_0_12108_0,axiom,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X1,X2),X3,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X2,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X3),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12108]) ).

cnf(c_0_12111_0,axiom,
    c_IntDef_Onat(c_minus(X2,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12111]) ).

cnf(c_0_12114_0,axiom,
    c_Divides_Oop_Amod(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12114]) ).

cnf(c_0_12115_0,axiom,
    c_Divides_Oop_Amod(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12115]) ).

cnf(c_0_12116_0,axiom,
    c_Divides_Oop_Amod(c_plus(X1,c_times(X2,X3,tc_nat),tc_nat),X3,tc_nat) = c_Divides_Oop_Amod(X1,X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12116]) ).

cnf(c_0_12118_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_ONumb(X2,X3,X4),X3,X4) = c_Datatype__Universe_ONumb(X2,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12118]) ).

cnf(c_0_12119_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OLeaf(X2,X3,X4),X3,X4) = c_Datatype__Universe_OLeaf(X2,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12119]) ).

cnf(c_0_12120_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(X1),c_Datatype__Universe_OAtom(X2,X3,X4),X3,X4) = c_Datatype__Universe_OAtom(X2,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12120]) ).

cnf(c_0_12122_0,axiom,
    c_List_Onth(c_append(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize(X1,tc_List_Olist(X4)),X4) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12122]) ).

cnf(c_0_12124_0,axiom,
    c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X1,X2,X3),X4,tc_Event_Oevent)) = c_insert(X3,c_Event_Oknows(c_Message_Oagent_OSpy,X4),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12124]) ).

cnf(c_0_12148_0,axiom,
    c_List_Onth(c_append(X1,X2,X3),c_plus(c_Nat_Osize(X1,tc_List_Olist(X3)),X4,tc_nat),X3) = c_List_Onth(X2,X4,X3),
    inference(literals_permutation,[status(thm)],[c_0_12148]) ).

cnf(c_0_12155_0,axiom,
    c_union(c_Message_Oanalz(c_union(X1,X2,tc_Message_Omsg)),c_Message_Osynth(X1),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(X1),X2,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_12155]) ).

cnf(c_0_12191_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X1,X2,X3),X2,X3) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_12191]) ).

cnf(c_0_12192_0,axiom,
    c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X1,X2,X3),X2,X3) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_12192]) ).

cnf(c_0_12255_0,axiom,
    c_minus(c_minus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_minus(c_minus(X1,X2,tc_nat),X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12255]) ).

cnf(c_0_12264_0,axiom,
    c_List_Olast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3),X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12264]) ).

cnf(c_0_12265_0,axiom,
    c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3),X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12265]) ).

cnf(c_0_12267_0,axiom,
    c_List_Otake(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X1,X3,X4),X4),
    inference(literals_permutation,[status(thm)],[c_0_12267]) ).

cnf(c_0_12269_0,axiom,
    c_Relation_OImage(c_Relation_Odiag(X1,X2),X3,X2,X2) = c_inter(X1,X3,X2),
    inference(literals_permutation,[status(thm)],[c_0_12269]) ).

cnf(c_0_12281_0,axiom,
    c_union(X1,c_insert(X2,X3,X4),X4) = c_insert(X2,c_union(X1,X3,X4),X4),
    inference(literals_permutation,[status(thm)],[c_0_12281]) ).

cnf(c_0_12282_0,axiom,
    c_union(c_insert(X1,X2,X3),X4,X3) = c_insert(X1,c_union(X2,X4,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12282]) ).

cnf(c_0_12283_0,axiom,
    c_append(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_append(X2,X4,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12283]) ).

cnf(c_0_12284_0,axiom,
    c_List_Oitrev(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Oitrev(X2,c_List_Olist_OCons(X1,X4,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12284]) ).

cnf(c_0_12285_0,axiom,
    c_append(c_append(X1,X2,X3),X4,X3) = c_append(X1,c_append(X2,X4,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12285]) ).

cnf(c_0_12291_0,axiom,
    c_List_Otake(X1,c_List_Otake(X2,X3,X4),X4) = c_List_Otake(c_Orderings_Omin(X1,X2,tc_nat),X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12291]) ).

cnf(c_0_12292_0,axiom,
    c_List_Otake(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_Orderings_Omin(X1,X2,tc_nat),X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12292]) ).

cnf(c_0_12293_0,axiom,
    c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_minus(X2,X1,tc_nat),X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12293]) ).

cnf(c_0_12294_0,axiom,
    c_List_Odrop(X1,c_List_Odrop(X2,X3,X4),X4) = c_List_Odrop(c_plus(X1,X2,tc_nat),X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12294]) ).

cnf(c_0_12333_0,axiom,
    c_minus(c_minus(X1,X2,tc_nat),X3,tc_nat) = c_minus(X1,c_plus(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12333]) ).

cnf(c_0_12351_0,axiom,
    c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12351]) ).

cnf(c_0_12353_0,axiom,
    c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil,X3),X3) = c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12353]) ).

cnf(c_0_12382_0,axiom,
    c_plus(c_plus(c_Nat_Osize(X1,tc_Message_Omsg),c_Nat_Osize(X2,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OMPair(X1,X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12382]) ).

cnf(c_0_12384_0,axiom,
    c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X2,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12384]) ).

cnf(c_0_12423_0,axiom,
    c_append(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12423]) ).

cnf(c_0_12437_0,axiom,
    c_inter(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3) = c_uminus(c_union(X1,X2,X3),tc_set(X3)),
    inference(literals_permutation,[status(thm)],[c_0_12437]) ).

cnf(c_0_12438_0,axiom,
    c_union(c_uminus(X1,tc_set(X3)),c_uminus(X2,tc_set(X3)),X3) = c_uminus(c_inter(X1,X2,X3),tc_set(X3)),
    inference(literals_permutation,[status(thm)],[c_0_12438]) ).

cnf(c_0_12440_0,axiom,
    c_plus(c_Nat_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize(X2,tc_List_Olist(X3)),tc_nat) = c_Nat_Osize(c_append(X1,X2,X3),tc_List_Olist(X3)),
    inference(literals_permutation,[status(thm)],[c_0_12440]) ).

cnf(c_0_12464_0,axiom,
    c_Public_Okeymode_Okeymode__rec(X1,X2,c_Public_Okeymode_OEncryption,X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12464]) ).

cnf(c_0_12465_0,axiom,
    c_Public_Okeymode_Okeymode__rec(X1,X2,c_Public_Okeymode_OSignature,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12465]) ).

cnf(c_0_12466_0,axiom,
    c_Public_Okeymode_Okeymode__case(X1,X2,c_Public_Okeymode_OEncryption,X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12466]) ).

cnf(c_0_12467_0,axiom,
    c_Public_Okeymode_Okeymode__case(X1,X2,c_Public_Okeymode_OSignature,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12467]) ).

cnf(c_0_12468_0,axiom,
    c_Relation_OImage(c_Relation_OId,X1,X2,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12468]) ).

cnf(c_0_12469_0,axiom,
    c_Numeral_Obit_Obit__rec(X1,X2,c_Numeral_Obit_OB1,X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12469]) ).

cnf(c_0_12470_0,axiom,
    c_Numeral_Obit_Obit__rec(X1,X2,c_Numeral_Obit_OB0,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12470]) ).

cnf(c_0_12471_0,axiom,
    c_Numeral_Obit_Obit__case(X1,X2,c_Numeral_Obit_OB1,X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12471]) ).

cnf(c_0_12472_0,axiom,
    c_Numeral_Obit_Obit__case(X1,X2,c_Numeral_Obit_OB0,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12472]) ).

cnf(c_0_12473_0,axiom,
    c_Extraction_Osumbool_Osumbool__rec(X1,X2,c_Extraction_Osumbool_ORight,X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12473]) ).

cnf(c_0_12474_0,axiom,
    c_Extraction_Osumbool_Osumbool__rec(X1,X2,c_Extraction_Osumbool_OLeft,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12474]) ).

cnf(c_0_12475_0,axiom,
    c_Extraction_Osumbool_Osumbool__case(X1,X2,c_Extraction_Osumbool_ORight,X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12475]) ).

cnf(c_0_12476_0,axiom,
    c_Extraction_Osumbool_Osumbool__case(X1,X2,c_Extraction_Osumbool_OLeft,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12476]) ).

cnf(c_0_12479_0,axiom,
    c_Relation_OImage(X1,c_emptyset,X2,X3) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_12479]) ).

cnf(c_0_12480_0,axiom,
    c_List_Ozip(c_List_Olist_ONil,X1,X2,X3) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_12480]) ).

cnf(c_0_12481_0,axiom,
    c_List_Ozip(X1,c_List_Olist_ONil,X2,X3) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_12481]) ).

cnf(c_0_12483_0,axiom,
    c_List_Olist__update(c_List_Olist_ONil,X1,X2,X3) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_12483]) ).

cnf(c_0_12484_0,axiom,
    c_Datatype__Universe_Ontrunc(c_0,X1,X2,X3) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_12484]) ).

cnf(c_0_12485_0,axiom,
    c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_12485]) ).

cnf(c_0_12495_0,axiom,
    c_minus(c_minus(X1,X2,tc_set(X3)),X2,tc_set(X3)) = c_minus(X1,X2,tc_set(X3)),
    inference(literals_permutation,[status(thm)],[c_0_12495]) ).

cnf(c_0_12496_0,axiom,
    c_union(c_Union(X1,X3),c_Union(X2,X3),X3) = c_Union(c_union(X1,X2,tc_set(X3)),X3),
    inference(literals_permutation,[status(thm)],[c_0_12496]) ).

cnf(c_0_12502_0,axiom,
    c_append(c_List_Oconcat(X1,X3),c_List_Oconcat(X2,X3),X3) = c_List_Oconcat(c_append(X1,X2,tc_List_Olist(X3)),X3),
    inference(literals_permutation,[status(thm)],[c_0_12502]) ).

cnf(c_0_12528_0,axiom,
    c_inter(c_Pow(X1,X3),c_Pow(X2,X3),tc_set(X3)) = c_Pow(c_inter(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12528]) ).

cnf(c_0_12529_0,axiom,
    c_inter(c_List_Olists(X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) = c_List_Olists(c_inter(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12529]) ).

cnf(c_0_12534_0,axiom,
    c_uminus(c_minus(X1,X2,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X1,tc_set(X3)),X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12534]) ).

cnf(c_0_12546_0,axiom,
    c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Suc(c_0),c_Numeral_Onumber__of(X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12546]) ).

cnf(c_0_12553_0,axiom,
    c_Message_Oanalz(c_union(c_Message_Oanalz(X1),X2,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X1,X2,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_12553]) ).

cnf(c_0_12554_0,axiom,
    c_union(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_union(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12554]) ).

cnf(c_0_12555_0,axiom,
    c_union(c_minus(X1,X2,tc_set(X3)),X2,X3) = c_union(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12555]) ).

cnf(c_0_12557_0,axiom,
    c_union(c_List_Oset(X1,X3),c_List_Oset(X2,X3),X3) = c_List_Oset(c_append(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12557]) ).

cnf(c_0_12558_0,axiom,
    c_append(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3) = c_List_Orev(c_append(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12558]) ).

cnf(c_0_12563_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X1,X2),X3,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X1),c_Message_OkeysFor(X3),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12563]) ).

cnf(c_0_12566_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,X1,tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_12566]) ).

cnf(c_0_12567_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X2,X1,tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_12567]) ).

cnf(c_0_12574_0,axiom,
    c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_Suc(X1),X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12574]) ).

cnf(c_0_12575_0,axiom,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X3) = c_List_Onth(X2,X4,X3),
    inference(literals_permutation,[status(thm)],[c_0_12575]) ).

cnf(c_0_12576_0,axiom,
    c_List_Odrop(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(X1,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_12576]) ).

cnf(c_0_12578_0,axiom,
    c_Nat_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X2,tc_List_Olist(X3)),c_Suc(c_0),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12578]) ).

cnf(c_0_12583_0,axiom,
    c_Nat_Osize(c_List_Otake(X1,X2,X3),tc_List_Olist(X3)) = c_Orderings_Omin(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12583]) ).

cnf(c_0_12584_0,axiom,
    c_Nat_Osize(c_List_Odrop(X1,X2,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12584]) ).

cnf(c_0_12601_0,axiom,
    c_union(X1,c_union(X2,X1,X3),X3) = c_union(X2,X1,X3),
    inference(literals_permutation,[status(thm)],[c_0_12601]) ).

cnf(c_0_12602_0,axiom,
    c_insert(X1,c_insert(X1,X2,X3),X3) = c_insert(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12602]) ).

cnf(c_0_12603_0,axiom,
    c_times(X1,c_Nat_Opower(X1,X2,tc_nat),tc_nat) = c_Nat_Opower(X1,c_Suc(X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12603]) ).

cnf(c_0_12604_0,axiom,
    c_plus(X2,c_times(X1,X2,tc_nat),tc_nat) = c_times(c_Suc(X1),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12604]) ).

cnf(c_0_12605_0,axiom,
    c_plus(X1,c_times(X1,X2,tc_nat),tc_nat) = c_times(X1,c_Suc(X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12605]) ).

cnf(c_0_12606_0,axiom,
    c_times(X1,c_Nat_Opower(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X1,c_Suc(X2),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12606]) ).

cnf(c_0_12608_0,axiom,
    c_Divides_Oop_Amod(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12608]) ).

cnf(c_0_12609_0,axiom,
    c_Union(c_insert(X1,X2,tc_set(X3)),X3) = c_union(X1,c_Union(X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12609]) ).

cnf(c_0_12610_0,axiom,
    c_Inter(c_insert(X1,X2,tc_set(X3)),X3) = c_inter(X1,c_Inter(X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12610]) ).

cnf(c_0_12611_0,axiom,
    c_List_Olistset(c_List_Olist_OCons(X1,X2,tc_set(X3)),X3) = c_List_Oset__Cons(X1,c_List_Olistset(X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12611]) ).

cnf(c_0_12612_0,axiom,
    c_List_Oconcat(c_List_Olist_OCons(X1,X2,tc_List_Olist(X3)),X3) = c_append(X1,c_List_Oconcat(X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12612]) ).

cnf(c_0_12615_0,axiom,
    c_plus(X1,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_Suc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_12615]) ).

cnf(c_0_12616_0,axiom,
    c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1,tc_nat) = c_Suc(c_Suc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_12616]) ).

cnf(c_0_12618_0,axiom,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12618]) ).

cnf(c_0_12619_0,axiom,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(X2,X1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12619]) ).

cnf(c_0_12620_0,axiom,
    c_Divides_Oop_Amod(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12620]) ).

cnf(c_0_12621_0,axiom,
    c_Divides_Oop_Amod(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12621]) ).

cnf(c_0_12622_0,axiom,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X1,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12622]) ).

cnf(c_0_12623_0,axiom,
    c_Divides_Oop_Amod(c_plus(X1,X2,tc_nat),X1,tc_nat) = c_Divides_Oop_Amod(X2,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12623]) ).

