%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWV908-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n026.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 19:23:13 EDT 2022
% Result : Unsatisfiable 5.68s 5.96s
% Output : CNFRefutation 5.68s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)),
input ).
fof(cls_ATP__Linkup_OCOMBB__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R))
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).
cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
c_COMBC(V_P,V_Q,V_R,T_b,T_c,T_a) = hAPP(hAPP(V_P,V_R),V_Q),
input ).
fof(cls_ATP__Linkup_OCOMBC__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( c_COMBC(V_P,V_Q,V_R,T_b,T_c,T_a) = hAPP(hAPP(V_P,V_R),V_Q)
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0]) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
input ).
fof(clsarity_bool__HOL_Oord_0,plain,
( class_HOL_Oord(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__HOL_Oord]) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
input ).
fof(clsarity_bool__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Obot]) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
input ).
fof(clsarity_bool__Orderings_Otop_0,plain,
( class_Orderings_Otop(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Otop]) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Oorder]) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Olattice_0,plain,
( class_Lattices_Olattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Olattice]) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Opreorder]) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
input ).
fof(clsarity_bool__Finite__Set_Ofinite_Ofinite_0,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Obounded__lattice_0,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice]) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Oupper__semilattice_0,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice]) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat),
input ).
fof(clsarity_nat__HOL_Oord_0,plain,
( class_HOL_Oord(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__HOL_Oord]) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
input ).
fof(clsarity_nat__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Obot]) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Olattice_0,plain,
( class_Lattices_Olattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Olattice]) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Oupper__semilattice_0,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice]) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)),
input ).
fof(cls_COMBB__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R))
| $false ),
inference(orientation,[status(thm)],[cls_COMBB__def_0]) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a),
input ).
fof(cls_image__image_0_0,plain,
! [T_a,T_b,T_c,V_A,V_f,V_g] :
( c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_image__image_0]) ).
cnf(cls_the_Osimps_0,axiom,
hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x,
input ).
fof(cls_the_Osimps_0_0,plain,
! [T_a,V_x] :
( hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_the_Osimps_0]) ).
cnf(cls_finite__dom__body_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
input ).
fof(cls_finite__dom__body_0_0,plain,
( c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| $false ),
inference(orientation,[status(thm)],[cls_finite__dom__body_0]) ).
cnf(cls_range__composition_0,axiom,
c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a),
input ).
fof(cls_range__composition_0_0,plain,
! [T_a,T_b,T_c,V_f,V_g] :
( c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_range__composition_0]) ).
cnf(cls_MGT__def__raw_0,axiom,
hAPP(c_Hoare__Mirabelle_OMGT,v_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),v_c),c_Natural_Oevalc(v_c)),
input ).
fof(cls_MGT__def__raw_0_0,plain,
( hAPP(c_Hoare__Mirabelle_OMGT,v_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),v_c),c_Natural_Oevalc(v_c))
| $false ),
inference(orientation,[status(thm)],[cls_MGT__def__raw_0]) ).
cnf(cls_WT_OAssign_0,axiom,
c_Com_OWT(c_Com_Ocom_OAss(V_X,V_a)),
input ).
fof(cls_WT_OAssign_0_0,plain,
! [V_X,V_a] :
( c_Com_OWT(c_Com_Ocom_OAss(V_X,V_a))
| $false ),
inference(orientation,[status(thm)],[cls_WT_OAssign_0]) ).
cnf(cls_WT_OSkip_0,axiom,
c_Com_OWT(c_Com_Ocom_OSKIP),
input ).
fof(cls_WT_OSkip_0_0,plain,
( c_Com_OWT(c_Com_Ocom_OSKIP)
| $false ),
inference(orientation,[status(thm)],[cls_WT_OSkip_0]) ).
cnf(cls_dom__const_0,axiom,
c_Map_Odom(c_COMBK(hAPP(c_Option_Ooption_OSome(T_b),V_y),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),
input ).
fof(cls_dom__const_0_0,plain,
! [T_a,T_b,V_y] :
( c_Map_Odom(c_COMBK(hAPP(c_Option_Ooption_OSome(T_b),V_y),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_dom__const_0]) ).
cnf(cls_empty_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a),
input ).
fof(cls_empty_0_0,plain,
! [T_a,V_G] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty_0]) ).
cnf(cls_com_Osimps_I18_J_0,axiom,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H),
input ).
fof(cls_com_Osimps_I18_J_0_0,plain,
! [V_pname_H] :
( c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I18_J_0]) ).
cnf(cls_com_Osimps_I70_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,hAPP(c_Com_Ocom_OBODY,V_pname),T_a) = hAPP(V_f7,V_pname),
input ).
fof(cls_com_Osimps_I70_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_pname] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,hAPP(c_Com_Ocom_OBODY,V_pname),T_a) = hAPP(V_f7,V_pname)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I70_J_0]) ).
cnf(cls_com_Osimps_I62_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I62_J_0_0,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( hAPP(c_Com_Ocom_OBODY,V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I62_J_0]) ).
cnf(cls_com_Osimps_I40_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
input ).
fof(cls_com_Osimps_I40_J_0_0,plain,
! [V_com,V_fun,V_loc,V_pname_H] :
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I40_J_0]) ).
cnf(cls_com_Osimps_I48_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
input ).
fof(cls_com_Osimps_I48_J_0_0,plain,
! [V_com1,V_com2,V_pname_H] :
( c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I48_J_0]) ).
cnf(cls_com_Osimps_I49_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
input ).
fof(cls_com_Osimps_I49_J_0_0,plain,
! [V_com1,V_com2,V_pname_H] :
( hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I49_J_0]) ).
cnf(cls_com_Osimps_I63_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != hAPP(c_Com_Ocom_OBODY,V_pname),
input ).
fof(cls_com_Osimps_I63_J_0_0,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != hAPP(c_Com_Ocom_OBODY,V_pname)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I63_J_0]) ).
cnf(cls_com_Osimps_I59_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OWhile(V_fun,V_com),
input ).
fof(cls_com_Osimps_I59_J_0_0,plain,
! [V_com,V_fun,V_pname_H] :
( hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OWhile(V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I59_J_0]) ).
cnf(cls_com_Osimps_I41_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com),
input ).
fof(cls_com_Osimps_I41_J_0_0,plain,
! [V_com,V_fun,V_loc,V_pname_H] :
( hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I41_J_0]) ).
cnf(cls_com_Osimps_I30_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
input ).
fof(cls_com_Osimps_I30_J_0_0,plain,
! [V_fun,V_pname_H,V_vname] :
( c_Com_Ocom_OAss(V_vname,V_fun) != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I30_J_0]) ).
cnf(cls_com_Osimps_I31_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OAss(V_vname,V_fun),
input ).
fof(cls_com_Osimps_I31_J_0_0,plain,
! [V_fun,V_pname_H,V_vname] :
( hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OAss(V_vname,V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I31_J_0]) ).
cnf(cls_com_Osimps_I54_J_0,axiom,
c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
input ).
fof(cls_com_Osimps_I54_J_0_0,plain,
! [V_com1,V_com2,V_fun,V_pname_H] :
( c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I54_J_0]) ).
cnf(cls_com_Osimps_I55_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2),
input ).
fof(cls_com_Osimps_I55_J_0_0,plain,
! [V_com1,V_com2,V_fun,V_pname_H] :
( hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I55_J_0]) ).
cnf(cls_com_Orecs_I7_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,hAPP(c_Com_Ocom_OBODY,V_pname),T_a) = hAPP(V_f7,V_pname),
input ).
fof(cls_com_Orecs_I7_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_pname] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,hAPP(c_Com_Ocom_OBODY,V_pname),T_a) = hAPP(V_f7,V_pname)
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I7_J_0]) ).
cnf(cls_com_Osimps_I58_J_0,axiom,
c_Com_Ocom_OWhile(V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H),
input ).
fof(cls_com_Osimps_I58_J_0_0,plain,
! [V_com,V_fun,V_pname_H] :
( c_Com_Ocom_OWhile(V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I58_J_0]) ).
cnf(cls_com_Osimps_I19_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I19_J_0_0,plain,
! [V_pname_H] :
( hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I19_J_0]) ).
cnf(cls_option__map__Some_0,axiom,
c_Option_Omap(V_f,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_b,T_a) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f,V_x)),
input ).
fof(cls_option__map__Some_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Option_Omap(V_f,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_b,T_a) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f,V_x))
| $false ),
inference(orientation,[status(thm)],[cls_option__map__Some_0]) ).
cnf(cls_option_Osimps_I2_J_0,axiom,
c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H),
input ).
fof(cls_option_Osimps_I2_J_0_0,plain,
! [T_a,V_a_H] :
( c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I2_J_0]) ).
cnf(cls_not__Some__eq_1,axiom,
c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y),
input ).
fof(cls_not__Some__eq_1_0,plain,
! [T_a,V_y] :
( c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y)
| $false ),
inference(orientation,[status(thm)],[cls_not__Some__eq_1]) ).
cnf(cls_option_Osimps_I5_J_0,axiom,
c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a),
input ).
fof(cls_option_Osimps_I5_J_0_0,plain,
! [T_a,T_b,V_a,V_f1,V_f2] :
( c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I5_J_0]) ).
cnf(cls_option_Osimps_I3_J_0,axiom,
hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a),
input ).
fof(cls_option_Osimps_I3_J_0_0,plain,
! [T_a,V_a_H] :
( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I3_J_0]) ).
cnf(cls_not__None__eq_1,axiom,
hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a),
input ).
fof(cls_not__None__eq_1_0,plain,
! [T_a,V_xa] :
( hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__None__eq_1]) ).
cnf(cls_is__none__code_I2_J_0,axiom,
~ c_Option_Ois__none(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a),
input ).
fof(cls_is__none__code_I2_J_0_0,plain,
! [T_a,V_x] :
( ~ c_Option_Ois__none(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_is__none__code_I2_J_0]) ).
cnf(cls_inj__Some_0,axiom,
c_Fun_Oinj__on(c_Option_Ooption_OSome(T_a),V_A,T_a,tc_Option_Ooption(T_a)),
input ).
fof(cls_inj__Some_0_0,plain,
! [T_a,V_A] :
( c_Fun_Oinj__on(c_Option_Ooption_OSome(T_a),V_A,T_a,tc_Option_Ooption(T_a))
| $false ),
inference(orientation,[status(thm)],[cls_inj__Some_0]) ).
cnf(cls_map__upd__Some__unfold_3,axiom,
hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x),
input ).
fof(cls_map__upd__Some__unfold_3_0,plain,
! [T_a,T_aa,V_m,V_x,V_xa] :
( hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x)
| $false ),
inference(orientation,[status(thm)],[cls_map__upd__Some__unfold_3]) ).
cnf(cls_option_Orecs_I2_J_0,axiom,
c_Option_Ooption_Ooption__rec(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a),
input ).
fof(cls_option_Orecs_I2_J_0_0,plain,
! [T_a,T_b,V_a,V_f1,V_f2] :
( c_Option_Ooption_Ooption__rec(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Orecs_I2_J_0]) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a),
input ).
fof(cls_empty__is__image_1_0,plain,
! [T_a,T_b,V_f] :
( c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_empty__is__image_1]) ).
cnf(cls_image__id_0,axiom,
c_Set_Oimage(c_Fun_Oid(T_a),V_Y,T_a,T_a) = V_Y,
input ).
fof(cls_image__id_0_0,plain,
! [T_a,V_Y] :
( c_Set_Oimage(c_Fun_Oid(T_a),V_Y,T_a,T_a) = V_Y
| $false ),
inference(orientation,[status(thm)],[cls_image__id_0]) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I12_J_0_0,plain,
! [V_com1_H,V_com2_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I12_J_0]) ).
cnf(cls_com_Osimps_I42_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I42_J_0_0,plain,
! [V_com,V_fun,V_fun_H,V_loc,V_pname_H,V_vname_H] :
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I42_J_0]) ).
cnf(cls_Un__empty_2,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__empty_2_0,plain,
! [T_a] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty_2]) ).
cnf(cls_com_Osimps_I9_J_0,axiom,
c_Com_Ocom_OAss(V_vname_H,V_fun_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I9_J_0_0,plain,
! [V_fun_H,V_vname_H] :
( c_Com_Ocom_OAss(V_vname_H,V_fun_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I9_J_0]) ).
cnf(cls_com_Osimps_I68_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCond(V_fun,V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(V_f5,V_fun),V_com1),V_com2),
input ).
fof(cls_com_Osimps_I68_J_0_0,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCond(V_fun,V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(V_f5,V_fun),V_com1),V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I68_J_0]) ).
cnf(cls_singleton__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
input ).
fof(cls_singleton__iff_1_0,plain,
! [T_a,V_x] :
( c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_singleton__iff_1]) ).
cnf(cls_com_Osimps_I21_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I21_J_0_0,plain,
! [V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I21_J_0]) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__refl_0_0,plain,
! [T_a,V_A] :
( c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__refl_0]) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)),
input ).
fof(cls_equalityE_0_0,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_equalityE_0]) ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n),
input ).
fof(cls_n__not__Suc__n_0_0,plain,
! [V_n] :
( V_n != c_Suc(V_n)
| $false ),
inference(orientation,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n,
input ).
fof(cls_Suc__n__not__n_0_0,plain,
! [V_n] :
( c_Suc(V_n) != V_n
| $false ),
inference(orientation,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(cls_com_Osimps_I47_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
input ).
fof(cls_com_Osimps_I47_J_0_0,plain,
! [V_com1,V_com2,V_com_H,V_fun_H] :
( c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSemi(V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I47_J_0]) ).
cnf(cls_com_Osimps_I20_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I20_J_0_0,plain,
! [V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I20_J_0]) ).
cnf(cls_map__add__upd_0,axiom,
c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),
input ).
fof(cls_map__add__upd_0_0,plain,
! [T_a,T_b,V_f,V_g,V_x,V_y] :
( c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b))
| $false ),
inference(orientation,[status(thm)],[cls_map__add__upd_0]) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
input ).
fof(cls_insert__code_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_insert__code_1]) ).
cnf(cls_hoare__derivs_OSkip_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSKIP),V_P),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a),
input ).
fof(cls_hoare__derivs_OSkip_0_0,plain,
! [T_a,V_G,V_P] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSKIP),V_P),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_hoare__derivs_OSkip_0]) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I13_J_0_0,plain,
! [V_com1_H,V_com2_H] :
( c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I13_J_0]) ).
cnf(cls_com_Osimps_I33_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OAss(V_vname,V_fun),
input ).
fof(cls_com_Osimps_I33_J_0_0,plain,
! [V_fun,V_fun_H,V_pname_H,V_vname,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OAss(V_vname,V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I33_J_0]) ).
cnf(cls_subset__UNIV_0,axiom,
c_lessequals(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__UNIV_0_0,plain,
! [T_a,V_A] :
( c_lessequals(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__UNIV_0]) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_ex__in__conv_0_0,plain,
! [T_a,V_x] :
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_ex__in__conv_0]) ).
cnf(cls_empty__iff_0,axiom,
~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_empty__iff_0_0,plain,
! [T_a,V_c] :
( ~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty__iff_0]) ).
cnf(cls_emptyE_0,axiom,
~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_emptyE_0_0,plain,
! [T_a,V_a] :
( ~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_emptyE_0]) ).
cnf(cls_com_Osimps_I69_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OWhile(V_fun,V_com),T_a) = hAPP(hAPP(V_f6,V_fun),V_com),
input ).
fof(cls_com_Osimps_I69_J_0_0,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OWhile(V_fun,V_com),T_a) = hAPP(hAPP(V_f6,V_fun),V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I69_J_0]) ).
cnf(cls_com_Osimps_I66_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OLocal(V_loc,V_fun,V_com),T_a) = hAPP(hAPP(hAPP(V_f3,V_loc),V_fun),V_com),
input ).
fof(cls_com_Osimps_I66_J_0_0,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_loc] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OLocal(V_loc,V_fun,V_com),T_a) = hAPP(hAPP(hAPP(V_f3,V_loc),V_fun),V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I66_J_0]) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
input ).
fof(cls_empty__not__insert_0_0,plain,
! [T_a,V_A,V_a] :
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty__not__insert_0]) ).
cnf(cls_com_Osimps_I29_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun),
input ).
fof(cls_com_Osimps_I29_J_0_0,plain,
! [V_com_H,V_fun,V_fun_H,V_vname] :
( c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I29_J_0]) ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__empty_1_0,plain,
! [T_a] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__empty_1]) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f,
input ).
fof(cls_fun__upd__idem__iff_1_0,plain,
! [T_a,T_aa,V_f,V_x] :
( c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__idem__iff_1]) ).
cnf(cls_fun__upd__apply_0,axiom,
hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y,
input ).
fof(cls_fun__upd__apply_0_0,plain,
! [T_a,T_aa,V_f,V_x,V_y] :
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__apply_0]) ).
cnf(cls_fun__upd__triv_0,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f,
input ).
fof(cls_fun__upd__triv_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__triv_0]) ).
cnf(cls_fun__upd__same_0,axiom,
hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y,
input ).
fof(cls_fun__upd__same_0_0,plain,
! [T_a,T_b,V_f,V_x,V_y] :
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__same_0]) ).
cnf(cls_fun__upd__idem_0,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f,
input ).
fof(cls_fun__upd__idem_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__idem_0]) ).
cnf(cls_com_Osimps_I8_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I8_J_0_0,plain,
! [V_fun_H,V_vname_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I8_J_0]) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__empty_0_0,plain,
! [T_a,T_b,V_f] :
( c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__empty_0]) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a),
input ).
fof(cls_image__insert_0_0,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_image__insert_0]) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__Un_0]) ).
cnf(cls_com_Orecs_I5_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCond(V_fun,V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5,V_fun),V_com1),V_com2),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com1,T_a)),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com2,T_a)),
input ).
fof(cls_com_Orecs_I5_J_0_0,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCond(V_fun,V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5,V_fun),V_com1),V_com2),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com1,T_a)),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com2,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I5_J_0]) ).
cnf(cls_id__apply_0,axiom,
hAPP(c_Fun_Oid(T_a),V_x) = V_x,
input ).
fof(cls_id__apply_0_0,plain,
! [T_a,V_x] :
( hAPP(c_Fun_Oid(T_a),V_x) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_id__apply_0]) ).
cnf(cls_com_Orecs_I6_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OWhile(V_fun,V_com),T_a) = hAPP(hAPP(hAPP(V_f6,V_fun),V_com),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com,T_a)),
input ).
fof(cls_com_Orecs_I6_J_0_0,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OWhile(V_fun,V_com),T_a) = hAPP(hAPP(hAPP(V_f6,V_fun),V_com),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I6_J_0]) ).
cnf(cls_com_Osimps_I27_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun),
input ).
fof(cls_com_Osimps_I27_J_0_0,plain,
! [V_com1_H,V_com2_H,V_fun,V_fun_H,V_vname] :
( c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I27_J_0]) ).
cnf(cls_com_Orecs_I2_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OAss(V_vname,V_fun),T_a) = hAPP(hAPP(V_f2,V_vname),V_fun),
input ).
fof(cls_com_Orecs_I2_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_vname] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OAss(V_vname,V_fun),T_a) = hAPP(hAPP(V_f2,V_vname),V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I2_J_0]) ).
cnf(cls_com_Osimps_I50_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I50_J_0_0,plain,
! [V_com1,V_com2,V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I50_J_0]) ).
cnf(cls_MGT__def_0,axiom,
hAPP(c_Hoare__Mirabelle_OMGT,V_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),V_c),c_Natural_Oevalc(V_c)),
input ).
fof(cls_MGT__def_0_0,plain,
! [V_c] :
( hAPP(c_Hoare__Mirabelle_OMGT,V_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),V_c),c_Natural_Oevalc(V_c))
| $false ),
inference(orientation,[status(thm)],[cls_MGT__def_0]) ).
cnf(cls_com_Osimps_I53_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2),
input ).
fof(cls_com_Osimps_I53_J_0_0,plain,
! [V_com1,V_com2,V_com_H,V_fun,V_fun_H] :
( c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I53_J_0]) ).
cnf(cls_com_Osimps_I15_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I15_J_0_0,plain,
! [V_com1_H,V_com2_H,V_fun_H] :
( c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I15_J_0]) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__absorb_0]) ).
cnf(cls_option__map__None_0,axiom,
c_Option_Omap(V_f,c_Option_Ooption_ONone(T_b),T_b,T_a) = c_Option_Ooption_ONone(T_a),
input ).
fof(cls_option__map__None_0_0,plain,
! [T_a,T_b,V_f] :
( c_Option_Omap(V_f,c_Option_Ooption_ONone(T_b),T_b,T_a) = c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_option__map__None_0]) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_insert__is__Un_0_0,plain,
! [T_a,V_A,V_a] :
( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_insert__is__Un_0]) ).
cnf(cls_com_Orecs_I8_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCall(V_vname,V_pname,V_fun),T_a) = hAPP(hAPP(hAPP(V_f8,V_vname),V_pname),V_fun),
input ).
fof(cls_com_Orecs_I8_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_pname,V_vname] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCall(V_vname,V_pname,V_fun),T_a) = hAPP(hAPP(hAPP(V_f8,V_vname),V_pname),V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I8_J_0]) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__commute_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__commute_0]) ).
cnf(cls_com_Osimps_I34_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I34_J_0_0,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_loc] :
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I34_J_0]) ).
cnf(cls_com_Osimps_I67_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSemi(V_com1,V_com2),T_a) = hAPP(hAPP(V_f4,V_com1),V_com2),
input ).
fof(cls_com_Osimps_I67_J_0_0,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSemi(V_com1,V_com2),T_a) = hAPP(hAPP(V_f4,V_com1),V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I67_J_0]) ).
cnf(cls_com_Osimps_I61_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OWhile(V_fun,V_com),
input ).
fof(cls_com_Osimps_I61_J_0_0,plain,
! [V_com,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OWhile(V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I61_J_0]) ).
cnf(cls_com_Osimps_I43_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com),
input ).
fof(cls_com_Osimps_I43_J_0_0,plain,
! [V_com,V_fun,V_fun_H,V_loc,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I43_J_0]) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__constant__conv_0_0,plain,
! [T_a,T_b,V_c] :
( c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__constant__conv_0]) ).
cnf(cls_dom__eq__singleton__conv_1,axiom,
c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_dom__eq__singleton__conv_1_0,plain,
! [T_a,T_b,V_x,V_xa] :
( c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_dom__eq__singleton__conv_1]) ).
cnf(cls_com_Osimps_I32_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I32_J_0_0,plain,
! [V_fun,V_fun_H,V_pname_H,V_vname,V_vname_H] :
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I32_J_0]) ).
cnf(cls_com_Osimps_I14_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I14_J_0_0,plain,
! [V_com1_H,V_com2_H,V_fun_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I14_J_0]) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__upper1_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper1_0]) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__upper2_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper2_0]) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__assoc_0]) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__commute_0]) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b),
input ).
fof(cls_inj__on__empty_0_0,plain,
! [T_a,T_b,V_f] :
( c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_inj__on__empty_0]) ).
cnf(cls_option_Orecs_I1_J_0,axiom,
c_Option_Ooption_Ooption__rec(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1,
input ).
fof(cls_option_Orecs_I1_J_0_0,plain,
! [T_a,T_b,V_f1,V_f2] :
( c_Option_Ooption_Ooption__rec(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_option_Orecs_I1_J_0]) ).
cnf(cls_option_Osimps_I4_J_0,axiom,
c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1,
input ).
fof(cls_option_Osimps_I4_J_0_0,plain,
! [T_a,T_b,V_f1,V_f2] :
( c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I4_J_0]) ).
cnf(cls_is__none__def_1,axiom,
c_Option_Ois__none(c_Option_Ooption_ONone(T_a),T_a),
input ).
fof(cls_is__none__def_1_0,plain,
! [T_a] :
( c_Option_Ois__none(c_Option_Ooption_ONone(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_is__none__def_1]) ).
cnf(cls_evaln_OSkip_0,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s),
input ).
fof(cls_evaln_OSkip_0_0,plain,
! [V_n,V_s] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s)
| $false ),
inference(orientation,[status(thm)],[cls_evaln_OSkip_0]) ).
cnf(cls_com_Osimps_I11_J_0,axiom,
c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I11_J_0_0,plain,
! [V_com_H,V_fun_H,V_loc_H] :
( c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I11_J_0]) ).
cnf(cls_com_Osimps_I25_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun),
input ).