cnf(c_0_12653_0,axiom,
    c_insert(X1,c_List_Oset(X2,X3),X3) = c_List_Oset(c_List_Olist_OCons(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12653]) ).

cnf(c_0_12654_0,axiom,
    c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12654]) ).

cnf(c_0_12663_0,axiom,
    c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12663]) ).

cnf(c_0_12672_0,axiom,
    c_List_Odrop(X1,c_List_Oupt(X2,X3),tc_nat) = c_List_Oupt(c_plus(X2,X1,tc_nat),X3),
    inference(literals_permutation,[status(thm)],[c_0_12672]) ).

cnf(c_0_12705_0,axiom,
    c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12705]) ).

cnf(c_0_12706_0,axiom,
    c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12706]) ).

cnf(c_0_12707_0,axiom,
    c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12707]) ).

cnf(c_0_12708_0,axiom,
    c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12708]) ).

cnf(c_0_12709_0,axiom,
    c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X1),c_Message_Oparts(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12709]) ).

cnf(c_0_12710_0,axiom,
    c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12710]) ).

cnf(c_0_12711_0,axiom,
    c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12711]) ).

cnf(c_0_12712_0,axiom,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12712]) ).

cnf(c_0_12713_0,axiom,
    c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X1),c_Message_Oanalz(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12713]) ).

cnf(c_0_12718_0,axiom,
    c_Transitive__Closure_Otrancl(c_union(X1,c_Relation_OId,tc_prod(X2,X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_12718]) ).

cnf(c_0_12719_0,axiom,
    c_Transitive__Closure_Ortrancl(c_union(X1,c_Relation_OId,tc_prod(X2,X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_12719]) ).

cnf(c_0_12731_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_Oused(X3),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12731]) ).

cnf(c_0_12732_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X1,X2))),c_Event_OinitState(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12732]) ).

cnf(c_0_12733_0,axiom,
    c_List_Orotate1(c_List_Orotate(X1,X2,X3),X3) = c_List_Orotate(c_Suc(X1),X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12733]) ).

cnf(c_0_12734_0,axiom,
    c_lessequals(c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)),c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12734]) ).

cnf(c_0_12737_0,axiom,
    c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,X3),
    inference(literals_permutation,[status(thm)],[c_0_12737]) ).

cnf(c_0_12751_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12751]) ).

cnf(c_0_12752_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat) = c_minus(c_Suc(X2),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12752]) ).

cnf(c_0_12754_0,axiom,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12754]) ).

cnf(c_0_12764_0,axiom,
    c_inter(X1,c_minus(X2,X1,tc_set(X3)),X3) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_12764]) ).

cnf(c_0_12783_0,axiom,
    c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg) = c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_12783]) ).

cnf(c_0_12784_0,axiom,
    c_union(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_nat) = c_Message_OkeysFor(c_union(X1,X2,tc_Message_Omsg)),
    inference(literals_permutation,[status(thm)],[c_0_12784]) ).

cnf(c_0_12785_0,axiom,
    c_Orderings_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omin(X1,X2,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12785]) ).

cnf(c_0_12786_0,axiom,
    c_Orderings_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omax(X1,X2,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12786]) ).

cnf(c_0_12788_0,axiom,
    c_plus(c_IntDef_Oint(X1),c_IntDef_Oint(X2),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(X1,X2,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12788]) ).

cnf(c_0_12811_0,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),
    inference(literals_permutation,[status(thm)],[c_0_12811]) ).

cnf(c_0_12812_0,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),
    inference(literals_permutation,[status(thm)],[c_0_12812]) ).

cnf(c_0_12822_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12822]) ).

cnf(c_0_12823_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat) = c_minus(X2,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12823]) ).

cnf(c_0_12838_0,axiom,
    c_Suc(c_plus(X1,X2,tc_nat)) = c_plus(c_Suc(X1),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12838]) ).

cnf(c_0_12839_0,axiom,
    c_Suc(c_plus(X1,X2,tc_nat)) = c_plus(X1,c_Suc(X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12839]) ).

cnf(c_0_12846_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_OHPair(X1,X2),X3,tc_Message_Omsg)) = c_Message_OkeysFor(X3),
    inference(literals_permutation,[status(thm)],[c_0_12846]) ).

cnf(c_0_12847_0,axiom,
    c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X1,X2),X3,tc_Event_Oevent)) = c_Event_Oused(X3),
    inference(literals_permutation,[status(thm)],[c_0_12847]) ).

cnf(c_0_12848_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X1,X2),X3,tc_Message_Omsg)) = c_Message_OkeysFor(X3),
    inference(literals_permutation,[status(thm)],[c_0_12848]) ).

cnf(c_0_12851_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X3)),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12851]) ).

cnf(c_0_12854_0,axiom,
    c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12854]) ).

cnf(c_0_12855_0,axiom,
    c_List_Oremove1(X1,c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_12855]) ).

cnf(c_0_12856_0,axiom,
    c_in(X1,c_insert(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12856]) ).

cnf(c_0_12857_0,axiom,
    c_List_Oop_Amem(X1,c_List_Olist_OCons(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_12857]) ).

cnf(c_0_12858_0,axiom,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_0,X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12858]) ).

cnf(c_0_12861_0,axiom,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_12861]) ).

cnf(c_0_12862_0,axiom,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12862]) ).

cnf(c_0_12863_0,axiom,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_12863]) ).

cnf(c_0_12864_0,axiom,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12864]) ).

cnf(c_0_12865_0,axiom,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_12865]) ).

cnf(c_0_12866_0,axiom,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12866]) ).

cnf(c_0_12867_0,axiom,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_12867]) ).

cnf(c_0_12868_0,axiom,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_12868]) ).

cnf(c_0_12877_0,axiom,
    c_in(X1,c_insert(X1,c_emptyset,X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_12877]) ).

cnf(c_0_12881_0,axiom,
    c_lessequals(X1,c_plus(X2,X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12881]) ).

cnf(c_0_12882_0,axiom,
    c_lessequals(X1,c_plus(X1,X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12882]) ).

cnf(c_0_12884_0,axiom,
    c_lessequals(c_minus(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12884]) ).

cnf(c_0_12885_0,axiom,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12885]) ).

cnf(c_0_12886_0,axiom,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12886]) ).

cnf(c_0_12887_0,axiom,
    c_div(c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12887]) ).

cnf(c_0_12888_0,axiom,
    c_div(c_Divides_Oop_Amod(X1,X2,tc_nat),X2,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12888]) ).

cnf(c_0_12889_0,axiom,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_nat),X2,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12889]) ).

cnf(c_0_12890_0,axiom,
    c_Divides_Oop_Amod(c_times(X1,X2,tc_nat),X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12890]) ).

cnf(c_0_12891_0,axiom,
    c_lessequals(c_div(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12891]) ).

cnf(c_0_12892_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12892]) ).

cnf(c_0_12893_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12893]) ).

cnf(c_0_12894_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12894]) ).

cnf(c_0_12895_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12895]) ).

cnf(c_0_12911_0,axiom,
    c_minus(X1,c_uminus(X2,tc_set(X3)),tc_set(X3)) = c_inter(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12911]) ).

cnf(c_0_12914_0,axiom,
    c_less(c_0,c_Nat_Opower(X1,c_0,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12914]) ).

cnf(c_0_12915_0,axiom,
    c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12915]) ).

cnf(c_0_12930_0,axiom,
    c_Nat_Osize(c_List_Orotate(X1,X2,X3),tc_List_Olist(X3)) = c_Nat_Osize(X2,tc_List_Olist(X3)),
    inference(literals_permutation,[status(thm)],[c_0_12930]) ).

cnf(c_0_12931_0,axiom,
    c_Nat_Osize(c_Sum__Type_OInr(X1,X2,X3),tc_sum(X3,X2)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12931]) ).

cnf(c_0_12932_0,axiom,
    c_Nat_Osize(c_Sum__Type_OInl(X1,X2,X3),tc_sum(X2,X3)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_12932]) ).

cnf(c_0_12945_0,axiom,
    c_plus(c_Binomial_Obinomial(X1,X2),c_Binomial_Obinomial(X1,c_Suc(X2)),tc_nat) = c_Binomial_Obinomial(c_Suc(X1),c_Suc(X2)),
    inference(literals_permutation,[status(thm)],[c_0_12945]) ).

cnf(c_0_12979_0,axiom,
    c_Nat_Osize(c_List_Otl(X1,X2),tc_List_Olist(X2)) = c_minus(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12979]) ).

cnf(c_0_12980_0,axiom,
    c_Nat_Osize(c_List_Obutlast(X1,X2),tc_List_Olist(X2)) = c_minus(c_Nat_Osize(X1,tc_List_Olist(X2)),c_1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_12980]) ).

cnf(c_0_12982_0,axiom,
    c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
    inference(literals_permutation,[status(thm)],[c_0_12982]) ).

cnf(c_0_12983_0,axiom,
    c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
    inference(literals_permutation,[status(thm)],[c_0_12983]) ).

cnf(c_0_12984_0,axiom,
    c_List_Oset(c_List_Orotate(X1,X2,X3),X3) = c_List_Oset(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12984]) ).

cnf(c_0_12985_0,axiom,
    c_append(c_List_Orev(X1,X3),X2,X3) = c_List_Oitrev(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_12985]) ).

cnf(c_0_12988_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_Oknows(c_Message_Oagent_OSpy,X3),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_12988]) ).

cnf(c_0_12992_0,axiom,
    c_in(X1,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_12992]) ).

cnf(c_0_12993_0,axiom,
    c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X3) = c_List_Otake(X2,X1,X3),
    inference(literals_permutation,[status(thm)],[c_0_12993]) ).

cnf(c_0_12994_0,axiom,
    c_List_Olast(c_append(X1,c_List_Olist_ONil,X2),X2) = c_List_Olast(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_12994]) ).

cnf(c_0_12998_0,axiom,
    c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_12998]) ).

cnf(c_0_12999_0,axiom,
    c_Nat_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_12999]) ).

cnf(c_0_13003_0,axiom,
    c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X1,X2),c_Numeral_Obit_OB0),X2) = c_Numeral_Obin__mult(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),X2),
    inference(literals_permutation,[status(thm)],[c_0_13003]) ).

cnf(c_0_13006_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(literals_permutation,[status(thm)],[c_0_13006]) ).

cnf(c_0_13007_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(literals_permutation,[status(thm)],[c_0_13007]) ).

cnf(c_0_13008_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(literals_permutation,[status(thm)],[c_0_13008]) ).

cnf(c_0_13009_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(literals_permutation,[status(thm)],[c_0_13009]) ).

cnf(c_0_13010_0,axiom,
    c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X1),X2,tc_Message_Omsg)) = c_Message_OkeysFor(X2),
    inference(literals_permutation,[status(thm)],[c_0_13010]) ).

cnf(c_0_13016_0,axiom,
    c_List_Otl(c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    inference(literals_permutation,[status(thm)],[c_0_13016]) ).

cnf(c_0_13017_0,axiom,
    c_List_Ohd(c_List_Olist_OCons(X1,X2,X3),X3) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13017]) ).

cnf(c_0_13027_0,axiom,
    c_Nat_Osize(c_Event_Oevent_OSays(X1,X2,X3),tc_Event_Oevent) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13027]) ).

cnf(c_0_13030_0,axiom,
    c_union(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId,tc_prod(X2,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13030]) ).

cnf(c_0_13031_0,axiom,
    c_Set_Ocontents(c_insert(X1,c_emptyset,X2),X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13031]) ).

cnf(c_0_13032_0,axiom,
    c_List_Olast(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13032]) ).

cnf(c_0_13034_0,axiom,
    c_less(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13034]) ).

cnf(c_0_13035_0,axiom,
    c_minus(c_Suc(X1),c_Suc(X2),tc_nat) = c_minus(X1,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13035]) ).

cnf(c_0_13036_0,axiom,
    c_List_Obutlast(c_List_Olist_OCons(X1,c_List_Olist_ONil,X2),X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13036]) ).

cnf(c_0_13038_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_Oused(X3),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13038]) ).

cnf(c_0_13039_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X1,X2)),c_Event_OinitState(X3),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13039]) ).

cnf(c_0_13040_0,axiom,
    c_Nat_Osize(c_Message_Omsg_OCrypt(X1,X2),tc_Message_Omsg) = c_plus(c_Nat_Osize(X2,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13040]) ).

cnf(c_0_13049_0,axiom,
    c_Nat_Opower(X1,c_1,tc_set(tc_prod(X2,X2))) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13049]) ).

cnf(c_0_13050_0,axiom,
    c_Nat_Opower(X1,c_0,tc_set(tc_prod(X2,X2))) = c_Relation_OId,
    inference(literals_permutation,[status(thm)],[c_0_13050]) ).

cnf(c_0_13051_0,axiom,
    c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13051]) ).

cnf(c_0_13052_0,axiom,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),c_Numeral_OBit(X2,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,c_Numeral_Obin__succ(X2)),c_Numeral_Obit_OB0),
    inference(literals_permutation,[status(thm)],[c_0_13052]) ).

cnf(c_0_13073_0,axiom,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),c_Numeral_OBit(X2,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_13073]) ).

cnf(c_0_13074_0,axiom,
    c_times(X1,c_0,tc_nat) = c_times(X2,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13074]) ).

cnf(c_0_13075_0,axiom,
    c_times(c_0,X1,tc_nat) = c_times(c_0,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13075]) ).

cnf(c_0_13089_0,axiom,
    c_Numeral_Obin__add(c_Numeral_OBit(X1,c_Numeral_Obit_OB1),c_Numeral_OBit(X2,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X1,X2),c_Numeral_Obit_OB1),
    inference(literals_permutation,[status(thm)],[c_0_13089]) ).

cnf(c_0_13098_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oknows(X1,X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13098]) ).

cnf(c_0_13099_0,axiom,
    c_plus(c_Nat_Osize(X1,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(X1),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13099]) ).

cnf(c_0_13102_0,axiom,
    c_Nat_Osize(c_List_Oupt(X1,X2),tc_List_Olist(tc_nat)) = c_minus(X2,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13102]) ).

cnf(c_0_13105_0,axiom,
    c_Relation_Oconverse(c_Relation_Odiag(X1,X2),X2,X2) = c_Relation_Odiag(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13105]) ).

cnf(c_0_13106_0,axiom,
    c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13106]) ).

cnf(c_0_13112_0,axiom,
    c_inter(X1,c_uminus(X1,tc_set(X2)),X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13112]) ).

cnf(c_0_13113_0,axiom,
    c_inter(c_uminus(X1,tc_set(X2)),X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13113]) ).

cnf(c_0_13114_0,axiom,
    c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2) = c_insert(X1,c_emptyset,X2),
    inference(literals_permutation,[status(thm)],[c_0_13114]) ).

cnf(c_0_13166_0,axiom,
    c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),X2) = c_Message_OHPair(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13166]) ).

cnf(c_0_13167_0,axiom,
    c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X1,X2)),X2) = c_Message_OHPair(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13167]) ).

cnf(c_0_13171_0,axiom,
    c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13171]) ).

cnf(c_0_13172_0,axiom,
    c_in(c_List_Olist_ONil,c_List_Olists(X1,X2),tc_List_Olist(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13172]) ).

cnf(c_0_13173_0,axiom,
    c_in(c_List_Oset(X1,X2),c_Finite__Set_OFinites,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13173]) ).

cnf(c_0_13189_0,axiom,
    c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13189]) ).

cnf(c_0_13190_0,axiom,
    c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13190]) ).

cnf(c_0_13193_0,axiom,
    c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13193]) ).

cnf(c_0_13194_0,axiom,
    c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13194]) ).

cnf(c_0_13195_0,axiom,
    c_in(c_SetInterval_OlessThan(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_13195]) ).

cnf(c_0_13196_0,axiom,
    c_in(c_SetInterval_OatMost(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_13196]) ).

cnf(c_0_13201_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_Oused(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13201]) ).

cnf(c_0_13202_0,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(X1)),c_Event_OinitState(X1),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13202]) ).

cnf(c_0_13206_0,axiom,
    c_union(c_Message_Oparts(X1),c_Message_Osynth(X1),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(X1)),
    inference(literals_permutation,[status(thm)],[c_0_13206]) ).

cnf(c_0_13207_0,axiom,
    c_union(c_Message_Oanalz(X1),c_Message_Osynth(X1),tc_Message_Omsg) = c_Message_Oanalz(c_Message_Osynth(X1)),
    inference(literals_permutation,[status(thm)],[c_0_13207]) ).

cnf(c_0_13208_0,axiom,
    c_Numeral_Obin__mult(c_Numeral_OBit(X1,c_Numeral_Obit_OB0),X2) = c_Numeral_OBit(c_Numeral_Obin__mult(X1,X2),c_Numeral_Obit_OB0),
    inference(literals_permutation,[status(thm)],[c_0_13208]) ).

cnf(c_0_13213_0,axiom,
    c_Divides_Oop_Amod(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13213]) ).

cnf(c_0_13215_0,axiom,
    c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13215]) ).

cnf(c_0_13216_0,axiom,
    c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13216]) ).

cnf(c_0_13219_0,axiom,
    c_insert(c_emptyset,c_emptyset,tc_set(X1)) = c_Pow(c_emptyset,X1),
    inference(literals_permutation,[status(thm)],[c_0_13219]) ).

cnf(c_0_13220_0,axiom,
    c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)) = c_List_Olistset(c_List_Olist_ONil,X1),
    inference(literals_permutation,[status(thm)],[c_0_13220]) ).

cnf(c_0_13230_0,axiom,
    c_plus(c_1,c_IntDef_Oint(X1),tc_IntDef_Oint) = c_IntDef_Oint(c_Suc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_13230]) ).

cnf(c_0_13239_0,axiom,
    c_Nat_Osize(c_List_Orotate1(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13239]) ).

cnf(c_0_13240_0,axiom,
    c_Nat_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13240]) ).

cnf(c_0_13246_0,axiom,
    c_in(c_Message_Omsg_ONumber(X1),c_Message_Osynth(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13246]) ).

cnf(c_0_13247_0,axiom,
    c_in(c_Message_Omsg_OAgent(X1),c_Message_Osynth(X2),tc_Message_Omsg),
    inference(literals_permutation,[status(thm)],[c_0_13247]) ).

cnf(c_0_13268_0,axiom,
    c_minus(X1,X1,tc_set(X2)) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13268]) ).

cnf(c_0_13269_0,axiom,
    c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatMost(c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13269]) ).

cnf(c_0_13271_0,axiom,
    c_lessequals(X1,X1,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13271]) ).

cnf(c_0_13278_0,axiom,
    c_minus(X1,c_emptyset,tc_set(X2)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13278]) ).

cnf(c_0_13279_0,axiom,
    c_lessequals(X1,c_UNIV,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13279]) ).

cnf(c_0_13280_0,axiom,
    c_minus(c_emptyset,X1,tc_set(X2)) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13280]) ).

cnf(c_0_13281_0,axiom,
    c_uminus(c_uminus(X1,tc_set(X2)),tc_set(X2)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13281]) ).

cnf(c_0_13282_0,axiom,
    c_minus(X1,c_UNIV,tc_set(X2)) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13282]) ).

cnf(c_0_13283_0,axiom,
    c_Divides_Oop_Advd(c_Suc(c_0),c_Suc(c_0),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13283]) ).

cnf(c_0_13284_0,axiom,
    c_lessequals(c_emptyset,X1,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_13284]) ).

cnf(c_0_13285_0,axiom,
    c_less(X1,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13285]) ).

cnf(c_0_13293_0,axiom,
    c_in(c_Public_OshrK(X1),c_Message_OsymKeys,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13293]) ).

cnf(c_0_13294_0,axiom,
    c_lessequals(c_emptyset,c_emptyset,tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_13294]) ).

cnf(c_0_13295_0,axiom,
    c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X1)),c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)),
    inference(literals_permutation,[status(thm)],[c_0_13295]) ).

cnf(c_0_13296_0,axiom,
    c_lessequals(c_0,c_IntDef_Oint(X1),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13296]) ).

cnf(c_0_13297_0,axiom,
    c_less(c_0,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13297]) ).

cnf(c_0_13298_0,axiom,
    c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_13298]) ).

cnf(c_0_13299_0,axiom,
    c_div(X1,c_Suc(c_0),tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13299]) ).

cnf(c_0_13300_0,axiom,
    c_Divides_Oop_Amod(X1,c_Suc(c_0),tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13300]) ).

cnf(c_0_13301_0,axiom,
    c_Divides_Oop_Advd(c_Suc(c_0),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13301]) ).

cnf(c_0_13303_0,axiom,
    c_union(X1,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13303]) ).

cnf(c_0_13304_0,axiom,
    c_inter(X1,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13304]) ).

cnf(c_0_13306_0,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13306]) ).

cnf(c_0_13308_0,axiom,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13308]) ).

cnf(c_0_13310_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13310]) ).

cnf(c_0_13311_0,axiom,
    c_union(X1,c_emptyset,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13311]) ).

cnf(c_0_13312_0,axiom,
    c_union(c_emptyset,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13312]) ).

cnf(c_0_13313_0,axiom,
    c_inter(X1,c_UNIV,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13313]) ).

cnf(c_0_13314_0,axiom,
    c_inter(c_UNIV,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13314]) ).

cnf(c_0_13315_0,axiom,
    c_List_Oset(c_List_Orotate1(X1,X2),X2) = c_List_Oset(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13315]) ).

cnf(c_0_13316_0,axiom,
    c_List_Oset(c_List_Orev(X1,X2),X2) = c_List_Oset(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13316]) ).

cnf(c_0_13317_0,axiom,
    c_List_Oset(c_List_Oremdups(X1,X2),X2) = c_List_Oset(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_13317]) ).

cnf(c_0_13318_0,axiom,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13318]) ).

cnf(c_0_13319_0,axiom,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13319]) ).

cnf(c_0_13320_0,axiom,
    c_List_Oitrev(c_List_Olist_ONil,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13320]) ).

cnf(c_0_13321_0,axiom,
    c_List_Odrop(c_0,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13321]) ).

cnf(c_0_13322_0,axiom,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13322]) ).

cnf(c_0_13323_0,axiom,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13323]) ).

cnf(c_0_13324_0,axiom,
    c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13324]) ).

cnf(c_0_13325_0,axiom,
    c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13325]) ).

cnf(c_0_13336_0,axiom,
    c_union(X1,c_UNIV,X2) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13336]) ).

cnf(c_0_13337_0,axiom,
    c_union(c_UNIV,X1,X2) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13337]) ).

cnf(c_0_13338_0,axiom,
    c_inter(X1,c_emptyset,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13338]) ).

cnf(c_0_13339_0,axiom,
    c_inter(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13339]) ).

cnf(c_0_13340_0,axiom,
    c_Relation_Oconverse(c_Relation_OId,X1,X1) = c_Relation_OId,
    inference(literals_permutation,[status(thm)],[c_0_13340]) ).

cnf(c_0_13341_0,axiom,
    c_Relation_ORange(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13341]) ).

cnf(c_0_13342_0,axiom,
    c_Relation_ORange(c_Relation_OId,X1,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13342]) ).

cnf(c_0_13343_0,axiom,
    c_Relation_ODomain(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13343]) ).

cnf(c_0_13344_0,axiom,
    c_Relation_ODomain(c_Relation_OId,X1,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13344]) ).

cnf(c_0_13346_0,axiom,
    c_minus(X1,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13346]) ).

cnf(c_0_13347_0,axiom,
    c_List_Otake(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13347]) ).

cnf(c_0_13348_0,axiom,
    c_List_Otake(c_0,X1,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13348]) ).

cnf(c_0_13349_0,axiom,
    c_List_Osublist(c_List_Olist_ONil,X1,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13349]) ).

cnf(c_0_13350_0,axiom,
    c_List_Osublist(X1,c_emptyset,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13350]) ).

cnf(c_0_13351_0,axiom,
    c_List_Orotate(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13351]) ).

cnf(c_0_13352_0,axiom,
    c_List_Oreplicate(c_0,X1,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13352]) ).

cnf(c_0_13353_0,axiom,
    c_List_Oremove1(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13353]) ).

cnf(c_0_13354_0,axiom,
    c_List_Olist__inter(c_List_Olist_ONil,X1,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13354]) ).

cnf(c_0_13355_0,axiom,
    c_List_Olexn(X1,c_0,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13355]) ).

cnf(c_0_13356_0,axiom,
    c_List_Odrop(X1,c_List_Olist_ONil,X2) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13356]) ).

cnf(c_0_13357_0,axiom,
    c_Divides_Oop_Amod(X1,X1,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13357]) ).

cnf(c_0_13358_0,axiom,
    c_Divides_Oop_Advd(X1,X1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13358]) ).

cnf(c_0_13359_0,axiom,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13359]) ).

cnf(c_0_13360_0,axiom,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13360]) ).

cnf(c_0_13361_0,axiom,
    c_Divides_Oop_Amod(X1,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13361]) ).

cnf(c_0_13362_0,axiom,
    c_Divides_Oop_Advd(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13362]) ).

cnf(c_0_13363_0,axiom,
    c_in(X1,c_UNIV,X2),
    inference(literals_permutation,[status(thm)],[c_0_13363]) ).

cnf(c_0_13364_0,axiom,
    c_minus(X1,c_0,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13364]) ).

cnf(c_0_13365_0,axiom,
    c_plus(c_0,X1,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13365]) ).

cnf(c_0_13366_0,axiom,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    inference(literals_permutation,[status(thm)],[c_0_13366]) ).

cnf(c_0_13367_0,axiom,
    c_times(c_1,c_1,tc_nat) = c_Suc(c_0),
    inference(literals_permutation,[status(thm)],[c_0_13367]) ).

cnf(c_0_13368_0,axiom,
    c_Orderings_Omax(X1,c_0,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13368]) ).

cnf(c_0_13369_0,axiom,
    c_Orderings_Omax(c_0,X1,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13369]) ).

cnf(c_0_13370_0,axiom,
    c_plus(X1,c_0,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13370]) ).

cnf(c_0_13371_0,axiom,
    c_div(X1,c_1,tc_IntDef_Oint) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13371]) ).

cnf(c_0_13372_0,axiom,
    c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13372]) ).

cnf(c_0_13373_0,axiom,
    c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13373]) ).

cnf(c_0_13374_0,axiom,
    c_union(c_emptyset,c_emptyset,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13374]) ).

cnf(c_0_13375_0,axiom,
    c_inter(c_UNIV,c_UNIV,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13375]) ).

cnf(c_0_13376_0,axiom,
    c_Nat_Opower(X1,c_0,tc_nat) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_13376]) ).

cnf(c_0_13377_0,axiom,
    c_times(c_0,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13377]) ).

cnf(c_0_13378_0,axiom,
    c_times(X1,c_0,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13378]) ).

cnf(c_0_13379_0,axiom,
    c_Orderings_Omin(X1,c_0,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13379]) ).

cnf(c_0_13380_0,axiom,
    c_Orderings_Omin(c_0,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13380]) ).

cnf(c_0_13381_0,axiom,
    c_minus(c_0,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13381]) ).

cnf(c_0_13382_0,axiom,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13382]) ).

cnf(c_0_13383_0,axiom,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13383]) ).

cnf(c_0_13384_0,axiom,
    c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13384]) ).

cnf(c_0_13385_0,axiom,
    c_Divides_Oop_Amod(X1,c_1,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13385]) ).

cnf(c_0_13386_0,axiom,
    c_div(c_0,X1,tc_IntDef_Oint) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13386]) ).

cnf(c_0_13387_0,axiom,
    c_Nat_Opower(X1,c_0,tc_IntDef_Oint) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_13387]) ).

cnf(c_0_13388_0,axiom,
    c_Divides_Oop_Amod(c_0,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13388]) ).

cnf(c_0_13389_0,axiom,
    c_div(c_0,X1,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13389]) ).

cnf(c_0_13390_0,axiom,
    c_div(X1,c_0,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13390]) ).

cnf(c_0_13391_0,axiom,
    c_lessequals(c_0,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13391]) ).

cnf(c_0_13392_0,axiom,
    c_Divides_Oop_Advd(c_1,X1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13392]) ).

cnf(c_0_13393_0,axiom,
    c_Divides_Oop_Advd(X1,c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13393]) ).

cnf(c_0_13394_0,axiom,
    c_Divides_Oop_Advd(X1,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13394]) ).

cnf(c_0_13399_0,axiom,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    inference(literals_permutation,[status(thm)],[c_0_13399]) ).

cnf(c_0_13401_0,axiom,
    c_less(c_0,c_1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13401]) ).

cnf(c_0_13402_0,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13402]) ).

cnf(c_0_13403_0,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13403]) ).

cnf(c_0_13404_0,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_13404]) ).

cnf(c_0_13405_0,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13405]) ).

cnf(c_0_13426_0,axiom,
    c_Nat_Osize(c_Datatype_Ooption_OSome(X1,X2),tc_Datatype_Ooption(X2)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13426]) ).

cnf(c_0_13427_0,axiom,
    c_Numeral_Obin__succ(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X1),c_Numeral_Obit_OB0),
    inference(literals_permutation,[status(thm)],[c_0_13427]) ).

cnf(c_0_13428_0,axiom,
    c_Numeral_Obin__pred(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X1),c_Numeral_Obit_OB1),
    inference(literals_permutation,[status(thm)],[c_0_13428]) ).

cnf(c_0_13429_0,axiom,
    c_Numeral_Obin__minus(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X1),c_Numeral_Obit_OB0),
    inference(literals_permutation,[status(thm)],[c_0_13429]) ).

cnf(c_0_13442_0,axiom,
    c_Union(c_Pow(X1,X2),X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13442]) ).

cnf(c_0_13443_0,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13443]) ).

cnf(c_0_13444_0,axiom,
    c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X2),X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13444]) ).

cnf(c_0_13445_0,axiom,
    c_List_Odistinct(c_List_Oremdups(X1,X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_13445]) ).