fof(cls_com_Osimps_I25_J_0_0,plain,
! [V_com1_H,V_com2_H,V_fun,V_vname] :
( c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I25_J_0]) ).
cnf(cls_evalc_OSkip_0,axiom,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
input ).
fof(cls_evalc_OSkip_0_0,plain,
! [V_s] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s))
| $false ),
inference(orientation,[status(thm)],[cls_evalc_OSkip_0]) ).
cnf(cls_com_Osimps_I60_J_0,axiom,
c_Com_Ocom_OWhile(V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I60_J_0_0,plain,
! [V_com,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OWhile(V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I60_J_0]) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)),
input ).
fof(cls_top1I_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_top1I_0]) ).
cnf(cls_fun__upd__upd_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b),
input ).
fof(cls_fun__upd__upd_0_0,plain,
! [T_a,T_b,V_f,V_x,V_y,V_z] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__upd_0]) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_UNIV__not__empty_0_0,plain,
! [T_a] :
( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_UNIV__not__empty_0]) ).
cnf(cls_com_Osimps_I10_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I10_J_0_0,plain,
! [V_com_H,V_fun_H,V_loc_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I10_J_0]) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
input ).
fof(cls_bot1E_0_0,plain,
! [T_a,V_x] :
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_bot1E_0]) ).
cnf(cls_com_Osimps_I16_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I16_J_0_0,plain,
! [V_com_H,V_fun_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I16_J_0]) ).
cnf(cls_com_Osimps_I26_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I26_J_0_0,plain,
! [V_com1_H,V_com2_H,V_fun,V_fun_H,V_vname] :
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I26_J_0]) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Un__empty__right_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty__right_0]) ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
input ).
fof(cls_Un__empty__left_0_0,plain,
! [T_a,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty__left_0]) ).
cnf(cls_com_Osimps_I38_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OWhile(V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I38_J_0_0,plain,
! [V_com,V_com_H,V_fun,V_fun_H,V_loc] :
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I38_J_0]) ).
cnf(cls_com_Osimps_I64_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSKIP,T_a) = V_f1,
input ).
fof(cls_com_Osimps_I64_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSKIP,T_a) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I64_J_0]) ).
cnf(cls_com_Osimps_I22_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I22_J_0_0,plain,
! [V_com_H,V_fun,V_fun_H,V_loc_H,V_vname] :
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I22_J_0]) ).
cnf(cls_map__add__assoc_0,axiom,
c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b),
input ).
fof(cls_map__add__assoc_0_0,plain,
! [T_a,T_b,V_m1,V_m2,V_m3] :
( c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__add__assoc_0]) ).
cnf(cls_com_Osimps_I28_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OWhile(V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I28_J_0_0,plain,
! [V_com_H,V_fun,V_fun_H,V_vname] :
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I28_J_0]) ).
cnf(cls_com_Osimps_I57_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2),
input ).
fof(cls_com_Osimps_I57_J_0_0,plain,
! [V_com1,V_com2,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I57_J_0]) ).
cnf(cls_UNIV__I_0,axiom,
c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_UNIV__I_0_0,plain,
! [T_a,V_x] :
( c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_UNIV__I_0]) ).
cnf(cls_com_Osimps_I45_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
input ).
fof(cls_com_Osimps_I45_J_0_0,plain,
! [V_com1,V_com1_H,V_com2,V_com2_H,V_fun_H] :
( c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSemi(V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I45_J_0]) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_finite_OemptyI_0_0,plain,
! [T_a] :
( c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_finite_OemptyI_0]) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__insertI_0_0,plain,
! [T_a,V_B,V_a] :
( c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__insertI_0]) ).
cnf(cls_com_Osimps_I37_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com),
input ).
fof(cls_com_Osimps_I37_J_0_0,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_fun_H,V_loc] :
( c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I37_J_0]) ).
cnf(cls_dom__map__add_0,axiom,
c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(V_n,T_a,T_b),c_Map_Odom(V_m,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_dom__map__add_0_0,plain,
! [T_a,T_b,V_m,V_n] :
( c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(V_n,T_a,T_b),c_Map_Odom(V_m,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_dom__map__add_0]) ).
cnf(cls_com_Osimps_I52_J_0,axiom,
c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I52_J_0_0,plain,
! [V_com1,V_com2,V_com_H,V_fun,V_fun_H] :
( c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I52_J_0]) ).
cnf(cls_com_Osimps_I23_J_0,axiom,
c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun),
input ).
fof(cls_com_Osimps_I23_J_0_0,plain,
! [V_com_H,V_fun,V_fun_H,V_loc_H,V_vname] :
( c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I23_J_0]) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a),
input ).
fof(cls_insert__absorb2_0_0,plain,
! [T_a,V_A,V_x] :
( c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__absorb2_0]) ).
cnf(cls_map__upd__nonempty_0,axiom,
c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),
input ).
fof(cls_map__upd__nonempty_0_0,plain,
! [T_a,T_b,V_k,V_t,V_x] :
( c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__upd__nonempty_0]) ).
cnf(cls_com_Osimps_I35_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com),
input ).
fof(cls_com_Osimps_I35_J_0_0,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_loc] :
( c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I35_J_0]) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_insert__not__empty_0_0,plain,
! [T_a,V_A,V_a] :
( c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_insert__not__empty_0]) ).
cnf(cls_com_Osimps_I44_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I44_J_0_0,plain,
! [V_com1,V_com1_H,V_com2,V_com2_H,V_fun_H] :
( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I44_J_0]) ).
cnf(cls_Un__UNIV__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__UNIV__right_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__UNIV__right_0]) ).
cnf(cls_Un__UNIV__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__UNIV__left_0_0,plain,
! [T_a,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__UNIV__left_0]) ).
cnf(cls_com_Osimps_I46_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H),
input ).
fof(cls_com_Osimps_I46_J_0_0,plain,
! [V_com1,V_com2,V_com_H,V_fun_H] :
( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I46_J_0]) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_empty__subsetI_0_0,plain,
! [T_a,V_A] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_empty__subsetI_0]) ).
cnf(cls_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_Un__insert__right_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__right_0]) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_Un__insert__left_0_0,plain,
! [T_a,V_B,V_C,V_a] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__left_0]) ).
cnf(cls_com_Osimps_I39_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com),
input ).
fof(cls_com_Osimps_I39_J_0_0,plain,
! [V_com,V_com_H,V_fun,V_fun_H,V_loc] :
( c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I39_J_0]) ).
cnf(cls_com_Osimps_I17_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I17_J_0_0,plain,
! [V_com_H,V_fun_H] :
( c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I17_J_0]) ).
cnf(cls_com_Orecs_I4_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSemi(V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f4,V_com1),V_com2),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com1,T_a)),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com2,T_a)),
input ).
fof(cls_com_Orecs_I4_J_0_0,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSemi(V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f4,V_com1),V_com2),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com1,T_a)),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com2,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I4_J_0]) ).
cnf(cls_empty__map__add_0,axiom,
c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m,
input ).
fof(cls_empty__map__add_0_0,plain,
! [T_a,T_b,V_m] :
( c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_empty__map__add_0]) ).
cnf(cls_map__add__empty_0,axiom,
c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m,
input ).
fof(cls_map__add__empty_0_0,plain,
! [T_a,T_b,V_m] :
( c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_map__add__empty_0]) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
input ).
fof(cls_doubleton__eq__iff_4_0,plain,
! [T_a,V_x,V_xa] :
( c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_doubleton__eq__iff_4]) ).
cnf(cls_rangeI_0,axiom,
c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a),
input ).
fof(cls_rangeI_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rangeI_0]) ).
cnf(cls_com_Osimps_I65_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OAss(V_vname,V_fun),T_a) = hAPP(hAPP(V_f2,V_vname),V_fun),
input ).
fof(cls_com_Osimps_I65_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_vname] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OAss(V_vname,V_fun),T_a) = hAPP(hAPP(V_f2,V_vname),V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I65_J_0]) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)),
input ).
fof(cls_COMBS__def_0_0,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R))
| $false ),
inference(orientation,[status(thm)],[cls_COMBS__def_0]) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P,
input ).
fof(cls_COMBK__def_0_0,plain,
! [T_a,T_b,V_P,V_Q] :
( hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P
| $false ),
inference(orientation,[status(thm)],[cls_COMBK__def_0]) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a),
input ).
fof(cls_insert__commute_0_0,plain,
! [T_a,V_A,V_x,V_y] :
( c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__commute_0]) ).
cnf(cls_com_Osimps_I71_J_0,axiom,
c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCall(V_vname,V_pname,V_fun),T_a) = hAPP(hAPP(hAPP(V_f8,V_vname),V_pname),V_fun),
input ).
fof(cls_com_Osimps_I71_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_pname,V_vname] :
( c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCall(V_vname,V_pname,V_fun),T_a) = hAPP(hAPP(hAPP(V_f8,V_vname),V_pname),V_fun)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I71_J_0]) ).
cnf(cls_inj__on__id_0,axiom,
c_Fun_Oinj__on(c_Fun_Oid(T_a),V_A,T_a,T_a),
input ).
fof(cls_inj__on__id_0_0,plain,
! [T_a,V_A] :
( c_Fun_Oinj__on(c_Fun_Oid(T_a),V_A,T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_inj__on__id_0]) ).
cnf(cls_insertCI_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
input ).
fof(cls_insertCI_1_0,plain,
! [T_a,V_B,V_x] :
( c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insertCI_1]) ).
cnf(cls_insertI1_0,axiom,
c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a),
input ).
fof(cls_insertI1_0_0,plain,
! [T_a,V_B,V_a] :
( c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insertI1_0]) ).
cnf(cls_insert__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
input ).
fof(cls_insert__iff_1_0,plain,
! [T_a,V_A,V_x] :
( c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__iff_1]) ).
cnf(cls_com_Osimps_I51_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
input ).
fof(cls_com_Osimps_I51_J_0_0,plain,
! [V_com1,V_com2,V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSemi(V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I51_J_0]) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Un__absorb_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__absorb_0]) ).
cnf(cls_com_Osimps_I56_J_0,axiom,
c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H),
input ).
fof(cls_com_Osimps_I56_J_0_0,plain,
! [V_com1,V_com2,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I56_J_0]) ).
cnf(cls_com_Osimps_I36_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I36_J_0_0,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_fun_H,V_loc] :
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I36_J_0]) ).
cnf(cls_dom__empty_0,axiom,
c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_dom__empty_0_0,plain,
! [T_a,T_b] :
( c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_dom__empty_0]) ).
cnf(cls_com_Orecs_I1_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSKIP,T_a) = V_f1,
input ).
fof(cls_com_Orecs_I1_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSKIP,T_a) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I1_J_0]) ).
cnf(cls_com_Osimps_I24_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I24_J_0_0,plain,
! [V_com1_H,V_com2_H,V_fun,V_vname] :
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I24_J_0]) ).
cnf(cls_com_Orecs_I3_J_0,axiom,
c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OLocal(V_loc,V_fun,V_com),T_a) = hAPP(hAPP(hAPP(hAPP(V_f3,V_loc),V_fun),V_com),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com,T_a)),
input ).
fof(cls_com_Orecs_I3_J_0_0,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_loc] :
( c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OLocal(V_loc,V_fun,V_com),T_a) = hAPP(hAPP(hAPP(hAPP(V_f3,V_loc),V_fun),V_com),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_com_Orecs_I3_J_0]) ).
fof(def_lhs_atom1,axiom,
! [V_loc,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a] :
( lhs_atom1(V_loc,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OLocal(V_loc,V_fun,V_com),T_a) = hAPP(hAPP(hAPP(hAPP(V_f3,V_loc),V_fun),V_com),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_0,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_loc] :
( lhs_atom1(V_loc,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I3_J_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_vname,V_fun,V_com2_H,V_com1_H] :
( lhs_atom2(V_vname,V_fun,V_com2_H,V_com1_H)
<=> c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_1,plain,
! [V_com1_H,V_com2_H,V_fun,V_vname] :
( lhs_atom2(V_vname,V_fun,V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I24_J_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom3(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSKIP,T_a) = V_f1 ),
inference(definition,[],[]) ).