cnf(c_0_13446_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OatMost(X1,tc_nat),tc_nat) = c_Suc(X1),
    inference(literals_permutation,[status(thm)],[c_0_13446]) ).

cnf(c_0_13447_0,axiom,
    c_Numeral_Obin__succ(c_Numeral_OBit(X1,c_Numeral_Obit_OB0)) = c_Numeral_OBit(X1,c_Numeral_Obit_OB1),
    inference(literals_permutation,[status(thm)],[c_0_13447]) ).

cnf(c_0_13448_0,axiom,
    c_Numeral_Obin__pred(c_Numeral_OBit(X1,c_Numeral_Obit_OB1)) = c_Numeral_OBit(X1,c_Numeral_Obit_OB0),
    inference(literals_permutation,[status(thm)],[c_0_13448]) ).

cnf(c_0_13449_0,axiom,
    c_IntDef_Onat(c_Numeral_Onumber__of(X1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13449]) ).

cnf(c_0_13450_0,axiom,
    c_IntDef_Onat(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13450]) ).

cnf(c_0_13451_0,axiom,
    c_Nat_Osize(c_Event_Oevent_ONotes(X1,X2),tc_Event_Oevent) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13451]) ).

cnf(c_0_13452_0,axiom,
    c_Nat_Osize(c_Event_Oevent_OGets(X1,X2),tc_Event_Oevent) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13452]) ).

cnf(c_0_13453_0,axiom,
    c_List_Odistinct(c_List_Oupt(X1,X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_13453]) ).

cnf(c_0_13454_0,axiom,
    c_Nat_Osize(c_List_Ochar_OChar(X1,X2),tc_List_Ochar) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13454]) ).

cnf(c_0_13465_0,axiom,
    c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13465]) ).

cnf(c_0_13467_0,axiom,
    c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_13467]) ).

cnf(c_0_13478_0,axiom,
    class_Nat_Opower(tc_fun(X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_13478]) ).

cnf(c_0_13497_0,axiom,
    c_Binomial_Obinomial(c_Suc(X1),X1) = c_Suc(X1),
    inference(literals_permutation,[status(thm)],[c_0_13497]) ).

cnf(c_0_13506_0,axiom,
    c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X1))) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13506]) ).

cnf(c_0_13507_0,axiom,
    c_HOL_Oabs(c_IntDef_Oint(X1),tc_IntDef_Oint) = c_IntDef_Oint(X1),
    inference(literals_permutation,[status(thm)],[c_0_13507]) ).

cnf(c_0_13524_0,axiom,
    c_Nat_Osize(c_Message_Omsg_OKey(X1),tc_Message_Omsg) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13524]) ).

cnf(c_0_13525_0,axiom,
    c_Nat_Osize(c_Message_Omsg_ONonce(X1),tc_Message_Omsg) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13525]) ).

cnf(c_0_13526_0,axiom,
    c_Nat_Osize(c_Message_Omsg_ONumber(X1),tc_Message_Omsg) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13526]) ).

cnf(c_0_13527_0,axiom,
    c_Nat_Osize(c_Message_Omsg_OAgent(X1),tc_Message_Omsg) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13527]) ).

cnf(c_0_13528_0,axiom,
    c_Nat_Osize(c_Message_Oagent_OFriend(X1),tc_Message_Oagent) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13528]) ).

cnf(c_0_13529_0,axiom,
    c_uminus(c_emptyset,tc_set(X1)) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13529]) ).

cnf(c_0_13530_0,axiom,
    c_uminus(c_UNIV,tc_set(X1)) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13530]) ).

cnf(c_0_13531_0,axiom,
    c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13531]) ).

cnf(c_0_13532_0,axiom,
    c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13532]) ).

cnf(c_0_13533_0,axiom,
    c_Binomial_Obinomial(c_0,c_Suc(X1)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13533]) ).

cnf(c_0_13534_0,axiom,
    c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
    inference(literals_permutation,[status(thm)],[c_0_13534]) ).

cnf(c_0_13535_0,axiom,
    c_Binomial_Obinomial(X1,c_Suc(c_0)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13535]) ).

cnf(c_0_13539_0,axiom,
    c_Event_Oknows(X1,c_List_Olist_ONil) = c_Event_OinitState(X1),
    inference(literals_permutation,[status(thm)],[c_0_13539]) ).

cnf(c_0_13540_0,axiom,
    c_Numeral_Obin__mult(c_Numeral_OMin,X1) = c_Numeral_Obin__minus(X1),
    inference(literals_permutation,[status(thm)],[c_0_13540]) ).

cnf(c_0_13541_0,axiom,
    c_Numeral_Obin__add(X1,c_Numeral_OMin) = c_Numeral_Obin__pred(X1),
    inference(literals_permutation,[status(thm)],[c_0_13541]) ).

cnf(c_0_13542_0,axiom,
    c_Numeral_Obin__add(c_Numeral_OMin,X1) = c_Numeral_Obin__pred(X1),
    inference(literals_permutation,[status(thm)],[c_0_13542]) ).

cnf(c_0_13553_0,axiom,
    c_Fun_Oid(X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13553]) ).

cnf(c_0_13554_0,axiom,
    c_Message_OinvKey(c_Public_OshrK(X1)) = c_Public_OshrK(X1),
    inference(literals_permutation,[status(thm)],[c_0_13554]) ).

cnf(c_0_13555_0,axiom,
    c_Message_Oparts(c_Message_Oparts(X1)) = c_Message_Oparts(X1),
    inference(literals_permutation,[status(thm)],[c_0_13555]) ).

cnf(c_0_13556_0,axiom,
    c_Message_Oparts(c_Message_Oanalz(X1)) = c_Message_Oparts(X1),
    inference(literals_permutation,[status(thm)],[c_0_13556]) ).

cnf(c_0_13557_0,axiom,
    c_Message_Oanalz(c_Message_Oparts(X1)) = c_Message_Oparts(X1),
    inference(literals_permutation,[status(thm)],[c_0_13557]) ).

cnf(c_0_13558_0,axiom,
    c_Message_Oanalz(c_Message_Oanalz(X1)) = c_Message_Oanalz(X1),
    inference(literals_permutation,[status(thm)],[c_0_13558]) ).

cnf(c_0_13559_0,axiom,
    c_Binomial_Obinomial(X1,X1) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_13559]) ).

cnf(c_0_13560_0,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
    inference(literals_permutation,[status(thm)],[c_0_13560]) ).

cnf(c_0_13561_0,axiom,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OMin),
    inference(literals_permutation,[status(thm)],[c_0_13561]) ).

cnf(c_0_13562_0,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
    inference(literals_permutation,[status(thm)],[c_0_13562]) ).

cnf(c_0_13563_0,axiom,
    c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13563]) ).

cnf(c_0_13564_0,axiom,
    c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13564]) ).

cnf(c_0_13565_0,axiom,
    c_NatArith_Oof__nat(X1,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_13565]) ).

cnf(c_0_13566_0,axiom,
    c_Transitive__Closure_Otrancl(c_emptyset,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13566]) ).

cnf(c_0_13567_0,axiom,
    c_Transitive__Closure_Ortrancl(c_emptyset,X1) = c_Relation_OId,
    inference(literals_permutation,[status(thm)],[c_0_13567]) ).

cnf(c_0_13568_0,axiom,
    c_Union(c_emptyset,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13568]) ).

cnf(c_0_13569_0,axiom,
    c_Union(c_UNIV,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13569]) ).

cnf(c_0_13570_0,axiom,
    c_Pow(c_UNIV,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13570]) ).

cnf(c_0_13571_0,axiom,
    c_Inter(c_emptyset,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13571]) ).

cnf(c_0_13572_0,axiom,
    c_Inter(c_UNIV,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13572]) ).

cnf(c_0_13573_0,axiom,
    c_Relation_Odiag(c_emptyset,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13573]) ).

cnf(c_0_13574_0,axiom,
    c_Numeral_Obin__mult(c_Numeral_OPls,X1) = c_Numeral_OPls,
    inference(literals_permutation,[status(thm)],[c_0_13574]) ).

cnf(c_0_13575_0,axiom,
    c_List_Oupt(X1,c_0) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13575]) ).

cnf(c_0_13576_0,axiom,
    c_List_Otl(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13576]) ).

cnf(c_0_13577_0,axiom,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13577]) ).

cnf(c_0_13578_0,axiom,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13578]) ).

cnf(c_0_13579_0,axiom,
    c_List_Orotate1(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13579]) ).

cnf(c_0_13580_0,axiom,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13580]) ).

cnf(c_0_13581_0,axiom,
    c_List_Oremdups(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13581]) ).

cnf(c_0_13582_0,axiom,
    c_List_Oremdups(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13582]) ).

cnf(c_0_13583_0,axiom,
    c_List_Onull(c_List_Olist_ONil,X1),
    inference(literals_permutation,[status(thm)],[c_0_13583]) ).

cnf(c_0_13584_0,axiom,
    c_List_Olists(c_UNIV,X1) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_13584]) ).

cnf(c_0_13585_0,axiom,
    c_List_Odistinct(c_List_Olist_ONil,X1),
    inference(literals_permutation,[status(thm)],[c_0_13585]) ).

cnf(c_0_13586_0,axiom,
    c_List_Oconcat(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13586]) ).

cnf(c_0_13587_0,axiom,
    c_List_Obutlast(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13587]) ).

cnf(c_0_13588_0,axiom,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_13588]) ).

cnf(c_0_13589_0,axiom,
    c_Finite__Set_Ocard(c_emptyset,X1) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_13589]) ).

cnf(c_0_13590_0,axiom,
    c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_13590]) ).

cnf(c_0_13591_0,axiom,
    c_Binomial_Obinomial(X1,c_0) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_13591]) ).

cnf(c_0_13592_0,axiom,
    c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    inference(literals_permutation,[status(thm)],[c_0_13592]) ).

cnf(c_0_14500_0,axiom,
    c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14500]) ).

cnf(c_0_14501_0,axiom,
    c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14501]) ).

cnf(c_0_14502_0,axiom,
    c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_14502]) ).

cnf(c_0_14503_0,axiom,
    c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14503]) ).

cnf(c_0_14504_0,axiom,
    c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14504]) ).

cnf(c_0_14505_0,axiom,
    c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_14505]) ).

cnf(c_0_14506_0,axiom,
    c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
    inference(literals_permutation,[status(thm)],[c_0_14506]) ).

cnf(c_0_14507_0,axiom,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14507]) ).

cnf(c_0_14508_0,axiom,
    c_Parity_Oeven(c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14508]) ).

cnf(c_0_14509_0,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14509]) ).

cnf(c_0_14510_0,axiom,
    c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14510]) ).

cnf(c_0_14511_0,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_OPls,
    inference(literals_permutation,[status(thm)],[c_0_14511]) ).

cnf(c_0_14512_0,axiom,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_OMin,
    inference(literals_permutation,[status(thm)],[c_0_14512]) ).

cnf(c_0_14513_0,axiom,
    c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14513]) ).

cnf(c_0_14514_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14514]) ).

cnf(c_0_14515_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14515]) ).

cnf(c_0_14516_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14516]) ).

cnf(c_0_14517_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14517]) ).

cnf(c_0_14518_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14518]) ).

cnf(c_0_14519_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14519]) ).

cnf(c_0_14520_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14520]) ).

cnf(c_0_14521_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14521]) ).

cnf(c_0_14522_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14522]) ).

cnf(c_0_14523_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14523]) ).

cnf(c_0_14524_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14524]) ).

cnf(c_0_14525_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14525]) ).

cnf(c_0_14526_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14526]) ).

cnf(c_0_14527_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14527]) ).

cnf(c_0_14528_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14528]) ).

cnf(c_0_14529_0,axiom,
    c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14529]) ).

cnf(c_0_14530_0,axiom,
    c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_14530]) ).

cnf(c_0_14531_0,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14531]) ).

cnf(c_0_14532_0,axiom,
    c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14532]) ).

cnf(c_0_14533_0,axiom,
    c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14533]) ).

cnf(c_0_14534_0,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14534]) ).

cnf(c_0_14535_0,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14535]) ).

cnf(c_0_14536_0,axiom,
    class_Nat_Opower(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_14536]) ).

cnf(c_0_14537_0,axiom,
    class_Orderings_Oorder(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_14537]) ).

cnf(c_0_14538_0,axiom,
    class_Orderings_Oord(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_14538]) ).

cnf(c_0_14539_0,axiom,
    class_HOL_Ominus(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_14539]) ).

cnf(c_0_14549_0,axiom,
    c_IntDef_Onat(c_1) = c_Suc(c_0),
    inference(literals_permutation,[status(thm)],[c_0_14549]) ).

cnf(c_0_14550_0,axiom,
    c_Message_Oanalz(c_emptyset) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_14550]) ).

cnf(c_0_14551_0,axiom,
    c_Message_Oparts(c_emptyset) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_14551]) ).

cnf(c_0_14552_0,axiom,
    c_Message_OkeysFor(c_emptyset) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_14552]) ).

cnf(c_0_14553_0,axiom,
    c_Numeral_Obin__succ(c_Numeral_OMin) = c_Numeral_OPls,
    inference(literals_permutation,[status(thm)],[c_0_14553]) ).

cnf(c_0_14554_0,axiom,
    c_Numeral_Obin__pred(c_Numeral_OPls) = c_Numeral_OMin,
    inference(literals_permutation,[status(thm)],[c_0_14554]) ).

cnf(c_0_14555_0,axiom,
    c_Numeral_Obin__minus(c_Numeral_OPls) = c_Numeral_OPls,
    inference(literals_permutation,[status(thm)],[c_0_14555]) ).

cnf(c_0_14556_0,axiom,
    c_Suc(c_0) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_14556]) ).

cnf(c_0_14557_0,axiom,
    c_IntDef_Onat(c_0) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14557]) ).

cnf(c_0_14558_0,axiom,
    c_IntDef_Oint(c_0) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_14558]) ).

cnf(c_0_14559_0,axiom,
    c_IntDef_Oint(c_1) = c_1,
    inference(literals_permutation,[status(thm)],[c_0_14559]) ).

cnf(c_0_14560_0,axiom,
    class_HOL_Ominus(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14560]) ).

cnf(c_0_14561_0,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14561]) ).

cnf(c_0_14562_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14562]) ).

cnf(c_0_14563_0,axiom,
    class_LOrder_Olorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14563]) ).

cnf(c_0_14564_0,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14564]) ).

cnf(c_0_14565_0,axiom,
    class_Parity_Oeven__odd(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14565]) ).

cnf(c_0_14566_0,axiom,
    class_Numeral_Onumber(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14566]) ).

cnf(c_0_14567_0,axiom,
    class_Power_Orecpower(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14567]) ).

cnf(c_0_14568_0,axiom,
    class_Divides_Odiv(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14568]) ).

cnf(c_0_14569_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14569]) ).

cnf(c_0_14570_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14570]) ).

cnf(c_0_14571_0,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14571]) ).

cnf(c_0_14572_0,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14572]) ).