fof(to_be_clausified_2,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( lhs_atom3(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I1_J_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [T_b,T_a] :
( lhs_atom4(T_b,T_a)
<=> c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_3,plain,
! [T_a,T_b] :
( lhs_atom4(T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__empty_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_loc,V_fun_H,V_fun,V_com2_H,V_com1_H,V_com] :
( lhs_atom5(V_loc,V_fun_H,V_fun,V_com2_H,V_com1_H,V_com)
<=> c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_4,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_fun_H,V_loc] :
( lhs_atom5(V_loc,V_fun_H,V_fun,V_com2_H,V_com1_H,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I36_J_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_vname_H,V_pname_H,V_fun_H,V_fun,V_com2,V_com1] :
( lhs_atom6(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com2,V_com1)
<=> c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_5,plain,
! [V_com1,V_com2,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom6(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I56_J_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_A,T_a] :
( lhs_atom7(V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_6,plain,
! [T_a,V_A] :
( lhs_atom7(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__absorb_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_vname_H,V_pname_H,V_fun_H,V_com2,V_com1] :
( lhs_atom8(V_vname_H,V_pname_H,V_fun_H,V_com2,V_com1)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_7,plain,
! [V_com1,V_com2,V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom8(V_vname_H,V_pname_H,V_fun_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I51_J_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_x,V_A,T_a] :
( lhs_atom9(V_x,V_A,T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_8,plain,
! [T_a,V_A,V_x] :
( lhs_atom9(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__iff_1_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_a,V_B,T_a] :
( lhs_atom10(V_a,V_B,T_a)
<=> c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_9,plain,
! [T_a,V_B,V_a] :
( lhs_atom10(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertI1_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_x,V_B,T_a] :
( lhs_atom11(V_x,V_B,T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_10,plain,
! [T_a,V_B,V_x] :
( lhs_atom11(V_x,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertCI_1_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_A,T_a] :
( lhs_atom12(V_A,T_a)
<=> c_Fun_Oinj__on(c_Fun_Oid(T_a),V_A,T_a,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_11,plain,
! [T_a,V_A] :
( lhs_atom12(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_inj__on__id_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_vname,V_pname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom13(V_vname,V_pname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCall(V_vname,V_pname,V_fun),T_a) = hAPP(hAPP(hAPP(V_f8,V_vname),V_pname),V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_12,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_pname,V_vname] :
( lhs_atom13(V_vname,V_pname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I71_J_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_y,V_x,V_A,T_a] :
( lhs_atom14(V_y,V_x,V_A,T_a)
<=> c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_13,plain,
! [T_a,V_A,V_x,V_y] :
( lhs_atom14(V_y,V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__commute_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_Q,V_P,T_b,T_a] :
( lhs_atom15(V_Q,V_P,T_b,T_a)
<=> hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ),
inference(definition,[],[]) ).
fof(to_be_clausified_14,plain,
! [T_a,T_b,V_P,V_Q] :
( lhs_atom15(V_Q,V_P,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBK__def_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom16(V_R,V_Q,V_P,T_c,T_b,T_a)
<=> hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_15,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom16(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBS__def_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_vname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom17(V_vname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OAss(V_vname,V_fun),T_a) = hAPP(hAPP(V_f2,V_vname),V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_16,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_vname] :
( lhs_atom17(V_vname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I65_J_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom18(V_x,V_f,T_b,T_a)
<=> c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_17,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom18(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rangeI_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom19(V_xa,V_x,T_a)
<=> c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_18,plain,
! [T_a,V_x,V_xa] :
( lhs_atom19(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_doubleton__eq__iff_4_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_m,T_b,T_a] :
( lhs_atom20(V_m,T_b,T_a)
<=> c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_19,plain,
! [T_a,T_b,V_m] :
( lhs_atom20(V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__empty_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_m,T_b,T_a] :
( lhs_atom21(V_m,T_b,T_a)
<=> c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_20,plain,
! [T_a,T_b,V_m] :
( lhs_atom21(V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__map__add_0_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a] :
( lhs_atom22(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSemi(V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f4,V_com1),V_com2),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com1,T_a)),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com2,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_21,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( lhs_atom22(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I4_J_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_fun_H,V_com_H] :
( lhs_atom23(V_fun_H,V_com_H)
<=> c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_22,plain,
! [V_com_H,V_fun_H] :
( lhs_atom23(V_fun_H,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I17_J_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_loc,V_fun_H,V_fun,V_com_H,V_com] :
( lhs_atom24(V_loc,V_fun_H,V_fun,V_com_H,V_com)
<=> c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_23,plain,
! [V_com,V_com_H,V_fun,V_fun_H,V_loc] :
( lhs_atom24(V_loc,V_fun_H,V_fun,V_com_H,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I39_J_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_a,V_C,V_B,T_a] :
( lhs_atom25(V_a,V_C,V_B,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_24,plain,
! [T_a,V_B,V_C,V_a] :
( lhs_atom25(V_a,V_C,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__left_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom26(V_a,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_25,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom26(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__right_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_A,T_a] :
( lhs_atom27(V_A,T_a)
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_26,plain,
! [T_a,V_A] :
( lhs_atom27(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__subsetI_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_fun_H,V_com_H,V_com2,V_com1] :
( lhs_atom28(V_fun_H,V_com_H,V_com2,V_com1)
<=> c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_27,plain,
! [V_com1,V_com2,V_com_H,V_fun_H] :
( lhs_atom28(V_fun_H,V_com_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I46_J_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_B,T_a] :
( lhs_atom29(V_B,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_28,plain,
! [T_a,V_B] :
( lhs_atom29(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__UNIV__left_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_A,T_a] :
( lhs_atom30(V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_29,plain,
! [T_a,V_A] :
( lhs_atom30(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__UNIV__right_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_fun_H,V_com2_H,V_com2,V_com1_H,V_com1] :
( lhs_atom31(V_fun_H,V_com2_H,V_com2,V_com1_H,V_com1)
<=> c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_30,plain,
! [V_com1,V_com1_H,V_com2,V_com2_H,V_fun_H] :
( lhs_atom31(V_fun_H,V_com2_H,V_com2,V_com1_H,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I44_J_0_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_a,V_A,T_a] :
( lhs_atom32(V_a,V_A,T_a)
<=> c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_31,plain,
! [T_a,V_A,V_a] :
( lhs_atom32(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__not__empty_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_loc,V_fun,V_com2_H,V_com1_H,V_com] :
( lhs_atom33(V_loc,V_fun,V_com2_H,V_com1_H,V_com)
<=> c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_32,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_loc] :
( lhs_atom33(V_loc,V_fun,V_com2_H,V_com1_H,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I35_J_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_x,V_t,V_k,T_b,T_a] :
( lhs_atom34(V_x,V_t,V_k,T_b,T_a)
<=> c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_33,plain,
! [T_a,T_b,V_k,V_t,V_x] :
( lhs_atom34(V_x,V_t,V_k,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__upd__nonempty_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_x,V_A,T_a] :
( lhs_atom35(V_x,V_A,T_a)
<=> c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_34,plain,
! [T_a,V_A,V_x] :
( lhs_atom35(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__absorb2_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_vname,V_loc_H,V_fun_H,V_fun,V_com_H] :
( lhs_atom36(V_vname,V_loc_H,V_fun_H,V_fun,V_com_H)
<=> c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_35,plain,
! [V_com_H,V_fun,V_fun_H,V_loc_H,V_vname] :
( lhs_atom36(V_vname,V_loc_H,V_fun_H,V_fun,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I23_J_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_fun_H,V_fun,V_com_H,V_com2,V_com1] :
( lhs_atom37(V_fun_H,V_fun,V_com_H,V_com2,V_com1)
<=> c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_36,plain,
! [V_com1,V_com2,V_com_H,V_fun,V_fun_H] :
( lhs_atom37(V_fun_H,V_fun,V_com_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I52_J_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_n,V_m,T_b,T_a] :
( lhs_atom38(V_n,V_m,T_b,T_a)
<=> c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(V_n,T_a,T_b),c_Map_Odom(V_m,T_a,T_b),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_37,plain,
! [T_a,T_b,V_m,V_n] :
( lhs_atom38(V_n,V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__map__add_0_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [V_loc,V_fun_H,V_fun,V_com2_H,V_com1_H,V_com] :
( lhs_atom39(V_loc,V_fun_H,V_fun,V_com2_H,V_com1_H,V_com)
<=> c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_38,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_fun_H,V_loc] :
( lhs_atom39(V_loc,V_fun_H,V_fun,V_com2_H,V_com1_H,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I37_J_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_a,V_B,T_a] :
( lhs_atom40(V_a,V_B,T_a)
<=> c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_39,plain,
! [T_a,V_B,V_a] :
( lhs_atom40(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__insertI_0_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [T_a] :
( lhs_atom41(T_a)
<=> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_40,plain,
! [T_a] :
( lhs_atom41(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_finite_OemptyI_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_fun_H,V_com2_H,V_com2,V_com1_H,V_com1] :
( lhs_atom42(V_fun_H,V_com2_H,V_com2,V_com1_H,V_com1)
<=> c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_41,plain,
! [V_com1,V_com1_H,V_com2,V_com2_H,V_fun_H] :
( lhs_atom42(V_fun_H,V_com2_H,V_com2,V_com1_H,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I45_J_0_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_x,T_a] :
( lhs_atom43(V_x,T_a)
<=> c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_42,plain,
! [T_a,V_x] :
( lhs_atom43(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UNIV__I_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_vname_H,V_pname_H,V_fun_H,V_fun,V_com2,V_com1] :
( lhs_atom44(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com2,V_com1)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_43,plain,
! [V_com1,V_com2,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom44(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I57_J_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V_vname,V_fun_H,V_fun,V_com_H] :
( lhs_atom45(V_vname,V_fun_H,V_fun,V_com_H)
<=> c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_44,plain,
! [V_com_H,V_fun,V_fun_H,V_vname] :
( lhs_atom45(V_vname,V_fun_H,V_fun,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I28_J_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_m3,V_m2,V_m1,T_b,T_a] :
( lhs_atom46(V_m3,V_m2,V_m1,T_b,T_a)
<=> c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_45,plain,
! [T_a,T_b,V_m1,V_m2,V_m3] :
( lhs_atom46(V_m3,V_m2,V_m1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__assoc_0_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_vname,V_loc_H,V_fun_H,V_fun,V_com_H] :
( lhs_atom47(V_vname,V_loc_H,V_fun_H,V_fun,V_com_H)
<=> c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_46,plain,
! [V_com_H,V_fun,V_fun_H,V_loc_H,V_vname] :
( lhs_atom47(V_vname,V_loc_H,V_fun_H,V_fun,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I22_J_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom48(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSKIP,T_a) = V_f1 ),
inference(definition,[],[]) ).
fof(to_be_clausified_47,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( lhs_atom48(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I64_J_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_loc,V_fun_H,V_fun,V_com_H,V_com] :
( lhs_atom49(V_loc,V_fun_H,V_fun,V_com_H,V_com)
<=> c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_48,plain,
! [V_com,V_com_H,V_fun,V_fun_H,V_loc] :
( lhs_atom49(V_loc,V_fun_H,V_fun,V_com_H,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I38_J_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [V_B,T_a] :
( lhs_atom50(V_B,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ),
inference(definition,[],[]) ).
fof(to_be_clausified_49,plain,
! [T_a,V_B] :
( lhs_atom50(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__left_0_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_A,T_a] :
( lhs_atom51(V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],[]) ).