cnf(c_0_14573_0,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14573]) ).

cnf(c_0_14574_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14574]) ).

cnf(c_0_14575_0,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14575]) ).

cnf(c_0_14576_0,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14576]) ).

cnf(c_0_14577_0,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14577]) ).

cnf(c_0_14578_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14578]) ).

cnf(c_0_14579_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14579]) ).

cnf(c_0_14580_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14580]) ).

cnf(c_0_14581_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14581]) ).

cnf(c_0_14582_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14582]) ).

cnf(c_0_14583_0,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14583]) ).

cnf(c_0_14584_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14584]) ).

cnf(c_0_14585_0,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14585]) ).

cnf(c_0_14586_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14586]) ).

cnf(c_0_14587_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14587]) ).

cnf(c_0_14588_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14588]) ).

cnf(c_0_14589_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14589]) ).

cnf(c_0_14590_0,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14590]) ).

cnf(c_0_14591_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14591]) ).

cnf(c_0_14592_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14592]) ).

cnf(c_0_14593_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14593]) ).

cnf(c_0_14594_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14594]) ).

cnf(c_0_14595_0,axiom,
    class_Orderings_Oord(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14595]) ).

cnf(c_0_14596_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14596]) ).

cnf(c_0_14597_0,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14597]) ).

cnf(c_0_14598_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14598]) ).

cnf(c_0_14599_0,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14599]) ).

cnf(c_0_14600_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14600]) ).

cnf(c_0_14601_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14601]) ).

cnf(c_0_14602_0,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14602]) ).

cnf(c_0_14603_0,axiom,
    class_Nat_Opower(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14603]) ).

cnf(c_0_14604_0,axiom,
    class_HOL_Otimes(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14604]) ).

cnf(c_0_14605_0,axiom,
    class_HOL_Oplus(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14605]) ).

cnf(c_0_14606_0,axiom,
    class_HOL_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14606]) ).

cnf(c_0_14607_0,axiom,
    class_HOL_Oone(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_14607]) ).

cnf(c_0_14608_0,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    inference(literals_permutation,[status(thm)],[c_0_14608]) ).

cnf(c_0_14609_0,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(literals_permutation,[status(thm)],[c_0_14609]) ).

cnf(c_0_14610_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14610]) ).

cnf(c_0_14611_0,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14611]) ).

cnf(c_0_14612_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14612]) ).

cnf(c_0_14613_0,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14613]) ).

cnf(c_0_14614_0,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14614]) ).

cnf(c_0_14615_0,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14615]) ).

cnf(c_0_14616_0,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14616]) ).

cnf(c_0_14617_0,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14617]) ).

cnf(c_0_14618_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14618]) ).

cnf(c_0_14619_0,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14619]) ).

cnf(c_0_14620_0,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14620]) ).

cnf(c_0_14621_0,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14621]) ).

cnf(c_0_14622_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14622]) ).

cnf(c_0_14623_0,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14623]) ).

cnf(c_0_14624_0,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14624]) ).

cnf(c_0_14625_0,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14625]) ).

cnf(c_0_14626_0,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14626]) ).

cnf(c_0_14627_0,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14627]) ).

cnf(c_0_14628_0,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14628]) ).

cnf(c_0_14629_0,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14629]) ).

cnf(c_0_14630_0,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14630]) ).

cnf(c_0_14631_0,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14631]) ).

cnf(c_0_14632_0,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14632]) ).

cnf(c_0_14633_0,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14633]) ).

cnf(c_0_14634_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14634]) ).

cnf(c_0_14635_0,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14635]) ).

cnf(c_0_14636_0,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14636]) ).

cnf(c_0_14637_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14637]) ).

cnf(c_0_14638_0,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14638]) ).

cnf(c_0_14639_0,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14639]) ).

cnf(c_0_14640_0,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14640]) ).

cnf(c_0_14641_0,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14641]) ).

cnf(c_0_14642_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14642]) ).

cnf(c_0_14643_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14643]) ).

cnf(c_0_14644_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14644]) ).

cnf(c_0_14645_0,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14645]) ).

cnf(c_0_14646_0,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14646]) ).

cnf(c_0_14647_0,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14647]) ).

cnf(c_0_14648_0,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14648]) ).

cnf(c_0_14649_0,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14649]) ).

cnf(c_0_14650_0,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14650]) ).

cnf(c_0_14651_0,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14651]) ).

cnf(c_0_14652_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14652]) ).

cnf(c_0_14653_0,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14653]) ).

cnf(c_0_14654_0,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14654]) ).

cnf(c_0_14655_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14655]) ).

cnf(c_0_14656_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14656]) ).

cnf(c_0_14657_0,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14657]) ).

cnf(c_0_14658_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14658]) ).

cnf(c_0_14659_0,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14659]) ).

cnf(c_0_14660_0,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14660]) ).

cnf(c_0_14661_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14661]) ).

cnf(c_0_14662_0,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14662]) ).

cnf(c_0_14663_0,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14663]) ).

cnf(c_0_14664_0,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14664]) ).

cnf(c_0_14665_0,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14665]) ).

cnf(c_0_14666_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14666]) ).

cnf(c_0_14667_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14667]) ).

cnf(c_0_14668_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14668]) ).

cnf(c_0_14669_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14669]) ).

cnf(c_0_14670_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14670]) ).

cnf(c_0_14671_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14671]) ).

cnf(c_0_14672_0,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14672]) ).

cnf(c_0_14673_0,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14673]) ).

cnf(c_0_14674_0,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_14674]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
    ! [X1] : c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_1_002,negated_conjecture,
    ! [X1] : c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg),
    c_0_0 ).

fof(c_0_2_003,negated_conjecture,
    ! [X2] : c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(variable_rename,[status(thm)],[c_0_1]) ).

cnf(c_0_3_004,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4_005,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg),
    c_0_3,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_6306,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_e14db0.p',c_0_4) ).

cnf(c_8834,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(copy,[status(esa)],[c_6306]) ).

cnf(c_8838,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(copy,[status(esa)],[c_8834]) ).

cnf(c_8839,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(copy,[status(esa)],[c_8838]) ).

cnf(c_8840,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(copy,[status(esa)],[c_8839]) ).

cnf(c_27287,negated_conjecture,
    c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
    inference(copy,[status(esa)],[c_8840]) ).

cnf(c_3903,plain,
    ( ~ c_lessequals(v_sko__urX(X0),X1,tc_nat)
    | ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(X0),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_e14db0.p',c_0_12674_1) ).

cnf(c_22481,plain,
    ( ~ c_lessequals(v_sko__urX(X0),X1,tc_nat)
    | ~ c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(X0),tc_Message_Omsg) ),
    inference(copy,[status(esa)],[c_3903]) ).

cnf(c_27299,plain,
    ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat),
    inference(resolution,[status(thm)],[c_27287,c_22481]) ).

cnf(c_27300,plain,
    ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat),
    inference(rewriting,[status(thm)],[c_27299]) ).

cnf(c_440,plain,
    c_lessequals(X0,c_plus(X0,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_e14db0.p',c_0_12882_0) ).

cnf(c_15768,plain,
    c_lessequals(X0,c_plus(X0,X1,tc_nat),tc_nat),
    inference(copy,[status(esa)],[c_440]) ).