fof(to_be_clausified_50,plain,
! [T_a,V_A] :
( lhs_atom51(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__right_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_vname,V_fun_H,V_fun,V_com2_H,V_com1_H] :
( lhs_atom52(V_vname,V_fun_H,V_fun,V_com2_H,V_com1_H)
<=> c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_51,plain,
! [V_com1_H,V_com2_H,V_fun,V_fun_H,V_vname] :
( lhs_atom52(V_vname,V_fun_H,V_fun,V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I26_J_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_fun_H,V_com_H] :
( lhs_atom53(V_fun_H,V_com_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_52,plain,
! [V_com_H,V_fun_H] :
( lhs_atom53(V_fun_H,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I16_J_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_x,T_a] :
( lhs_atom54(V_x,T_a)
<=> ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_53,plain,
! [T_a,V_x] :
( lhs_atom54(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_bot1E_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [V_loc_H,V_fun_H,V_com_H] :
( lhs_atom55(V_loc_H,V_fun_H,V_com_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_54,plain,
! [V_com_H,V_fun_H,V_loc_H] :
( lhs_atom55(V_loc_H,V_fun_H,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I10_J_0_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
! [T_a] :
( lhs_atom56(T_a)
<=> c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_55,plain,
! [T_a] :
( lhs_atom56(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_UNIV__not__empty_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [V_z,V_y,V_x,V_f,T_b,T_a] :
( lhs_atom57(V_z,V_y,V_x,V_f,T_b,T_a)
<=> c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_56,plain,
! [T_a,T_b,V_f,V_x,V_y,V_z] :
( lhs_atom57(V_z,V_y,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__upd_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_x,T_a] :
( lhs_atom58(V_x,T_a)
<=> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_57,plain,
! [T_a,V_x] :
( lhs_atom58(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_top1I_0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
! [V_vname_H,V_pname_H,V_fun_H,V_fun,V_com] :
( lhs_atom59(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com)
<=> c_Com_Ocom_OWhile(V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_58,plain,
! [V_com,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom59(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I60_J_0_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_s] :
( lhs_atom60(V_s)
<=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_59,plain,
! [V_s] :
( lhs_atom60(V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_evalc_OSkip_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_vname,V_fun,V_com2_H,V_com1_H] :
( lhs_atom61(V_vname,V_fun,V_com2_H,V_com1_H)
<=> c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_60,plain,
! [V_com1_H,V_com2_H,V_fun,V_vname] :
( lhs_atom61(V_vname,V_fun,V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I25_J_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_loc_H,V_fun_H,V_com_H] :
( lhs_atom62(V_loc_H,V_fun_H,V_com_H)
<=> c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_61,plain,
! [V_com_H,V_fun_H,V_loc_H] :
( lhs_atom62(V_loc_H,V_fun_H,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I11_J_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_s,V_n] :
( lhs_atom63(V_s,V_n)
<=> c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ),
inference(definition,[],[]) ).
fof(to_be_clausified_62,plain,
! [V_n,V_s] :
( lhs_atom63(V_s,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_evaln_OSkip_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [T_a] :
( lhs_atom64(T_a)
<=> c_Option_Ois__none(c_Option_Ooption_ONone(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_63,plain,
! [T_a] :
( lhs_atom64(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_is__none__def_1_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [V_f2,V_f1,T_b,T_a] :
( lhs_atom65(V_f2,V_f1,T_b,T_a)
<=> c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1 ),
inference(definition,[],[]) ).
fof(to_be_clausified_64,plain,
! [T_a,T_b,V_f1,V_f2] :
( lhs_atom65(V_f2,V_f1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I4_J_0_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_f2,V_f1,T_b,T_a] :
( lhs_atom66(V_f2,V_f1,T_b,T_a)
<=> c_Option_Ooption_Ooption__rec(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1 ),
inference(definition,[],[]) ).
fof(to_be_clausified_65,plain,
! [T_a,T_b,V_f1,V_f2] :
( lhs_atom66(V_f2,V_f1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Orecs_I1_J_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_f,T_b,T_a] :
( lhs_atom67(V_f,T_b,T_a)
<=> c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_66,plain,
! [T_a,T_b,V_f] :
( lhs_atom67(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_inj__on__empty_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom68(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_67,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom68(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__commute_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom69(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_68,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom69(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__assoc_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_B,V_A,T_a] :
( lhs_atom70(V_B,V_A,T_a)
<=> c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_69,plain,
! [T_a,V_A,V_B] :
( lhs_atom70(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper2_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_B,V_A,T_a] :
( lhs_atom71(V_B,V_A,T_a)
<=> c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_70,plain,
! [T_a,V_A,V_B] :
( lhs_atom71(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper1_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_fun_H,V_com2_H,V_com1_H] :
( lhs_atom72(V_fun_H,V_com2_H,V_com1_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_71,plain,
! [V_com1_H,V_com2_H,V_fun_H] :
( lhs_atom72(V_fun_H,V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I14_J_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_vname_H,V_vname,V_pname_H,V_fun_H,V_fun] :
( lhs_atom73(V_vname_H,V_vname,V_pname_H,V_fun_H,V_fun)
<=> c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_72,plain,
! [V_fun,V_fun_H,V_pname_H,V_vname,V_vname_H] :
( lhs_atom73(V_vname_H,V_vname,V_pname_H,V_fun_H,V_fun)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I32_J_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_xa,V_x,T_b,T_a] :
( lhs_atom74(V_xa,V_x,T_b,T_a)
<=> c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_73,plain,
! [T_a,T_b,V_x,V_xa] :
( lhs_atom74(V_xa,V_x,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__eq__singleton__conv_1_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_c,T_b,T_a] :
( lhs_atom75(V_c,T_b,T_a)
<=> c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_74,plain,
! [T_a,T_b,V_c] :
( lhs_atom75(V_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__constant__conv_0_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_vname_H,V_pname_H,V_loc,V_fun_H,V_fun,V_com] :
( lhs_atom76(V_vname_H,V_pname_H,V_loc,V_fun_H,V_fun,V_com)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_75,plain,
! [V_com,V_fun,V_fun_H,V_loc,V_pname_H,V_vname_H] :
( lhs_atom76(V_vname_H,V_pname_H,V_loc,V_fun_H,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I43_J_0_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_vname_H,V_pname_H,V_fun_H,V_fun,V_com] :
( lhs_atom77(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OWhile(V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_76,plain,
! [V_com,V_fun,V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom77(V_vname_H,V_pname_H,V_fun_H,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I61_J_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a] :
( lhs_atom78(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OSemi(V_com1,V_com2),T_a) = hAPP(hAPP(V_f4,V_com1),V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_77,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8] :
( lhs_atom78(V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I67_J_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_loc,V_fun,V_com2_H,V_com1_H,V_com] :
( lhs_atom79(V_loc,V_fun,V_com2_H,V_com1_H,V_com)
<=> c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_78,plain,
! [V_com,V_com1_H,V_com2_H,V_fun,V_loc] :
( lhs_atom79(V_loc,V_fun,V_com2_H,V_com1_H,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I34_J_0_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_B,V_A,T_a] :
( lhs_atom80(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_79,plain,
! [T_a,V_A,V_B] :
( lhs_atom80(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__commute_0_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_vname,V_pname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom81(V_vname,V_pname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCall(V_vname,V_pname,V_fun),T_a) = hAPP(hAPP(hAPP(V_f8,V_vname),V_pname),V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_80,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_pname,V_vname] :
( lhs_atom81(V_vname,V_pname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I8_J_0_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [V_a,V_A,T_a] :
( lhs_atom82(V_a,V_A,T_a)
<=> c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_81,plain,
! [T_a,V_A,V_a] :
( lhs_atom82(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__is__Un_0_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [V_f,T_b,T_a] :
( lhs_atom83(V_f,T_b,T_a)
<=> c_Option_Omap(V_f,c_Option_Ooption_ONone(T_b),T_b,T_a) = c_Option_Ooption_ONone(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_82,plain,
! [T_a,T_b,V_f] :
( lhs_atom83(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option__map__None_0_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_B,V_A,T_a] :
( lhs_atom84(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_83,plain,
! [T_a,V_A,V_B] :
( lhs_atom84(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__absorb_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [V_fun_H,V_com2_H,V_com1_H] :
( lhs_atom85(V_fun_H,V_com2_H,V_com1_H)
<=> c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_84,plain,
! [V_com1_H,V_com2_H,V_fun_H] :
( lhs_atom85(V_fun_H,V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I15_J_0_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [V_fun_H,V_fun,V_com_H,V_com2,V_com1] :
( lhs_atom86(V_fun_H,V_fun,V_com_H,V_com2,V_com1)
<=> c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_85,plain,
! [V_com1,V_com2,V_com_H,V_fun,V_fun_H] :
( lhs_atom86(V_fun_H,V_fun,V_com_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I53_J_0_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_c] :
( lhs_atom87(V_c)
<=> hAPP(c_Hoare__Mirabelle_OMGT,V_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),V_c),c_Natural_Oevalc(V_c)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_86,plain,
! [V_c] :
( lhs_atom87(V_c)
| $false ),
inference(fold_definition,[status(thm)],[cls_MGT__def_0_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [V_vname_H,V_pname_H,V_fun_H,V_com2,V_com1] :
( lhs_atom88(V_vname_H,V_pname_H,V_fun_H,V_com2,V_com1)
<=> c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_87,plain,
! [V_com1,V_com2,V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom88(V_vname_H,V_pname_H,V_fun_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I50_J_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [V_vname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom89(V_vname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OAss(V_vname,V_fun),T_a) = hAPP(hAPP(V_f2,V_vname),V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_88,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_vname] :
( lhs_atom89(V_vname,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I2_J_0_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_vname,V_fun_H,V_fun,V_com2_H,V_com1_H] :
( lhs_atom90(V_vname,V_fun_H,V_fun,V_com2_H,V_com1_H)
<=> c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_89,plain,
! [V_com1_H,V_com2_H,V_fun,V_fun_H,V_vname] :
( lhs_atom90(V_vname,V_fun_H,V_fun,V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I27_J_0_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
! [V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a] :
( lhs_atom91(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OWhile(V_fun,V_com),T_a) = hAPP(hAPP(hAPP(V_f6,V_fun),V_com),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_90,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( lhs_atom91(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I6_J_0_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [V_x,T_a] :
( lhs_atom92(V_x,T_a)
<=> hAPP(c_Fun_Oid(T_a),V_x) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_91,plain,
! [T_a,V_x] :
( lhs_atom92(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_id__apply_0_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
! [V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a] :
( lhs_atom93(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCond(V_fun,V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5,V_fun),V_com1),V_com2),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com1,T_a)),c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_com2,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_92,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( lhs_atom93(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I5_J_0_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom94(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_93,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom94(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Un_0_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom95(V_f,V_a,V_B,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_94,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom95(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__insert_0_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_f,T_b,T_a] :
( lhs_atom96(V_f,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_95,plain,
! [T_a,T_b,V_f] :
( lhs_atom96(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__empty_0_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [V_vname_H,V_fun_H] :
( lhs_atom97(V_vname_H,V_fun_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_96,plain,
! [V_fun_H,V_vname_H] :
( lhs_atom97(V_vname_H,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I8_J_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom98(V_x,V_f,T_b,T_a)
<=> c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f ),
inference(definition,[],[]) ).
fof(to_be_clausified_97,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom98(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__idem_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_y,V_x,V_f,T_b,T_a] :
( lhs_atom99(V_y,V_x,V_f,T_b,T_a)
<=> hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y ),
inference(definition,[],[]) ).
fof(to_be_clausified_98,plain,
! [T_a,T_b,V_f,V_x,V_y] :
( lhs_atom99(V_y,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__same_0_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom100(V_x,V_f,T_b,T_a)
<=> c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f ),
inference(definition,[],[]) ).
fof(to_be_clausified_99,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom100(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__triv_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [V_y,V_x,V_f,T_aa,T_a] :
( lhs_atom101(V_y,V_x,V_f,T_aa,T_a)
<=> hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y ),
inference(definition,[],[]) ).
fof(to_be_clausified_100,plain,
! [T_a,T_aa,V_f,V_x,V_y] :
( lhs_atom101(V_y,V_x,V_f,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__apply_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_x,V_f,T_aa,T_a] :
( lhs_atom102(V_x,V_f,T_aa,T_a)
<=> c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f ),
inference(definition,[],[]) ).
fof(to_be_clausified_101,plain,
! [T_a,T_aa,V_f,V_x] :
( lhs_atom102(V_x,V_f,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__idem__iff_1_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [T_a] :
( lhs_atom103(T_a)
<=> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_102,plain,
! [T_a] :
( lhs_atom103(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__empty_1_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_vname,V_fun_H,V_fun,V_com_H] :
( lhs_atom104(V_vname,V_fun_H,V_fun,V_com_H)
<=> c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_103,plain,
! [V_com_H,V_fun,V_fun_H,V_vname] :
( lhs_atom104(V_vname,V_fun_H,V_fun,V_com_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I29_J_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_a,V_A,T_a] :
( lhs_atom105(V_a,V_A,T_a)
<=> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_104,plain,
! [T_a,V_A,V_a] :
( lhs_atom105(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__not__insert_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_loc,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a] :
( lhs_atom106(V_loc,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OLocal(V_loc,V_fun,V_com),T_a) = hAPP(hAPP(hAPP(V_f3,V_loc),V_fun),V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_105,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun,V_loc] :
( lhs_atom106(V_loc,V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I66_J_0_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a] :
( lhs_atom107(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OWhile(V_fun,V_com),T_a) = hAPP(hAPP(V_f6,V_fun),V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_106,plain,
! [T_a,V_com,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( lhs_atom107(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I69_J_0_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_a,T_a] :
( lhs_atom108(V_a,T_a)
<=> ~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_107,plain,
! [T_a,V_a] :
( lhs_atom108(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_emptyE_0_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_c,T_a] :
( lhs_atom109(V_c,T_a)
<=> ~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_108,plain,
! [T_a,V_c] :
( lhs_atom109(V_c,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__iff_0_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_x,T_a] :
( lhs_atom110(V_x,T_a)
<=> ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_109,plain,
! [T_a,V_x] :
( lhs_atom110(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ex__in__conv_0_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [V_A,T_a] :
( lhs_atom111(V_A,T_a)
<=> c_lessequals(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_110,plain,
! [T_a,V_A] :
( lhs_atom111(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__UNIV_0_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [V_vname_H,V_vname,V_pname_H,V_fun_H,V_fun] :
( lhs_atom112(V_vname_H,V_vname,V_pname_H,V_fun_H,V_fun)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OAss(V_vname,V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_111,plain,
! [V_fun,V_fun_H,V_pname_H,V_vname,V_vname_H] :
( lhs_atom112(V_vname_H,V_vname,V_pname_H,V_fun_H,V_fun)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I33_J_0_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
! [V_com2_H,V_com1_H] :
( lhs_atom113(V_com2_H,V_com1_H)
<=> c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_112,plain,
! [V_com1_H,V_com2_H] :
( lhs_atom113(V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I13_J_0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
! [V_P,V_G,T_a] :
( lhs_atom114(V_P,V_G,T_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSKIP),V_P),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_113,plain,
! [T_a,V_G,V_P] :
( lhs_atom114(V_P,V_G,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_hoare__derivs_OSkip_0_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
! [V_x,V_A,T_a] :
( lhs_atom115(V_x,V_A,T_a)
<=> hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_114,plain,
! [T_a,V_A,V_x] :
( lhs_atom115(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__code_1_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
! [V_y,V_x,V_g,V_f,T_b,T_a] :
( lhs_atom116(V_y,V_x,V_g,V_f,T_b,T_a)
<=> c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_115,plain,
! [T_a,T_b,V_f,V_g,V_x,V_y] :
( lhs_atom116(V_y,V_x,V_g,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__upd_0_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
! [V_vname_H,V_pname_H,V_fun_H] :
( lhs_atom117(V_vname_H,V_pname_H,V_fun_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_116,plain,
! [V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom117(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I20_J_0_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
! [V_fun_H,V_com_H,V_com2,V_com1] :
( lhs_atom118(V_fun_H,V_com_H,V_com2,V_com1)
<=> c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_117,plain,
! [V_com1,V_com2,V_com_H,V_fun_H] :
( lhs_atom118(V_fun_H,V_com_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I47_J_0_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
! [V_n] :
( lhs_atom119(V_n)
<=> c_Suc(V_n) != V_n ),
inference(definition,[],[]) ).
fof(to_be_clausified_118,plain,
! [V_n] :
( lhs_atom119(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Suc__n__not__n_0_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
! [V_n] :
( lhs_atom120(V_n)
<=> V_n != c_Suc(V_n) ),
inference(definition,[],[]) ).
fof(to_be_clausified_119,plain,
! [V_n] :
( lhs_atom120(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_n__not__Suc__n_0_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
! [V_x,T_a] :
( lhs_atom121(V_x,T_a)
<=> c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_120,plain,
! [T_a,V_x] :
( lhs_atom121(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_equalityE_0_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
! [V_A,T_a] :
( lhs_atom122(V_A,T_a)
<=> c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_121,plain,
! [T_a,V_A] :
( lhs_atom122(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__refl_0_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
! [V_vname_H,V_pname_H,V_fun_H] :
( lhs_atom123(V_vname_H,V_pname_H,V_fun_H)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_122,plain,
! [V_fun_H,V_pname_H,V_vname_H] :
( lhs_atom123(V_vname_H,V_pname_H,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I21_J_0_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
! [V_x,T_a] :
( lhs_atom124(V_x,T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_123,plain,
! [T_a,V_x] :
( lhs_atom124(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__iff_1_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
! [V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a] :
( lhs_atom125(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,c_Com_Ocom_OCond(V_fun,V_com1,V_com2),T_a) = hAPP(hAPP(hAPP(V_f5,V_fun),V_com1),V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_124,plain,
! [T_a,V_com1,V_com2,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_fun] :
( lhs_atom125(V_fun,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,V_com2,V_com1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I68_J_0_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
! [V_vname_H,V_fun_H] :
( lhs_atom126(V_vname_H,V_fun_H)
<=> c_Com_Ocom_OAss(V_vname_H,V_fun_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_125,plain,
! [V_fun_H,V_vname_H] :
( lhs_atom126(V_vname_H,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I9_J_0_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
! [T_a] :
( lhs_atom127(T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_126,plain,
! [T_a] :
( lhs_atom127(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty_2_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
! [V_vname_H,V_pname_H,V_loc,V_fun_H,V_fun,V_com] :
( lhs_atom128(V_vname_H,V_pname_H,V_loc,V_fun_H,V_fun,V_com)
<=> c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_127,plain,
! [V_com,V_fun,V_fun_H,V_loc,V_pname_H,V_vname_H] :
( lhs_atom128(V_vname_H,V_pname_H,V_loc,V_fun_H,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I42_J_0_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
! [V_com2_H,V_com1_H] :
( lhs_atom129(V_com2_H,V_com1_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_128,plain,
! [V_com1_H,V_com2_H] :
( lhs_atom129(V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I12_J_0_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
! [V_Y,T_a] :
( lhs_atom130(V_Y,T_a)
<=> c_Set_Oimage(c_Fun_Oid(T_a),V_Y,T_a,T_a) = V_Y ),
inference(definition,[],[]) ).
fof(to_be_clausified_129,plain,
! [T_a,V_Y] :
( lhs_atom130(V_Y,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__id_0_0,def_lhs_atom130]) ).
fof(to_be_clausified_130,plain,
! [T_a,T_b,V_f] :
( lhs_atom96(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__is__image_1_0,def_lhs_atom96]) ).
fof(def_lhs_atom131,axiom,
! [V_f2,V_f1,V_a,T_b,T_a] :
( lhs_atom131(V_f2,V_f1,V_a,T_b,T_a)
<=> c_Option_Ooption_Ooption__rec(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_131,plain,
! [T_a,T_b,V_a,V_f1,V_f2] :
( lhs_atom131(V_f2,V_f1,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Orecs_I2_J_0_0,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
! [V_xa,V_x,V_m,T_aa,T_a] :
( lhs_atom132(V_xa,V_x,V_m,T_aa,T_a)
<=> hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ),
inference(definition,[],[]) ).
fof(to_be_clausified_132,plain,
! [T_a,T_aa,V_m,V_x,V_xa] :
( lhs_atom132(V_xa,V_x,V_m,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__upd__Some__unfold_3_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
! [V_A,T_a] :
( lhs_atom133(V_A,T_a)
<=> c_Fun_Oinj__on(c_Option_Ooption_OSome(T_a),V_A,T_a,tc_Option_Ooption(T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_133,plain,
! [T_a,V_A] :
( lhs_atom133(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_inj__Some_0_0,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
! [V_x,T_a] :
( lhs_atom134(V_x,T_a)
<=> ~ c_Option_Ois__none(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_134,plain,
! [T_a,V_x] :
( lhs_atom134(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_is__none__code_I2_J_0_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
! [V_xa,T_a] :
( lhs_atom135(V_xa,T_a)
<=> hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_135,plain,
! [T_a,V_xa] :
( lhs_atom135(V_xa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__None__eq_1_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
! [V_a_H,T_a] :
( lhs_atom136(V_a_H,T_a)
<=> hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_136,plain,
! [T_a,V_a_H] :
( lhs_atom136(V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I3_J_0_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
! [V_f2,V_f1,V_a,T_b,T_a] :
( lhs_atom137(V_f2,V_f1,V_a,T_b,T_a)
<=> c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_137,plain,
! [T_a,T_b,V_a,V_f1,V_f2] :
( lhs_atom137(V_f2,V_f1,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I5_J_0_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
! [V_y,T_a] :
( lhs_atom138(V_y,T_a)
<=> c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y) ),
inference(definition,[],[]) ).
fof(to_be_clausified_138,plain,
! [T_a,V_y] :
( lhs_atom138(V_y,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Some__eq_1_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
! [V_a_H,T_a] :
( lhs_atom139(V_a_H,T_a)
<=> c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_139,plain,
! [T_a,V_a_H] :
( lhs_atom139(V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I2_J_0_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom140(V_x,V_f,T_b,T_a)
<=> c_Option_Omap(V_f,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_b,T_a) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f,V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_140,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom140(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option__map__Some_0_0,def_lhs_atom140]) ).
fof(def_lhs_atom141,axiom,
! [V_pname_H] :
( lhs_atom141(V_pname_H)
<=> hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],[]) ).
fof(to_be_clausified_141,plain,
! [V_pname_H] :
( lhs_atom141(V_pname_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I19_J_0_0,def_lhs_atom141]) ).
fof(def_lhs_atom142,axiom,
! [V_pname_H,V_fun,V_com] :
( lhs_atom142(V_pname_H,V_fun,V_com)
<=> c_Com_Ocom_OWhile(V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_142,plain,
! [V_com,V_fun,V_pname_H] :
( lhs_atom142(V_pname_H,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I58_J_0_0,def_lhs_atom142]) ).
fof(def_lhs_atom143,axiom,
! [V_pname,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom143(V_pname,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__rec(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,hAPP(c_Com_Ocom_OBODY,V_pname),T_a) = hAPP(V_f7,V_pname) ),
inference(definition,[],[]) ).
fof(to_be_clausified_143,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_pname] :
( lhs_atom143(V_pname,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Orecs_I7_J_0_0,def_lhs_atom143]) ).
fof(def_lhs_atom144,axiom,
! [V_pname_H,V_fun,V_com2,V_com1] :
( lhs_atom144(V_pname_H,V_fun,V_com2,V_com1)
<=> hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_144,plain,
! [V_com1,V_com2,V_fun,V_pname_H] :
( lhs_atom144(V_pname_H,V_fun,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I55_J_0_0,def_lhs_atom144]) ).
fof(def_lhs_atom145,axiom,
! [V_pname_H,V_fun,V_com2,V_com1] :
( lhs_atom145(V_pname_H,V_fun,V_com2,V_com1)
<=> c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_145,plain,
! [V_com1,V_com2,V_fun,V_pname_H] :
( lhs_atom145(V_pname_H,V_fun,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I54_J_0_0,def_lhs_atom145]) ).
fof(def_lhs_atom146,axiom,
! [V_vname,V_pname_H,V_fun] :
( lhs_atom146(V_vname,V_pname_H,V_fun)
<=> hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OAss(V_vname,V_fun) ),
inference(definition,[],[]) ).
fof(to_be_clausified_146,plain,
! [V_fun,V_pname_H,V_vname] :
( lhs_atom146(V_vname,V_pname_H,V_fun)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I31_J_0_0,def_lhs_atom146]) ).
fof(def_lhs_atom147,axiom,
! [V_vname,V_pname_H,V_fun] :
( lhs_atom147(V_vname,V_pname_H,V_fun)
<=> c_Com_Ocom_OAss(V_vname,V_fun) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_147,plain,
! [V_fun,V_pname_H,V_vname] :
( lhs_atom147(V_vname,V_pname_H,V_fun)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I30_J_0_0,def_lhs_atom147]) ).
fof(def_lhs_atom148,axiom,
! [V_pname_H,V_loc,V_fun,V_com] :
( lhs_atom148(V_pname_H,V_loc,V_fun,V_com)
<=> hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_148,plain,
! [V_com,V_fun,V_loc,V_pname_H] :
( lhs_atom148(V_pname_H,V_loc,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I41_J_0_0,def_lhs_atom148]) ).
fof(def_lhs_atom149,axiom,
! [V_pname_H,V_fun,V_com] :
( lhs_atom149(V_pname_H,V_fun,V_com)
<=> hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OWhile(V_fun,V_com) ),
inference(definition,[],[]) ).