cnf(c_27343,plain,
    $false,
    inference(resolution,[status(thm)],[c_27300,c_15768]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV280-1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13  % Command  : iprover_modulo %s %d
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 16:43:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.35  % Running in mono-core mode
% 0.63/0.82  % Orienting using strategy Equiv(ClausalAll)
% 0.63/0.82  % Orientation found
% 0.63/0.82  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_62772e.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_e14db0.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_4e9b7e | grep -v "SZS"
% 0.63/0.83  
% 0.63/0.83  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.63/0.83  
% 0.63/0.83  % 
% 0.63/0.83  % ------  iProver source info 
% 0.63/0.83  
% 0.63/0.83  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.63/0.83  % git: non_committed_changes: true
% 0.63/0.83  % git: last_make_outside_of_git: true
% 0.63/0.83  
% 0.63/0.83  % 
% 0.63/0.83  % ------ Input Options
% 0.63/0.83  
% 0.63/0.83  % --out_options                         all
% 0.63/0.83  % --tptp_safe_out                       true
% 0.63/0.83  % --problem_path                        ""
% 0.63/0.83  % --include_path                        ""
% 0.63/0.83  % --clausifier                          .//eprover
% 0.63/0.83  % --clausifier_options                  --tstp-format  
% 0.63/0.83  % --stdin                               false
% 0.63/0.83  % --dbg_backtrace                       false
% 0.63/0.83  % --dbg_dump_prop_clauses               false
% 0.63/0.83  % --dbg_dump_prop_clauses_file          -
% 0.63/0.83  % --dbg_out_stat                        false
% 0.63/0.83  
% 0.63/0.83  % ------ General Options
% 0.63/0.83  
% 0.63/0.83  % --fof                                 false
% 0.63/0.83  % --time_out_real                       150.
% 0.63/0.83  % --time_out_prep_mult                  0.2
% 0.63/0.83  % --time_out_virtual                    -1.
% 0.63/0.83  % --schedule                            none
% 0.63/0.83  % --ground_splitting                    input
% 0.63/0.83  % --splitting_nvd                       16
% 0.63/0.83  % --non_eq_to_eq                        false
% 0.63/0.83  % --prep_gs_sim                         true
% 0.63/0.83  % --prep_unflatten                      false
% 0.63/0.83  % --prep_res_sim                        true
% 0.63/0.83  % --prep_upred                          true
% 0.63/0.83  % --res_sim_input                       true
% 0.63/0.83  % --clause_weak_htbl                    true
% 0.63/0.83  % --gc_record_bc_elim                   false
% 0.63/0.83  % --symbol_type_check                   false
% 0.63/0.83  % --clausify_out                        false
% 0.63/0.83  % --large_theory_mode                   false
% 0.63/0.83  % --prep_sem_filter                     none
% 0.63/0.83  % --prep_sem_filter_out                 false
% 0.63/0.83  % --preprocessed_out                    false
% 0.63/0.83  % --sub_typing                          false
% 0.63/0.83  % --brand_transform                     false
% 0.63/0.83  % --pure_diseq_elim                     true
% 0.63/0.83  % --min_unsat_core                      false
% 0.63/0.83  % --pred_elim                           true
% 0.63/0.83  % --add_important_lit                   false
% 0.63/0.83  % --soft_assumptions                    false
% 0.63/0.83  % --reset_solvers                       false
% 0.63/0.83  % --bc_imp_inh                          []
% 0.63/0.83  % --conj_cone_tolerance                 1.5
% 0.63/0.83  % --prolific_symb_bound                 500
% 0.63/0.83  % --lt_threshold                        2000
% 0.63/0.83  
% 0.63/0.83  % ------ SAT Options
% 0.63/0.83  
% 0.63/0.83  % --sat_mode                            false
% 0.63/0.83  % --sat_fm_restart_options              ""
% 0.63/0.83  % --sat_gr_def                          false
% 0.63/0.83  % --sat_epr_types                       true
% 0.63/0.83  % --sat_non_cyclic_types                false
% 0.63/0.83  % --sat_finite_models                   false
% 0.63/0.83  % --sat_fm_lemmas                       false
% 0.63/0.83  % --sat_fm_prep                         false
% 0.63/0.83  % --sat_fm_uc_incr                      true
% 0.63/0.83  % --sat_out_model                       small
% 0.63/0.83  % --sat_out_clauses                     false
% 0.63/0.83  
% 0.63/0.83  % ------ QBF Options
% 0.63/0.83  
% 0.63/0.83  % --qbf_mode                            false
% 0.63/0.83  % --qbf_elim_univ                       true
% 0.63/0.83  % --qbf_sk_in                           true
% 0.63/0.83  % --qbf_pred_elim                       true
% 0.63/0.83  % --qbf_split                           32
% 0.63/0.83  
% 0.63/0.83  % ------ BMC1 Options
% 0.63/0.83  
% 0.63/0.83  % --bmc1_incremental                    false
% 0.63/0.83  % --bmc1_axioms                         reachable_all
% 0.63/0.83  % --bmc1_min_bound                      0
% 0.63/0.83  % --bmc1_max_bound                      -1
% 0.63/0.83  % --bmc1_max_bound_default              -1
% 0.63/0.83  % --bmc1_symbol_reachability            true
% 0.63/0.83  % --bmc1_property_lemmas                false
% 0.63/0.83  % --bmc1_k_induction                    false
% 0.63/0.83  % --bmc1_non_equiv_states               false
% 0.63/0.83  % --bmc1_deadlock                       false
% 0.63/0.83  % --bmc1_ucm                            false
% 0.63/0.83  % --bmc1_add_unsat_core                 none
% 0.63/0.83  % --bmc1_unsat_core_children            false
% 0.63/0.83  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.63/0.83  % --bmc1_out_stat                       full
% 0.63/0.83  % --bmc1_ground_init                    false
% 0.63/0.83  % --bmc1_pre_inst_next_state            false
% 0.63/0.83  % --bmc1_pre_inst_state                 false
% 0.63/0.83  % --bmc1_pre_inst_reach_state           false
% 0.63/0.83  % --bmc1_out_unsat_core                 false
% 0.63/0.83  % --bmc1_aig_witness_out                false
% 0.63/0.83  % --bmc1_verbose                        false
% 0.63/0.83  % --bmc1_dump_clauses_tptp              false
% 7.13/7.53  % --bmc1_dump_unsat_core_tptp           false
% 7.13/7.53  % --bmc1_dump_file                      -
% 7.13/7.53  % --bmc1_ucm_expand_uc_limit            128
% 7.13/7.53  % --bmc1_ucm_n_expand_iterations        6
% 7.13/7.53  % --bmc1_ucm_extend_mode                1
% 7.13/7.53  % --bmc1_ucm_init_mode                  2
% 7.13/7.53  % --bmc1_ucm_cone_mode                  none
% 7.13/7.53  % --bmc1_ucm_reduced_relation_type      0
% 7.13/7.53  % --bmc1_ucm_relax_model                4
% 7.13/7.53  % --bmc1_ucm_full_tr_after_sat          true
% 7.13/7.53  % --bmc1_ucm_expand_neg_assumptions     false
% 7.13/7.53  % --bmc1_ucm_layered_model              none
% 7.13/7.53  % --bmc1_ucm_max_lemma_size             10
% 7.13/7.53  
% 7.13/7.53  % ------ AIG Options
% 7.13/7.53  
% 7.13/7.53  % --aig_mode                            false
% 7.13/7.53  
% 7.13/7.53  % ------ Instantiation Options
% 7.13/7.53  
% 7.13/7.53  % --instantiation_flag                  true
% 7.13/7.53  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 7.13/7.53  % --inst_solver_per_active              750
% 7.13/7.53  % --inst_solver_calls_frac              0.5
% 7.13/7.53  % --inst_passive_queue_type             priority_queues
% 7.13/7.53  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 7.13/7.53  % --inst_passive_queues_freq            [25;2]
% 7.13/7.53  % --inst_dismatching                    true
% 7.13/7.53  % --inst_eager_unprocessed_to_passive   true
% 7.13/7.53  % --inst_prop_sim_given                 true
% 7.13/7.53  % --inst_prop_sim_new                   false
% 7.13/7.53  % --inst_orphan_elimination             true
% 7.13/7.53  % --inst_learning_loop_flag             true
% 7.13/7.53  % --inst_learning_start                 3000
% 7.13/7.53  % --inst_learning_factor                2
% 7.13/7.53  % --inst_start_prop_sim_after_learn     3
% 7.13/7.53  % --inst_sel_renew                      solver
% 7.13/7.53  % --inst_lit_activity_flag              true
% 7.13/7.53  % --inst_out_proof                      true
% 7.13/7.53  
% 7.13/7.53  % ------ Resolution Options
% 7.13/7.53  
% 7.13/7.53  % --resolution_flag                     true
% 7.13/7.53  % --res_lit_sel                         kbo_max
% 7.13/7.53  % --res_to_prop_solver                  none
% 7.13/7.53  % --res_prop_simpl_new                  false
% 7.13/7.53  % --res_prop_simpl_given                false
% 7.13/7.53  % --res_passive_queue_type              priority_queues
% 7.13/7.53  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 7.13/7.53  % --res_passive_queues_freq             [15;5]
% 7.13/7.53  % --res_forward_subs                    full
% 7.13/7.53  % --res_backward_subs                   full
% 7.13/7.53  % --res_forward_subs_resolution         true
% 7.13/7.53  % --res_backward_subs_resolution        true
% 7.13/7.53  % --res_orphan_elimination              false
% 7.13/7.53  % --res_time_limit                      1000.
% 7.13/7.53  % --res_out_proof                       true
% 7.13/7.53  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_62772e.s
% 7.13/7.53  % --modulo                              true
% 7.13/7.53  
% 7.13/7.53  % ------ Combination Options
% 7.13/7.53  
% 7.13/7.53  % --comb_res_mult                       1000
% 7.13/7.53  % --comb_inst_mult                      300
% 7.13/7.53  % ------ 
% 7.13/7.53  
% 7.13/7.53  % ------ Parsing...% successful
% 7.13/7.53  
% 7.13/7.53  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e  pe_s  pe_e  snvd_s sp: 0 0s snvd_e % 
% 7.13/7.53  
% 7.13/7.53  % ------ Proving...
% 7.13/7.53  % ------ Problem Properties 
% 7.13/7.53  
% 7.13/7.53  % 
% 7.13/7.53  % EPR                                   false
% 7.13/7.53  % Horn                                  false
% 7.13/7.53  % Has equality                          true
% 7.13/7.53  
% 7.13/7.53  % % ------ Input Options Time Limit: Unbounded
% 7.13/7.53  
% 7.13/7.53  
% 7.13/7.53  Compiling...
% 7.13/7.53  Loading plugin: done.
% 7.13/7.53  Compiling...
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% 35.23/35.68  Compiling...
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% 35.23/35.68  Compiling...
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% 35.23/35.68  Compiling...
% 35.23/35.68  Loading plugin: done.
% 35.23/35.68  % % ------ Current options:
% 35.23/35.68  
% 35.23/35.68  % ------ Input Options
% 35.23/35.68  
% 35.23/35.68  % --out_options                         all
% 35.23/35.68  % --tptp_safe_out                       true
% 35.23/35.68  % --problem_path                        ""
% 35.23/35.68  % --include_path                        ""
% 35.23/35.68  % --clausifier                          .//eprover
% 35.23/35.68  % --clausifier_options                  --tstp-format  
% 35.23/35.68  % --stdin                               false
% 35.23/35.68  % --dbg_backtrace                       false
% 35.23/35.68  % --dbg_dump_prop_clauses               false
% 35.23/35.68  % --dbg_dump_prop_clauses_file          -
% 35.23/35.68  % --dbg_out_stat                        false
% 35.23/35.68  
% 35.23/35.68  % ------ General Options
% 35.23/35.68  
% 35.23/35.68  % --fof                                 false
% 35.23/35.68  % --time_out_real                       150.
% 35.23/35.68  % --time_out_prep_mult                  0.2
% 35.23/35.68  % --time_out_virtual                    -1.
% 35.23/35.68  % --schedule                            none
% 35.23/35.68  % --ground_splitting                    input
% 35.23/35.68  % --splitting_nvd                       16
% 35.23/35.68  % --non_eq_to_eq                        false
% 35.23/35.68  % --prep_gs_sim                         true
% 35.23/35.68  % --prep_unflatten                      false
% 35.23/35.68  % --prep_res_sim                        true
% 35.23/35.68  % --prep_upred                          true
% 35.23/35.68  % --res_sim_input                       true
% 35.23/35.68  % --clause_weak_htbl                    true
% 35.23/35.68  % --gc_record_bc_elim                   false
% 35.23/35.68  % --symbol_type_check                   false
% 35.23/35.68  % --clausify_out                        false
% 35.23/35.68  % --large_theory_mode                   false
% 35.23/35.68  % --prep_sem_filter                     none
% 35.23/35.68  % --prep_sem_filter_out                 false
% 35.23/35.68  % --preprocessed_out                    false
% 35.23/35.68  % --sub_typing                          false
% 35.23/35.68  % --brand_transform                     false
% 35.23/35.68  % --pure_diseq_elim                     true
% 35.23/35.68  % --min_unsat_core                      false
% 35.23/35.68  % --pred_elim                           true
% 35.23/35.68  % --add_important_lit                   false
% 35.23/35.68  % --soft_assumptions                    false
% 35.23/35.68  % --reset_solvers                       false
% 35.23/35.68  % --bc_imp_inh                          []
% 35.23/35.68  % --conj_cone_tolerance                 1.5
% 35.23/35.68  % --prolific_symb_bound                 500
% 35.23/35.68  % --lt_threshold                        2000
% 35.23/35.68  
% 35.23/35.68  % ------ SAT Options
% 35.23/35.68  
% 35.23/35.68  % --sat_mode                            false
% 35.23/35.68  % --sat_fm_restart_options              ""
% 35.23/35.68  % --sat_gr_def                          false
% 35.23/35.68  % --sat_epr_types                       true
% 35.23/35.68  % --sat_non_cyclic_types                false
% 35.23/35.68  % --sat_finite_models                   false
% 35.23/35.68  % --sat_fm_lemmas                       false
% 35.23/35.68  % --sat_fm_prep                         false
% 35.23/35.68  % --sat_fm_uc_incr                      true
% 35.23/35.68  % --sat_out_model                       small
% 35.23/35.68  % --sat_out_clauses                     false
% 35.23/35.68  
% 35.23/35.68  % ------ QBF Options
% 35.23/35.68  
% 35.23/35.68  % --qbf_mode                            false
% 35.23/35.68  % --qbf_elim_univ                       true
% 35.23/35.68  % --qbf_sk_in                           true
% 35.23/35.68  % --qbf_pred_elim                       true
% 35.23/35.68  % --qbf_split                           32
% 35.23/35.68  
% 35.23/35.68  % ------ BMC1 Options
% 35.23/35.68  
% 35.23/35.68  % --bmc1_incremental                    false
% 35.23/35.68  % --bmc1_axioms                         reachable_all
% 35.23/35.68  % --bmc1_min_bound                      0
% 35.23/35.68  % --bmc1_max_bound                      -1
% 35.23/35.68  % --bmc1_max_bound_default              -1
% 150.39/150.83  % --bmc1_symbol_reachability            true
% 150.39/150.83  % --bmc1_property_lemmas                false
% 150.39/150.83  % --bmc1_k_induction                    false
% 150.39/150.83  % --bmc1_non_equiv_states               false
% 150.39/150.83  % --bmc1_deadlock                       false
% 150.39/150.83  % --bmc1_ucm                            false
% 150.39/150.83  % --bmc1_add_unsat_core                 none
% 150.39/150.83  % --bmc1_unsat_core_children            false
% 150.39/150.83  % --bmc1_unsat_core_extrapolate_axioms  false
% 150.39/150.83  % --bmc1_out_stat                       full
% 150.39/150.83  % --bmc1_ground_init                    false
% 150.39/150.83  % --bmc1_pre_inst_next_state            false
% 150.39/150.83  % --bmc1_pre_inst_state                 false
% 150.39/150.83  % --bmc1_pre_inst_reach_state           false
% 150.39/150.83  % --bmc1_out_unsat_core                 false
% 150.39/150.83  % --bmc1_aig_witness_out                false
% 150.39/150.83  % --bmc1_verbose                        false
% 150.39/150.83  % --bmc1_dump_clauses_tptp              false
% 150.39/150.83  % --bmc1_dump_unsat_core_tptp           false
% 150.39/150.83  % --bmc1_dump_file                      -
% 150.39/150.83  % --bmc1_ucm_expand_uc_limit            128
% 150.39/150.83  % --bmc1_ucm_n_expand_iterations        6
% 150.39/150.83  % --bmc1_ucm_extend_mode                1
% 150.39/150.83  % --bmc1_ucm_init_mode                  2
% 150.39/150.83  % --bmc1_ucm_cone_mode                  none
% 150.39/150.83  % --bmc1_ucm_reduced_relation_type      0
% 150.39/150.83  % --bmc1_ucm_relax_model                4
% 150.39/150.83  % --bmc1_ucm_full_tr_after_sat          true
% 150.39/150.83  % --bmc1_ucm_expand_neg_assumptions     false
% 150.39/150.83  % --bmc1_ucm_layered_model              none
% 150.39/150.83  % --bmc1_ucm_max_lemma_size             10
% 150.39/150.83  
% 150.39/150.83  % ------ AIG Options
% 150.39/150.83  
% 150.39/150.83  % --aig_mode                            false
% 150.39/150.83  
% 150.39/150.83  % ------ Instantiation Options
% 150.39/150.83  
% 150.39/150.83  % --instantiation_flag                  true
% 150.39/150.83  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 150.39/150.83  % --inst_solver_per_active              750