fof(to_be_clausified_149,plain,
! [V_com,V_fun,V_pname_H] :
( lhs_atom149(V_pname_H,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I59_J_0_0,def_lhs_atom149]) ).
fof(def_lhs_atom150,axiom,
! [V_vname_H,V_pname_H,V_pname,V_fun_H] :
( lhs_atom150(V_vname_H,V_pname_H,V_pname,V_fun_H)
<=> c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != hAPP(c_Com_Ocom_OBODY,V_pname) ),
inference(definition,[],[]) ).
fof(to_be_clausified_150,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( lhs_atom150(V_vname_H,V_pname_H,V_pname,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I63_J_0_0,def_lhs_atom150]) ).
fof(def_lhs_atom151,axiom,
! [V_pname_H,V_com2,V_com1] :
( lhs_atom151(V_pname_H,V_com2,V_com1)
<=> hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_151,plain,
! [V_com1,V_com2,V_pname_H] :
( lhs_atom151(V_pname_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I49_J_0_0,def_lhs_atom151]) ).
fof(def_lhs_atom152,axiom,
! [V_pname_H,V_com2,V_com1] :
( lhs_atom152(V_pname_H,V_com2,V_com1)
<=> c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_152,plain,
! [V_com1,V_com2,V_pname_H] :
( lhs_atom152(V_pname_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I48_J_0_0,def_lhs_atom152]) ).
fof(def_lhs_atom153,axiom,
! [V_pname_H,V_loc,V_fun,V_com] :
( lhs_atom153(V_pname_H,V_loc,V_fun,V_com)
<=> c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_153,plain,
! [V_com,V_fun,V_loc,V_pname_H] :
( lhs_atom153(V_pname_H,V_loc,V_fun,V_com)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I40_J_0_0,def_lhs_atom153]) ).
fof(def_lhs_atom154,axiom,
! [V_vname_H,V_pname_H,V_pname,V_fun_H] :
( lhs_atom154(V_vname_H,V_pname_H,V_pname,V_fun_H)
<=> hAPP(c_Com_Ocom_OBODY,V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_154,plain,
! [V_fun_H,V_pname,V_pname_H,V_vname_H] :
( lhs_atom154(V_vname_H,V_pname_H,V_pname,V_fun_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I62_J_0_0,def_lhs_atom154]) ).
fof(def_lhs_atom155,axiom,
! [V_pname,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a] :
( lhs_atom155(V_pname,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
<=> c_Com_Ocom_Ocom__case(V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,hAPP(c_Com_Ocom_OBODY,V_pname),T_a) = hAPP(V_f7,V_pname) ),
inference(definition,[],[]) ).
fof(to_be_clausified_155,plain,
! [T_a,V_f1,V_f2,V_f3,V_f4,V_f5,V_f6,V_f7,V_f8,V_pname] :
( lhs_atom155(V_pname,V_f8,V_f7,V_f6,V_f5,V_f4,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I70_J_0_0,def_lhs_atom155]) ).
fof(def_lhs_atom156,axiom,
! [V_pname_H] :
( lhs_atom156(V_pname_H)
<=> c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_156,plain,
! [V_pname_H] :
( lhs_atom156(V_pname_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I18_J_0_0,def_lhs_atom156]) ).
fof(def_lhs_atom157,axiom,
! [V_G,T_a] :
( lhs_atom157(V_G,T_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_157,plain,
! [T_a,V_G] :
( lhs_atom157(V_G,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty_0_0,def_lhs_atom157]) ).
fof(def_lhs_atom158,axiom,
! [V_y,T_b,T_a] :
( lhs_atom158(V_y,T_b,T_a)
<=> c_Map_Odom(c_COMBK(hAPP(c_Option_Ooption_OSome(T_b),V_y),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_158,plain,
! [T_a,T_b,V_y] :
( lhs_atom158(V_y,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__const_0_0,def_lhs_atom158]) ).
fof(def_lhs_atom159,axiom,
( lhs_atom159
<=> c_Com_OWT(c_Com_Ocom_OSKIP) ),
inference(definition,[],[]) ).
fof(to_be_clausified_159,plain,
( lhs_atom159
| $false ),
inference(fold_definition,[status(thm)],[cls_WT_OSkip_0_0,def_lhs_atom159]) ).
fof(def_lhs_atom160,axiom,
! [V_a,V_X] :
( lhs_atom160(V_a,V_X)
<=> c_Com_OWT(c_Com_Ocom_OAss(V_X,V_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_160,plain,
! [V_X,V_a] :
( lhs_atom160(V_a,V_X)
| $false ),
inference(fold_definition,[status(thm)],[cls_WT_OAssign_0_0,def_lhs_atom160]) ).
fof(def_lhs_atom161,axiom,
( lhs_atom161
<=> hAPP(c_Hoare__Mirabelle_OMGT,v_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),v_c),c_Natural_Oevalc(v_c)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_161,plain,
( lhs_atom161
| $false ),
inference(fold_definition,[status(thm)],[cls_MGT__def__raw_0_0,def_lhs_atom161]) ).
fof(def_lhs_atom162,axiom,
! [V_g,V_f,T_c,T_b,T_a] :
( lhs_atom162(V_g,V_f,T_c,T_b,T_a)
<=> c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_162,plain,
! [T_a,T_b,T_c,V_f,V_g] :
( lhs_atom162(V_g,V_f,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_range__composition_0_0,def_lhs_atom162]) ).
fof(def_lhs_atom163,axiom,
( lhs_atom163
<=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
inference(definition,[],[]) ).
fof(to_be_clausified_163,plain,
( lhs_atom163
| $false ),
inference(fold_definition,[status(thm)],[cls_finite__dom__body_0_0,def_lhs_atom163]) ).
fof(def_lhs_atom164,axiom,
! [V_x,T_a] :
( lhs_atom164(V_x,T_a)
<=> hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_164,plain,
! [T_a,V_x] :
( lhs_atom164(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_the_Osimps_0_0,def_lhs_atom164]) ).
fof(def_lhs_atom165,axiom,
! [V_g,V_f,V_A,T_c,T_b,T_a] :
( lhs_atom165(V_g,V_f,V_A,T_c,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_165,plain,
! [T_a,T_b,T_c,V_A,V_f,V_g] :
( lhs_atom165(V_g,V_f,V_A,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__image_0_0,def_lhs_atom165]) ).
fof(def_lhs_atom166,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom166(V_R,V_Q,V_P,T_c,T_b,T_a)
<=> hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_166,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom166(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBB__def_0_0,def_lhs_atom166]) ).
fof(def_lhs_atom167,axiom,
( lhs_atom167
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_167,plain,
( lhs_atom167
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice_0,def_lhs_atom167]) ).
fof(def_lhs_atom168,axiom,
( lhs_atom168
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_168,plain,
( lhs_atom168
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom168]) ).
fof(def_lhs_atom169,axiom,
( lhs_atom169
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_169,plain,
( lhs_atom169
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom169]) ).
fof(def_lhs_atom170,axiom,
( lhs_atom170
<=> class_Lattices_Olattice(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_170,plain,
( lhs_atom170
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olattice_0,def_lhs_atom170]) ).
fof(def_lhs_atom171,axiom,
( lhs_atom171
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_171,plain,
( lhs_atom171
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom171]) ).
fof(def_lhs_atom172,axiom,
( lhs_atom172
<=> class_Orderings_Obot(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_172,plain,
( lhs_atom172
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Obot_0,def_lhs_atom172]) ).
fof(def_lhs_atom173,axiom,
( lhs_atom173
<=> class_HOL_Oord(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_173,plain,
( lhs_atom173
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Oord_0,def_lhs_atom173]) ).
fof(def_lhs_atom174,axiom,
( lhs_atom174
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_174,plain,
( lhs_atom174
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice_0,def_lhs_atom174]) ).
fof(def_lhs_atom175,axiom,
( lhs_atom175
<=> class_Lattices_Obounded__lattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_175,plain,
( lhs_atom175
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice_0,def_lhs_atom175]) ).
fof(def_lhs_atom176,axiom,
( lhs_atom176
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_176,plain,
( lhs_atom176
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite_0,def_lhs_atom176]) ).
fof(def_lhs_atom177,axiom,
( lhs_atom177
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_177,plain,
( lhs_atom177
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom177]) ).
fof(def_lhs_atom178,axiom,
( lhs_atom178
<=> class_Lattices_Olattice(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_178,plain,
( lhs_atom178
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olattice_0,def_lhs_atom178]) ).
fof(def_lhs_atom179,axiom,
( lhs_atom179
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_179,plain,
( lhs_atom179
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom179]) ).
fof(def_lhs_atom180,axiom,
( lhs_atom180
<=> class_Orderings_Otop(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_180,plain,
( lhs_atom180
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Otop_0,def_lhs_atom180]) ).
fof(def_lhs_atom181,axiom,
( lhs_atom181
<=> class_Orderings_Obot(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_181,plain,
( lhs_atom181
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Obot_0,def_lhs_atom181]) ).
fof(def_lhs_atom182,axiom,
( lhs_atom182
<=> class_HOL_Oord(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_182,plain,
( lhs_atom182
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Oord_0,def_lhs_atom182]) ).
fof(def_lhs_atom183,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom183(V_R,V_Q,V_P,T_c,T_b,T_a)
<=> c_COMBC(V_P,V_Q,V_R,T_b,T_c,T_a) = hAPP(hAPP(V_P,V_R),V_Q) ),
inference(definition,[],[]) ).
fof(to_be_clausified_183,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom183(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0_0,def_lhs_atom183]) ).
fof(to_be_clausified_184,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom166(V_R,V_Q,V_P,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0_0,def_lhs_atom166]) ).
fof(def_lhs_atom184,axiom,
! [V_x,T_a] :
( lhs_atom184(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_185,plain,
! [T_a,V_x] :
( lhs_atom184(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom184]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] :
( lhs_atom125(X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_1,axiom,
! [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( lhs_atom106(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_2,axiom,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] :
( lhs_atom93(X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_3,axiom,
! [X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom81(X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_4,axiom,
! [X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom13(X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_5,axiom,
! [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( lhs_atom1(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_6,axiom,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( lhs_atom107(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_7,axiom,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( lhs_atom91(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_8,axiom,
! [X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom89(X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_9,axiom,
! [X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] :
( lhs_atom78(X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_10,axiom,
! [X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] :
( lhs_atom22(X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_11,axiom,
! [X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom17(X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_12,axiom,
! [X26,X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom155(X26,X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_155) ).
fof(c_0_13,axiom,
! [X26,X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom143(X26,X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_14,axiom,
! [X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom48(X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_15,axiom,
! [X3,X4,X5,X6,X7,X8,X9,X10,X12] :
( lhs_atom3(X3,X4,X5,X6,X7,X8,X9,X10,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_16,axiom,
! [X30,X28,X29,X31,X16,X12] :
( lhs_atom166(X30,X28,X29,X31,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_184) ).
fof(c_0_17,axiom,
! [X30,X28,X29,X31,X16,X12] :
( lhs_atom183(X30,X28,X29,X31,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_183) ).
fof(c_0_18,axiom,
! [X30,X28,X29,X31,X16,X12] :
( lhs_atom166(X30,X28,X29,X31,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_166) ).
fof(c_0_19,axiom,
! [X49,X32,X22,X31,X16,X12] :
( lhs_atom165(X49,X32,X22,X31,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_165) ).
fof(c_0_20,axiom,
! [X18,X19,X1,X17,X2,X11] :
( lhs_atom128(X18,X19,X1,X17,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_21,axiom,
! [X27,X23,X49,X32,X16,X12] :
( lhs_atom116(X27,X23,X49,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_22,axiom,
! [X18,X19,X1,X17,X2,X11] :
( lhs_atom76(X18,X19,X1,X17,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_23,axiom,
! [X44,X27,X23,X32,X16,X12] :
( lhs_atom57(X44,X27,X23,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_24,axiom,
! [X18,X19,X17,X2,X20,X21] :
( lhs_atom44(X18,X19,X17,X2,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_25,axiom,
! [X1,X17,X2,X14,X15,X11] :
( lhs_atom39(X1,X17,X2,X14,X15,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_26,axiom,
! [X30,X28,X29,X31,X16,X12] :
( lhs_atom16(X30,X28,X29,X31,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_27,axiom,
! [X18,X19,X17,X2,X20,X21] :
( lhs_atom6(X18,X19,X17,X2,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_28,axiom,
! [X1,X17,X2,X14,X15,X11] :
( lhs_atom5(X1,X17,X2,X14,X15,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_29,axiom,
! [X49,X32,X31,X16,X12] :
( lhs_atom162(X49,X32,X31,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_162) ).