% 150.39/150.83  % --inst_solver_calls_frac              0.5
% 150.39/150.83  % --inst_passive_queue_type             priority_queues
% 150.39/150.83  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.39/150.83  % --inst_passive_queues_freq            [25;2]
% 150.39/150.83  % --inst_dismatching                    true
% 150.39/150.83  % --inst_eager_unprocessed_to_passive   true
% 150.39/150.83  % --inst_prop_sim_given                 true
% 150.39/150.84  % --inst_prop_sim_new                   false
% 150.39/150.84  % --inst_orphan_elimination             true
% 150.39/150.84  % --inst_learning_loop_flag             true
% 150.39/150.84  % --inst_learning_start                 3000
% 150.39/150.84  % --inst_learning_factor                2
% 150.39/150.84  % --inst_start_prop_sim_after_learn     3
% 150.39/150.84  % --inst_sel_renew                      solver
% 150.39/150.84  % --inst_lit_activity_flag              true
% 150.39/150.84  % --inst_out_proof                      true
% 150.39/150.84  
% 150.39/150.84  % ------ Resolution Options
% 150.39/150.84  
% 150.39/150.84  % --resolution_flag                     true
% 150.39/150.84  % --res_lit_sel                         kbo_max
% 150.39/150.84  % --res_to_prop_solver                  none
% 150.39/150.84  % --res_prop_simpl_new                  false
% 150.39/150.84  % --res_prop_simpl_given                false
% 150.39/150.84  % --res_passive_queue_type              priority_queues
% 150.39/150.84  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.39/150.84  % --res_passive_queues_freq             [15;5]
% 150.39/150.84  % --res_forward_subs                    full
% 150.39/150.84  % --res_backward_subs                   full
% 150.39/150.84  % --res_forward_subs_resolution         true
% 150.39/150.84  % --res_backward_subs_resolution        true
% 150.39/150.84  % --res_orphan_elimination              false
% 150.39/150.84  % --res_time_limit                      1000.
% 150.39/150.84  % --res_out_proof                       true
% 150.39/150.84  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_62772e.s
% 150.39/150.84  % --modulo                              true
% 150.39/150.84  
% 150.39/150.84  % ------ Combination Options
% 150.39/150.84  
% 150.39/150.84  % --comb_res_mult                       1000
% 150.39/150.84  % --comb_inst_mult                      300
% 150.39/150.84  % ------ 
% 150.39/150.84  
% 150.39/150.84  
% 150.39/150.84  
% 150.39/150.84  % ------ Proving...
% 150.39/150.84  % 
% 150.39/150.84  
% 150.39/150.84  
% 150.39/150.84  % Time Out Real
% 150.39/150.84  
% 150.39/150.84  % ------                             Statistics
% 150.39/150.84  
% 150.39/150.84  % ------ General
% 150.39/150.84  
% 150.39/150.84  % num_of_input_clauses:                 6307
% 150.39/150.84  % num_of_input_neg_conjectures:         1
% 150.39/150.84  % num_of_splits:                        0
% 150.39/150.84  % num_of_split_atoms:                   0
% 150.39/150.84  % num_of_sem_filtered_clauses:          0
% 150.39/150.84  % num_of_subtypes:                      0
% 150.39/150.84  % monotx_restored_types:                0
% 150.39/150.84  % sat_num_of_epr_types:                 0
% 150.39/150.84  % sat_num_of_non_cyclic_types:          0
% 150.39/150.84  % sat_guarded_non_collapsed_types:      0
% 150.39/150.84  % is_epr:                               0
% 150.39/150.84  % is_horn:                              0
% 150.39/150.84  % has_eq:                               1
% 150.39/150.84  % num_pure_diseq_elim:                  0
% 150.39/150.84  % simp_replaced_by:                     0
% 150.39/150.84  % res_preprocessed:                     2
% 150.39/150.84  % prep_upred:                           0
% 150.39/150.84  % prep_unflattend:                      0
% 150.39/150.84  % pred_elim_cands:                      0
% 150.39/150.84  % pred_elim:                            0
% 150.39/150.84  % pred_elim_cl:                         0
% 150.39/150.84  % pred_elim_cycles:                     0
% 150.39/150.84  % forced_gc_time:                       0
% 150.39/150.84  % gc_basic_clause_elim:                 0
% 150.39/150.84  % parsing_time:                         0.18
% 150.39/150.84  % sem_filter_time:                      0.
% 150.39/150.84  % pred_elim_time:                       0.
% 150.39/150.84  % out_proof_time:                       0.
% 150.39/150.84  % monotx_time:                          0.
% 150.39/150.84  % subtype_inf_time:                     0.
% 150.39/150.84  % unif_index_cands_time:                0.101
% 150.39/150.84  % unif_index_add_time:                  0.04
% 150.39/150.84  % total_time:                           150.011
% 150.39/150.84  % num_of_symbols:                       380
% 150.39/150.84  % num_of_terms:                         653500
% 150.39/150.84  
% 150.39/150.84  % ------ Propositional Solver
% 150.39/150.84  
% 150.39/150.84  % prop_solver_calls:                    5
% 150.39/150.84  % prop_fast_solver_calls:               3
% 150.39/150.84  % prop_num_of_clauses:                  17392
% 150.39/150.84  % prop_preprocess_simplified:           41079
% 150.39/150.84  % prop_fo_subsumed:                     0
% 150.39/150.84  % prop_solver_time:                     0.003
% 150.39/150.84  % prop_fast_solver_time:                0.
% 150.39/150.84  % prop_unsat_core_time:                 0.
% 150.39/150.84  
% 150.39/150.84  % ------ QBF 
% 150.39/150.84  
% 150.39/150.84  % qbf_q_res:                            0
% 150.39/150.84  % qbf_num_tautologies:                  0
% 150.39/150.84  % qbf_prep_cycles:                      0
% 150.39/150.84  
% 150.39/150.84  % ------ BMC1
% 150.39/150.84  
% 150.39/150.84  % bmc1_current_bound:                   -1
% 150.39/150.84  % bmc1_last_solved_bound:               -1
% 150.39/150.84  % bmc1_unsat_core_size:                 -1
% 150.39/150.84  % bmc1_unsat_core_parents_size:         -1
% 150.39/150.84  % bmc1_merge_next_fun:                  0
% 150.39/150.84  % bmc1_unsat_core_clauses_time:         0.
% 150.39/150.84  
% 150.39/150.84  % ------ Instantiation
% 150.39/150.84  
% 150.39/150.84  % inst_num_of_clauses:                  11952
% 150.39/150.84  % inst_num_in_passive:                  9674
% 150.39/150.84  % inst_num_in_active:                   1434
% 150.39/150.84  % inst_num_in_unprocessed:              844
% 150.39/150.84  % inst_num_of_loops:                    1500
% 150.39/150.84  % inst_num_of_learning_restarts:        0
% 150.39/150.84  % inst_num_moves_active_passive:        65
% 150.39/150.84  % inst_lit_activity:                    501
% 150.39/150.84  % inst_lit_activity_moves:              1
% 150.39/150.84  % inst_num_tautologies:                 0
% 150.39/150.84  % inst_num_prop_implied:                0
% 150.39/150.84  % inst_num_existing_simplified:         0
% 150.39/150.84  % inst_num_eq_res_simplified:           0
% 150.39/150.84  % inst_num_child_elim:                  0
% 150.39/150.84  % inst_num_of_dismatching_blockings:    9304
% 150.39/150.84  % inst_num_of_non_proper_insts:         4772
% 150.39/150.84  % inst_num_of_duplicates:               6105
% 150.39/150.84  % inst_inst_num_from_inst_to_res:       0
% 150.39/150.84  % inst_dismatching_checking_time:       0.03
% 150.39/150.84  
% 150.39/150.84  % ------ Resolution
% 150.39/150.84  
% 150.39/150.84  % res_num_of_clauses:                   228654
% 150.39/150.84  % res_num_in_passive:                   218962
% 150.39/150.84  % res_num_in_active:                    5673
% 150.39/150.84  % res_num_of_loops:                     5883
% 150.39/150.84  % res_forward_subset_subsumed:          117472
% 150.39/150.84  % res_backward_subset_subsumed:         80
% 150.39/150.84  % res_forward_subsumed:                 2714
% 150.39/150.84  % res_backward_subsumed:                0
% 150.39/150.84  % res_forward_subsumption_resolution:   251
% 150.39/150.84  % res_backward_subsumption_resolution:  0
% 150.39/150.84  % res_clause_to_clause_subsumption:     245258
% 150.39/150.84  % res_orphan_elimination:               0
% 150.39/150.84  % res_tautology_del:                    3919
% 150.39/150.84  % res_num_eq_res_simplified:            0
% 150.39/150.84  % res_num_sel_changes:                  0
% 150.39/150.84  % res_moves_from_active_to_pass:        0
% 150.39/150.84  
% 150.39/150.84  % Status Unknown
% 150.48/151.18  % Orienting using strategy ClausalAll
% 150.48/151.18  % Orientation found
% 150.48/151.18  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_62772e.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_e14db0.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_b7721e | grep -v "SZS"
% 150.48/151.19  
% 150.48/151.19  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.48/151.19  
% 150.48/151.19  % 
% 150.48/151.19  % ------  iProver source info 
% 150.48/151.19  
% 150.48/151.19  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.48/151.19  % git: non_committed_changes: true
% 150.48/151.19  % git: last_make_outside_of_git: true
% 150.48/151.19  
% 150.48/151.19  % 
% 150.48/151.19  % ------ Input Options
% 150.48/151.19  
% 150.48/151.19  % --out_options                         all
% 150.48/151.19  % --tptp_safe_out                       true
% 150.48/151.19  % --problem_path                        ""
% 150.48/151.19  % --include_path                        ""
% 150.48/151.19  % --clausifier                          .//eprover
% 150.48/151.19  % --clausifier_options                  --tstp-format  
% 150.48/151.19  % --stdin                               false
% 150.48/151.19  % --dbg_backtrace                       false
% 150.48/151.19  % --dbg_dump_prop_clauses               false
% 150.48/151.19  % --dbg_dump_prop_clauses_file          -
% 150.48/151.19  % --dbg_out_stat                        false
% 150.48/151.19  
% 150.48/151.19  % ------ General Options
% 150.48/151.19  
% 150.48/151.19  % --fof                                 false
% 150.48/151.19  % --time_out_real                       150.
% 150.48/151.19  % --time_out_prep_mult                  0.2
% 150.48/151.19  % --time_out_virtual                    -1.
% 150.48/151.19  % --schedule                            none
% 150.48/151.19  % --ground_splitting                    input
% 150.48/151.19  % --splitting_nvd                       16
% 150.48/151.19  % --non_eq_to_eq                        false
% 150.48/151.19  % --prep_gs_sim                         true
% 150.48/151.19  % --prep_unflatten                      false
% 150.48/151.19  % --prep_res_sim                        true
% 150.48/151.19  % --prep_upred                          true
% 150.48/151.19  % --res_sim_input                       true
% 150.48/151.19  % --clause_weak_htbl                    true
% 150.48/151.19  % --gc_record_bc_elim                   false
% 150.48/151.19  % --symbol_type_check                   false
% 150.48/151.19  % --clausify_out                        false
% 150.48/151.19  % --large_theory_mode                   false
% 150.48/151.19  % --prep_sem_filter                     none
% 150.48/151.19  % --prep_sem_filter_out                 false
% 150.48/151.19  % --preprocessed_out                    false
% 150.48/151.19  % --sub_typing                          false
% 150.48/151.19  % --brand_transform                     false
% 150.48/151.19  % --pure_diseq_elim                     true
% 150.48/151.19  % --min_unsat_core                      false
% 150.48/151.19  % --pred_elim                           true
% 150.48/151.19  % --add_important_lit                   false
% 150.48/151.19  % --soft_assumptions                    false
% 150.48/151.19  % --reset_solvers                       false
% 150.48/151.19  % --bc_imp_inh                          []
% 150.48/151.19  % --conj_cone_tolerance                 1.5
% 150.48/151.19  % --prolific_symb_bound                 500
% 150.48/151.19  % --lt_threshold                        2000
% 150.48/151.19  
% 150.48/151.19  % ------ SAT Options
% 150.48/151.19  
% 150.48/151.19  % --sat_mode                            false
% 150.48/151.19  % --sat_fm_restart_options              ""
% 150.48/151.19  % --sat_gr_def                          false
% 150.48/151.19  % --sat_epr_types                       true
% 150.48/151.19  % --sat_non_cyclic_types                false
% 150.48/151.19  % --sat_finite_models                   false
% 150.48/151.19  % --sat_fm_lemmas                       false
% 150.48/151.19  % --sat_fm_prep                         false
% 150.48/151.19  % --sat_fm_uc_incr                      true
% 150.48/151.19  % --sat_out_model                       small
% 150.48/151.19  % --sat_out_clauses                     false
% 150.48/151.19  
% 150.48/151.19  % ------ QBF Options
% 150.48/151.19  
% 150.48/151.19  % --qbf_mode                            false
% 150.48/151.19  % --qbf_elim_univ                       true
% 150.48/151.19  % --qbf_sk_in                           true
% 150.48/151.19  % --qbf_pred_elim                       true
% 150.48/151.19  % --qbf_split                           32
% 150.48/151.19  
% 150.48/151.19  % ------ BMC1 Options
% 150.48/151.19  
% 150.48/151.19  % --bmc1_incremental                    false
% 150.48/151.19  % --bmc1_axioms                         reachable_all
% 150.48/151.19  % --bmc1_min_bound                      0
% 150.48/151.19  % --bmc1_max_bound                      -1
% 150.48/151.19  % --bmc1_max_bound_default              -1
% 150.48/151.19  % --bmc1_symbol_reachability            true
% 150.48/151.19  % --bmc1_property_lemmas                false
% 150.48/151.19  % --bmc1_k_induction                    false
% 150.48/151.19  % --bmc1_non_equiv_states               false
% 150.48/151.19  % --bmc1_deadlock                       false
% 150.48/151.19  % --bmc1_ucm                            false
% 150.48/151.19  % --bmc1_add_unsat_core                 none
% 150.48/151.19  % --bmc1_unsat_core_children            false
% 150.48/151.19  % --bmc1_unsat_core_extrapolate_axioms  false
% 150.48/151.19  % --bmc1_out_stat                       full
% 150.48/151.19  % --bmc1_ground_init                    false
% 150.48/151.19  % --bmc1_pre_inst_next_state            false
% 150.48/151.19  % --bmc1_pre_inst_state                 false
% 150.48/151.19  % --bmc1_pre_inst_reach_state           false
% 150.48/151.19  % --bmc1_out_unsat_core                 false
% 150.48/151.19  % --bmc1_aig_witness_out                false
% 150.48/151.19  % --bmc1_verbose                        false
% 150.48/151.19  % --bmc1_dump_clauses_tptp              false
% 161.20/161.63  % --bmc1_dump_unsat_core_tptp           false
% 161.20/161.63  % --bmc1_dump_file                      -
% 161.20/161.63  % --bmc1_ucm_expand_uc_limit            128
% 161.20/161.63  % --bmc1_ucm_n_expand_iterations        6
% 161.20/161.63  % --bmc1_ucm_extend_mode                1
% 161.20/161.63  % --bmc1_ucm_init_mode                  2
% 161.20/161.63  % --bmc1_ucm_cone_mode                  none
% 161.20/161.63  % --bmc1_ucm_reduced_relation_type      0
% 161.20/161.63  % --bmc1_ucm_relax_model                4
% 161.20/161.63  % --bmc1_ucm_full_tr_after_sat          true
% 161.20/161.63  % --bmc1_ucm_expand_neg_assumptions     false
% 161.20/161.63  % --bmc1_ucm_layered_model              none
% 161.20/161.63  % --bmc1_ucm_max_lemma_size             10
% 161.20/161.63  
% 161.20/161.63  % ------ AIG Options
% 161.20/161.63  
% 161.20/161.63  % --aig_mode                            false
% 161.20/161.63  
% 161.20/161.63  % ------ Instantiation Options
% 161.20/161.63  
% 161.20/161.63  % --instantiation_flag                  true
% 161.20/161.63  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 161.20/161.63  % --inst_solver_per_active              750
% 161.20/161.63  % --inst_solver_calls_frac              0.5
% 161.20/161.63  % --inst_passive_queue_type             priority_queues
% 161.20/161.63  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 161.20/161.63  % --inst_passive_queues_freq            [25;2]
% 161.20/161.63  % --inst_dismatching                    true
% 161.20/161.63  % --inst_eager_unprocessed_to_passive   true
% 161.20/161.63  % --inst_prop_sim_given                 true
% 161.20/161.63  % --inst_prop_sim_new                   false
% 161.20/161.63  % --inst_orphan_elimination             true
% 161.20/161.63  % --inst_learning_loop_flag             true
% 161.20/161.63  % --inst_learning_start                 3000
% 161.20/161.63  % --inst_learning_factor                2
% 161.20/161.63  % --inst_start_prop_sim_after_learn     3
% 161.20/161.63  % --inst_sel_renew                      solver
% 161.20/161.63  % --inst_lit_activity_flag              true
% 161.20/161.63  % --inst_out_proof                      true
% 161.20/161.63  
% 161.20/161.63  % ------ Resolution Options
% 161.20/161.63  
% 161.20/161.63  % --resolution_flag                     true
% 161.20/161.63  % --res_lit_sel                         kbo_max
% 161.20/161.63  % --res_to_prop_solver                  none
% 161.20/161.63  % --res_prop_simpl_new                  false
% 161.20/161.63  % --res_prop_simpl_given                false
% 161.20/161.63  % --res_passive_queue_type              priority_queues
% 161.20/161.63  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 161.20/161.63  % --res_passive_queues_freq             [15;5]
% 161.20/161.63  % --res_forward_subs                    full
% 161.20/161.63  % --res_backward_subs                   full
% 161.20/161.63  % --res_forward_subs_resolution         true
% 161.20/161.63  % --res_backward_subs_resolution        true
% 161.20/161.63  % --res_orphan_elimination              false
% 161.20/161.63  % --res_time_limit                      1000.
% 161.20/161.63  % --res_out_proof                       true
% 161.20/161.63  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_62772e.s
% 161.20/161.63  % --modulo                              true
% 161.20/161.63  
% 161.20/161.63  % ------ Combination Options
% 161.20/161.63  
% 161.20/161.63  % --comb_res_mult                       1000
% 161.20/161.63  % --comb_inst_mult                      300
% 161.20/161.63  % ------ 
% 161.20/161.63  
% 161.20/161.63  % ------ Parsing...% successful
% 161.20/161.63  
% 161.20/161.63  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e  pe_s  pe_e  snvd_s sp: 0 0s snvd_e % 
% 161.20/161.63  
% 161.20/161.63  % ------ Proving...
% 161.20/161.63  % ------ Problem Properties 
% 161.20/161.63  
% 161.20/161.63  % 
% 161.20/161.63  % EPR                                   false
% 161.20/161.63  % Horn                                  false
% 161.20/161.63  % Has equality                          true
% 161.20/161.63  
% 161.20/161.63  % % ------ Input Options Time Limit: Unbounded
% 161.20/161.63  
% 161.20/161.63  
% 161.20/161.63  Compiling...
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% 174.38/174.82  Loading plugin: done.
% 174.38/174.82  % % ------ Current options:
% 174.38/174.82  
% 174.38/174.82  % ------ Input Options
% 174.38/174.82  
% 174.38/174.82  % --out_options                         all
% 174.38/174.82  % --tptp_safe_out                       true
% 174.38/174.82  % --problem_path                        ""
% 174.38/174.82  % --include_path                        ""
% 174.38/174.82  % --clausifier                          .//eprover
% 174.38/174.82  % --clausifier_options                  --tstp-format  
% 174.38/174.82  % --stdin                               false
% 174.38/174.82  % --dbg_backtrace                       false
% 174.38/174.82  % --dbg_dump_prop_clauses               false
% 174.38/174.82  % --dbg_dump_prop_clauses_file          -
% 174.38/174.82  % --dbg_out_stat                        false
% 174.38/174.82  
% 174.38/174.82  % ------ General Options
% 174.38/174.82  
% 174.38/174.82  % --fof                                 false
% 174.38/174.82  % --time_out_real                       150.
% 174.38/174.82  % --time_out_prep_mult                  0.2
% 174.38/174.82  % --time_out_virtual                    -1.
% 174.38/174.82  % --schedule                            none
% 174.38/174.82  % --ground_splitting                    input
% 174.38/174.82  % --splitting_nvd                       16
% 174.38/174.82  % --non_eq_to_eq                        false
% 174.38/174.82  % --prep_gs_sim                         true
% 174.38/174.82  % --prep_unflatten                      false
% 174.38/174.82  % --prep_res_sim                        true
% 174.38/174.82  % --prep_upred                          true
% 174.38/174.82  % --res_sim_input                       true
% 174.38/174.82  % --clause_weak_htbl                    true
% 174.38/174.82  % --gc_record_bc_elim                   false
% 174.38/174.82  % --symbol_type_check                   false
% 174.38/174.82  % --clausify_out                        false
% 174.38/174.82  % --large_theory_mode                   false
% 174.38/174.82  % --prep_sem_filter                     none
% 174.38/174.82  % --prep_sem_filter_out                 false
% 174.38/174.82  % --preprocessed_out                    false
% 174.38/174.82  % --sub_typing                          false
% 174.38/174.82  % --brand_transform                     false
% 174.38/174.82  % --pure_diseq_elim                     true
% 174.38/174.82  % --min_unsat_core                      false
% 174.38/174.82  % --pred_elim                           true
% 174.38/174.82  % --add_important_lit                   false
% 174.38/174.82  % --soft_assumptions                    false
% 174.38/174.82  % --reset_solvers                       false
% 174.38/174.82  % --bc_imp_inh                          []
% 174.38/174.82  % --conj_cone_tolerance                 1.5
% 174.38/174.82  % --prolific_symb_bound                 500
% 174.38/174.82  % --lt_threshold                        2000
% 174.38/174.82  
% 174.38/174.82  % ------ SAT Options
% 174.38/174.82  
% 174.38/174.82  % --sat_mode                            false
% 174.38/174.82  % --sat_fm_restart_options              ""
% 174.38/174.82  % --sat_gr_def                          false
% 174.38/174.82  % --sat_epr_types                       true
% 174.38/174.82  % --sat_non_cyclic_types                false
% 174.38/174.82  % --sat_finite_models                   false
% 174.38/174.82  % --sat_fm_lemmas                       false
% 174.38/174.82  % --sat_fm_prep                         false
% 174.38/174.82  % --sat_fm_uc_incr                      true
% 174.38/174.82  % --sat_out_model                       small
% 174.38/174.82  % --sat_out_clauses                     false
% 174.38/174.82  
% 174.38/174.82  % ------ QBF Options
% 174.38/174.82  
% 174.38/174.82  % --qbf_mode                            false
% 174.38/174.82  % --qbf_elim_univ                       true
% 174.38/174.82  % --qbf_sk_in                           true
% 174.38/174.82  % --qbf_pred_elim                       true
% 174.38/174.82  % --qbf_split                           32
% 174.38/174.82  
% 174.38/174.82  % ------ BMC1 Options
% 174.38/174.82  
% 174.38/174.82  % --bmc1_incremental                    false
% 174.38/174.82  % --bmc1_axioms                         reachable_all
% 174.38/174.82  % --bmc1_min_bound                      0
% 174.38/174.82  % --bmc1_max_bound                      -1
% 174.38/174.82  % --bmc1_max_bound_default              -1
% 174.38/174.82  % --bmc1_symbol_reachability            true
% 174.38/174.82  % --bmc1_property_lemmas                false
% 174.38/174.82  % --bmc1_k_induction                    false
% 174.38/174.82  % --bmc1_non_equiv_states               false
% 174.38/174.82  % --bmc1_deadlock                       false
% 174.38/174.82  % --bmc1_ucm                            false
% 174.38/174.82  % --bmc1_add_unsat_core                 none
% 174.38/174.82  % --bmc1_unsat_core_children            false
% 174.38/174.82  % --bmc1_unsat_core_extrapolate_axioms  false
% 174.38/174.82  % --bmc1_out_stat                       full
% 174.38/174.82  % --bmc1_ground_init                    false
% 174.38/174.82  % --bmc1_pre_inst_next_state            false
% 174.38/174.82  % --bmc1_pre_inst_state                 false
% 174.38/174.82  % --bmc1_pre_inst_reach_state           false
% 174.38/174.82  % --bmc1_out_unsat_core                 false
% 174.38/174.82  % --bmc1_aig_witness_out                false
% 174.38/174.82  % --bmc1_verbose                        false
% 174.38/174.82  % --bmc1_dump_clauses_tptp              false
% 174.38/174.82  % --bmc1_dump_unsat_core_tptp           false
% 174.38/174.82  % --bmc1_dump_file                      -
% 174.38/174.82  % --bmc1_ucm_expand_uc_limit            128
% 174.38/174.82  % --bmc1_ucm_n_expand_iterations        6
% 174.38/174.82  % --bmc1_ucm_extend_mode                1
% 174.38/174.82  % --bmc1_ucm_init_mode                  2
% 174.38/174.82  % --bmc1_ucm_cone_mode                  none
% 174.38/174.82  % --bmc1_ucm_reduced_relation_type      0
% 174.38/174.82  % --bmc1_ucm_relax_model                4
% 174.38/174.82  % --bmc1_ucm_full_tr_after_sat          true
% 174.38/174.82  % --bmc1_ucm_expand_neg_assumptions     false
% 174.38/174.82  % --bmc1_ucm_layered_model              none
% 174.38/174.82  % --bmc1_ucm_max_lemma_size             10
% 174.38/174.82  
% 174.38/174.82  % ------ AIG Options
% 174.38/174.82  
% 174.38/174.82  % --aig_mode                            false
% 174.38/174.82  
% 174.38/174.82  % ------ Instantiation Options
% 174.38/174.82  
% 174.38/174.82  % --instantiation_flag                  true
% 174.38/174.82  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 174.38/174.82  % --inst_solver_per_active              750
% 174.38/174.82  % --inst_solver_calls_frac              0.5
% 174.38/174.82  % --inst_passive_queue_type             priority_queues
% 174.38/174.82  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 174.38/174.82  % --inst_passive_queues_freq            [25;2]
% 174.38/174.82  % --inst_dismatching                    true
% 174.38/174.82  % --inst_eager_unprocessed_to_passive   true
% 174.38/174.82  % --inst_prop_sim_given                 true
% 174.38/174.82  % --inst_prop_sim_new                   false
% 174.38/174.82  % --inst_orphan_elimination             true
% 174.38/174.82  % --inst_learning_loop_flag             true
% 174.38/174.82  % --inst_learning_start                 3000
% 174.38/174.82  % --inst_learning_factor                2
% 174.38/174.82  % --inst_start_prop_sim_after_learn     3
% 174.38/174.82  % --inst_sel_renew                      solver
% 174.38/174.82  % --inst_lit_activity_flag              true
% 174.38/174.82  % --inst_out_proof                      true
% 174.38/174.82  
% 174.38/174.82  % ------ Resolution Options
% 174.38/174.82  
% 174.38/174.82  % --resolution_flag                     true
% 174.38/174.82  % --res_lit_sel                         kbo_max
% 174.38/174.82  % --res_to_prop_solver                  none
% 174.38/174.82  % --res_prop_simpl_new                  false
% 174.38/174.82  % --res_prop_simpl_given                false
% 174.38/174.82  % --res_passive_queue_type              priority_queues
% 174.38/174.82  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 174.38/174.82  % --res_passive_queues_freq             [15;5]
% 174.38/174.82  % --res_forward_subs                    full
% 174.38/174.82  % --res_backward_subs                   full
% 174.38/174.82  % --res_forward_subs_resolution         true
% 174.38/174.82  % --res_backward_subs_resolution        true
% 174.38/174.82  % --res_orphan_elimination              false
% 174.38/174.82  % --res_time_limit                      1000.
% 174.38/174.82  % --res_out_proof                       true
% 174.38/174.82  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_62772e.s
% 174.38/174.82  % --modulo                              true
% 174.38/174.82  
% 174.38/174.82  % ------ Combination Options
% 174.38/174.82  
% 174.38/174.82  % --comb_res_mult                       1000
% 174.38/174.82  % --comb_inst_mult                      300
% 174.38/174.82  % ------ 
% 174.38/174.82  
% 174.38/174.82  
% 174.38/174.82  
% 174.38/174.82  % ------ Proving...
% 174.38/174.82  % 
% 174.38/174.82  
% 174.38/174.82  
% 174.38/174.82  %  Resolution empty clause
% 174.38/174.82  
% 174.38/174.82  % ------                             Statistics
% 174.38/174.82  
% 174.38/174.82  % ------ General
% 174.38/174.82  
% 174.38/174.82  % num_of_input_clauses:                 6307
% 174.38/174.82  % num_of_input_neg_conjectures:         1
% 174.38/174.82  % num_of_splits:                        0
% 174.38/174.82  % num_of_split_atoms:                   0
% 174.38/174.82  % num_of_sem_filtered_clauses:          0
% 174.38/174.82  % num_of_subtypes:                      0
% 174.38/174.82  % monotx_restored_types:                0
% 174.38/174.82  % sat_num_of_epr_types:                 0
% 174.38/174.82  % sat_num_of_non_cyclic_types:          0
% 174.38/174.82  % sat_guarded_non_collapsed_types:      0
% 174.38/174.82  % is_epr:                               0
% 174.38/174.82  % is_horn:                              0
% 174.38/174.82  % has_eq:                               1
% 174.38/174.82  % num_pure_diseq_elim:                  0
% 174.38/174.82  % simp_replaced_by:                     0
% 174.38/174.82  % res_preprocessed:                     2
% 174.38/174.82  % prep_upred:                           0
% 174.38/174.82  % prep_unflattend:                      0
% 174.38/174.82  % pred_elim_cands:                      0
% 174.38/174.82  % pred_elim:                            0
% 174.38/174.82  % pred_elim_cl:                         0
% 174.38/174.82  % pred_elim_cycles:                     0
% 174.38/174.82  % forced_gc_time:                       0
% 174.38/174.82  % gc_basic_clause_elim:                 0
% 174.38/174.82  % parsing_time:                         0.124
% 174.38/174.83  % sem_filter_time:                      0.
% 174.38/174.83  % pred_elim_time:                       0.
% 174.38/174.83  % out_proof_time:                       0.
% 174.38/174.83  % monotx_time:                          0.
% 174.38/174.83  % subtype_inf_time:                     0.
% 174.38/174.83  % unif_index_cands_time:                0.
% 174.38/174.83  % unif_index_add_time:                  0.004
% 174.38/174.83  % total_time:                           23.637
% 174.38/174.83  % num_of_symbols:                       380
% 174.38/174.83  % num_of_terms:                         10895
% 174.38/174.83  
% 174.38/174.83  % ------ Propositional Solver
% 174.38/174.83  
% 174.38/174.83  % prop_solver_calls:                    1
% 174.38/174.83  % prop_fast_solver_calls:               3
% 174.38/174.83  % prop_num_of_clauses:                  6475
% 174.38/174.83  % prop_preprocess_simplified:           18385
% 174.38/174.83  % prop_fo_subsumed:                     0
% 174.38/174.83  % prop_solver_time:                     0.
% 174.38/174.83  % prop_fast_solver_time:                0.
% 174.38/174.83  % prop_unsat_core_time:                 0.
% 174.38/174.83  
% 174.38/174.83  % ------ QBF 
% 174.38/174.83  
% 174.38/174.83  % qbf_q_res:                            0
% 174.38/174.83  % qbf_num_tautologies:                  0
% 174.38/174.83  % qbf_prep_cycles:                      0
% 174.38/174.83  
% 174.38/174.83  % ------ BMC1
% 174.38/174.83  
% 174.38/174.83  % bmc1_current_bound:                   -1
% 174.38/174.83  % bmc1_last_solved_bound:               -1
% 174.38/174.83  % bmc1_unsat_core_size:                 -1
% 174.38/174.83  % bmc1_unsat_core_parents_size:         -1
% 174.38/174.83  % bmc1_merge_next_fun:                  0
% 174.38/174.83  % bmc1_unsat_core_clauses_time:         0.
% 174.38/174.83  
% 174.38/174.83  % ------ Instantiation
% 174.38/174.83  
% 174.38/174.83  % inst_num_of_clauses:                  6176
% 174.38/174.83  % inst_num_in_passive:                  0
% 174.38/174.83  % inst_num_in_active:                   0
% 174.38/174.83  % inst_num_in_unprocessed:              6307
% 174.38/174.83  % inst_num_of_loops:                    0
% 174.38/174.83  % inst_num_of_learning_restarts:        0
% 174.38/174.83  % inst_num_moves_active_passive:        0
% 174.38/174.83  % inst_lit_activity:                    0
% 174.38/174.83  % inst_lit_activity_moves:              0
% 174.38/174.83  % inst_num_tautologies:                 0
% 174.38/174.83  % inst_num_prop_implied:                0
% 174.38/174.83  % inst_num_existing_simplified:         0
% 174.38/174.83  % inst_num_eq_res_simplified:           0
% 174.38/174.83  % inst_num_child_elim:                  0
% 174.38/174.83  % inst_num_of_dismatching_blockings:    0
% 174.38/174.83  % inst_num_of_non_proper_insts:         0
% 174.38/174.83  % inst_num_of_duplicates:               0
% 174.38/174.83  % inst_inst_num_from_inst_to_res:       0
% 174.38/174.83  % inst_dismatching_checking_time:       0.
% 174.38/174.83  
% 174.38/174.83  % ------ Resolution
% 174.38/174.83  
% 174.38/174.83  % res_num_of_clauses:                   6591
% 174.38/174.83  % res_num_in_passive:                   23
% 174.38/174.83  % res_num_in_active:                    2497
% 174.38/174.83  % res_num_of_loops:                     2
% 174.38/174.83  % res_forward_subset_subsumed:          3338
% 174.38/174.83  % res_backward_subset_subsumed:         0
% 174.38/174.83  % res_forward_subsumed:                 0
% 174.38/174.83  % res_backward_subsumed:                0
% 174.38/174.83  % res_forward_subsumption_resolution:   0
% 174.38/174.83  % res_backward_subsumption_resolution:  0
% 174.38/174.83  % res_clause_to_clause_subsumption:     0
% 174.38/174.83  % res_orphan_elimination:               0
% 174.38/174.83  % res_tautology_del:                    0
% 174.38/174.83  % res_num_eq_res_simplified:            0
% 174.38/174.83  % res_num_sel_changes:                  0
% 174.38/174.83  % res_moves_from_active_to_pass:        0
% 174.38/174.83  
% 174.38/174.83  % Status Unsatisfiable
% 174.38/174.83  % SZS status Unsatisfiable
% 174.38/174.83  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------