fof(c_0_30,axiom,
! [X9,X10,X24,X16,X12] :
( lhs_atom137(X9,X10,X24,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_31,axiom,
! [X33,X23,X34,X47,X12] :
( lhs_atom132(X33,X23,X34,X47,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_32,axiom,
! [X9,X10,X24,X16,X12] :
( lhs_atom131(X9,X10,X24,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_33,axiom,
! [X18,X13,X19,X17,X2] :
( lhs_atom112(X18,X13,X19,X17,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_34,axiom,
! [X27,X23,X32,X47,X12] :
( lhs_atom101(X27,X23,X32,X47,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_35,axiom,
! [X27,X23,X32,X16,X12] :
( lhs_atom99(X27,X23,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_36,axiom,
! [X32,X24,X25,X16,X12] :
( lhs_atom95(X32,X24,X25,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_37,axiom,
! [X32,X25,X22,X16,X12] :
( lhs_atom94(X32,X25,X22,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_38,axiom,
! [X13,X17,X2,X14,X15] :
( lhs_atom90(X13,X17,X2,X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_39,axiom,
! [X18,X19,X17,X20,X21] :
( lhs_atom88(X18,X19,X17,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_40,axiom,
! [X17,X2,X35,X20,X21] :
( lhs_atom86(X17,X2,X35,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_41,axiom,
! [X1,X2,X14,X15,X11] :
( lhs_atom79(X1,X2,X14,X15,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_42,axiom,
! [X18,X19,X17,X2,X11] :
( lhs_atom77(X18,X19,X17,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_43,axiom,
! [X18,X13,X19,X17,X2] :
( lhs_atom73(X18,X13,X19,X17,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_44,axiom,
! [X18,X19,X17,X2,X11] :
( lhs_atom59(X18,X19,X17,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_45,axiom,
! [X13,X17,X2,X14,X15] :
( lhs_atom52(X13,X17,X2,X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_46,axiom,
! [X1,X17,X2,X35,X11] :
( lhs_atom49(X1,X17,X2,X35,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_47,axiom,
! [X13,X39,X17,X2,X35] :
( lhs_atom47(X13,X39,X17,X2,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_48,axiom,
! [X41,X42,X43,X16,X12] :
( lhs_atom46(X41,X42,X43,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_49,axiom,
! [X17,X14,X20,X15,X21] :
( lhs_atom42(X17,X14,X20,X15,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_50,axiom,
! [X17,X2,X35,X20,X21] :
( lhs_atom37(X17,X2,X35,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_51,axiom,
! [X13,X39,X17,X2,X35] :
( lhs_atom36(X13,X39,X17,X2,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_52,axiom,
! [X23,X37,X38,X16,X12] :
( lhs_atom34(X23,X37,X38,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_53,axiom,
! [X1,X2,X14,X15,X11] :
( lhs_atom33(X1,X2,X14,X15,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_54,axiom,
! [X17,X14,X20,X15,X21] :
( lhs_atom31(X17,X14,X20,X15,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_55,axiom,
! [X1,X17,X2,X35,X11] :
( lhs_atom24(X1,X17,X2,X35,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_56,axiom,
! [X18,X19,X17,X20,X21] :
( lhs_atom8(X18,X19,X17,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_57,axiom,
! [X18,X19,X26,X17] :
( lhs_atom154(X18,X19,X26,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_154) ).
fof(c_0_58,axiom,
! [X19,X1,X2,X11] :
( lhs_atom153(X19,X1,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_153) ).
fof(c_0_59,axiom,
! [X18,X19,X26,X17] :
( lhs_atom150(X18,X19,X26,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_150) ).
fof(c_0_60,axiom,
! [X19,X1,X2,X11] :
( lhs_atom148(X19,X1,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_148) ).
fof(c_0_61,axiom,
! [X19,X2,X20,X21] :
( lhs_atom145(X19,X2,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_145) ).
fof(c_0_62,axiom,
! [X19,X2,X20,X21] :
( lhs_atom144(X19,X2,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_63,axiom,
! [X23,X32,X16,X12] :
( lhs_atom140(X23,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_64,axiom,
! [X17,X35,X20,X21] :
( lhs_atom118(X17,X35,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_65,axiom,
! [X13,X17,X2,X35] :
( lhs_atom104(X13,X17,X2,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_66,axiom,
! [X23,X32,X47,X12] :
( lhs_atom102(X23,X32,X47,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_67,axiom,
! [X23,X32,X16,X12] :
( lhs_atom100(X23,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_68,axiom,
! [X23,X32,X16,X12] :
( lhs_atom98(X23,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_69,axiom,
! [X33,X23,X16,X12] :
( lhs_atom74(X33,X23,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_70,axiom,
! [X36,X25,X22,X12] :
( lhs_atom69(X36,X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_71,axiom,
! [X36,X25,X22,X12] :
( lhs_atom68(X36,X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_72,axiom,
! [X9,X10,X16,X12] :
( lhs_atom66(X9,X10,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_73,axiom,
! [X9,X10,X16,X12] :
( lhs_atom65(X9,X10,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_74,axiom,
! [X13,X2,X14,X15] :
( lhs_atom61(X13,X2,X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_75,axiom,
! [X13,X17,X2,X35] :
( lhs_atom45(X13,X17,X2,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_76,axiom,
! [X40,X34,X16,X12] :
( lhs_atom38(X40,X34,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_77,axiom,
! [X17,X35,X20,X21] :
( lhs_atom28(X17,X35,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_78,axiom,
! [X24,X25,X22,X12] :
( lhs_atom26(X24,X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_79,axiom,
! [X24,X36,X25,X12] :
( lhs_atom25(X24,X36,X25,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_80,axiom,
! [X23,X32,X16,X12] :
( lhs_atom18(X23,X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_81,axiom,
! [X28,X29,X16,X12] :
( lhs_atom15(X28,X29,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_82,axiom,
! [X27,X23,X22,X12] :
( lhs_atom14(X27,X23,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_83,axiom,
! [X13,X2,X14,X15] :
( lhs_atom2(X13,X2,X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_84,axiom,
! [X27,X16,X12] :
( lhs_atom158(X27,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_158) ).
fof(c_0_85,axiom,
! [X19,X20,X21] :
( lhs_atom152(X19,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_152) ).
fof(c_0_86,axiom,
! [X19,X20,X21] :
( lhs_atom151(X19,X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_151) ).
fof(c_0_87,axiom,
! [X19,X2,X11] :
( lhs_atom149(X19,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_149) ).
fof(c_0_88,axiom,
! [X13,X19,X2] :
( lhs_atom147(X13,X19,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_147) ).
fof(c_0_89,axiom,
! [X13,X19,X2] :
( lhs_atom146(X13,X19,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_146) ).
fof(c_0_90,axiom,
! [X19,X2,X11] :
( lhs_atom142(X19,X2,X11)
| ~ $true ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_91,axiom,
! [X32,X16,X12] :
( lhs_atom96(X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_92,axiom,
! [X18,X19,X17] :
( lhs_atom123(X18,X19,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_93,axiom,
! [X18,X19,X17] :
( lhs_atom117(X18,X19,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_94,axiom,
! [X23,X22,X12] :
( lhs_atom115(X23,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_95,axiom,
! [X29,X48,X12] :
( lhs_atom114(X29,X48,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_96,axiom,
! [X24,X22,X12] :
( lhs_atom105(X24,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_97,axiom,
! [X32,X16,X12] :
( lhs_atom96(X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_98,axiom,
! [X17,X14,X15] :
( lhs_atom85(X17,X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_99,axiom,
! [X25,X22,X12] :
( lhs_atom84(X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_100,axiom,
! [X32,X16,X12] :
( lhs_atom83(X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_101,axiom,
! [X24,X22,X12] :
( lhs_atom82(X24,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_102,axiom,
! [X25,X22,X12] :
( lhs_atom80(X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_103,axiom,
! [X46,X16,X12] :
( lhs_atom75(X46,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_104,axiom,
! [X17,X14,X15] :
( lhs_atom72(X17,X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_105,axiom,
! [X25,X22,X12] :
( lhs_atom71(X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_106,axiom,
! [X25,X22,X12] :
( lhs_atom70(X25,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_107,axiom,
! [X32,X16,X12] :
( lhs_atom67(X32,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_108,axiom,
! [X39,X17,X35] :
( lhs_atom62(X39,X17,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_109,axiom,
! [X39,X17,X35] :
( lhs_atom55(X39,X17,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_110,axiom,
! [X24,X25,X12] :
( lhs_atom40(X24,X25,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_111,axiom,
! [X23,X22,X12] :
( lhs_atom35(X23,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_112,axiom,
! [X24,X22,X12] :
( lhs_atom32(X24,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_113,axiom,
! [X34,X16,X12] :
( lhs_atom21(X34,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_114,axiom,
! [X34,X16,X12] :
( lhs_atom20(X34,X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_115,axiom,
! [X33,X23,X12] :
( lhs_atom19(X33,X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_116,axiom,
! [X23,X25,X12] :
( lhs_atom11(X23,X25,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_117,axiom,
! [X24,X25,X12] :
( lhs_atom10(X24,X25,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_118,axiom,
! [X23,X22,X12] :
( lhs_atom9(X23,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_119,axiom,
! [X23,X12] :
( lhs_atom184(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_185) ).
fof(c_0_120,axiom,
! [X23,X12] :
( lhs_atom164(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_164) ).
fof(c_0_121,axiom,
! [X24,X52] :
( lhs_atom160(X24,X52)
| ~ $true ),
file('<stdin>',to_be_clausified_160) ).
fof(c_0_122,axiom,
! [X48,X12] :
( lhs_atom157(X48,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_157) ).
fof(c_0_123,axiom,
! [X51,X12] :
( lhs_atom139(X51,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_124,axiom,
! [X27,X12] :
( lhs_atom138(X27,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_125,axiom,
! [X51,X12] :
( lhs_atom136(X51,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_126,axiom,
! [X33,X12] :
( lhs_atom135(X33,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_127,axiom,
! [X23,X12] :
( lhs_atom134(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_128,axiom,
! [X22,X12] :
( lhs_atom133(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_129,axiom,
! [X50,X12] :
( lhs_atom130(X50,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_130,axiom,
! [X14,X15] :
( lhs_atom129(X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_131,axiom,
! [X18,X17] :
( lhs_atom126(X18,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_132,axiom,
! [X23,X12] :
( lhs_atom124(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_133,axiom,
! [X22,X12] :
( lhs_atom122(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_134,axiom,
! [X23,X12] :
( lhs_atom121(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_135,axiom,
! [X14,X15] :
( lhs_atom113(X14,X15)
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_136,axiom,
! [X22,X12] :
( lhs_atom111(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_137,axiom,
! [X23,X12] :
( lhs_atom110(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_138,axiom,
! [X46,X12] :
( lhs_atom109(X46,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_139,axiom,
! [X24,X12] :
( lhs_atom108(X24,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_140,axiom,
! [X18,X17] :
( lhs_atom97(X18,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_141,axiom,
! [X23,X12] :
( lhs_atom92(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_142,axiom,
! [X45,X40] :
( lhs_atom63(X45,X40)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_143,axiom,
! [X23,X12] :
( lhs_atom58(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_144,axiom,
! [X23,X12] :
( lhs_atom54(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_145,axiom,
! [X17,X35] :
( lhs_atom53(X17,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_146,axiom,
! [X22,X12] :
( lhs_atom51(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_147,axiom,
! [X25,X12] :
( lhs_atom50(X25,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_148,axiom,
! [X23,X12] :
( lhs_atom43(X23,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_149,axiom,
! [X22,X12] :
( lhs_atom30(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_150,axiom,
! [X25,X12] :
( lhs_atom29(X25,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_151,axiom,
! [X22,X12] :
( lhs_atom27(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_152,axiom,
! [X17,X35] :
( lhs_atom23(X17,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_153,axiom,
! [X22,X12] :
( lhs_atom12(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_154,axiom,
! [X22,X12] :
( lhs_atom7(X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_155,axiom,
! [X16,X12] :
( lhs_atom4(X16,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_156,axiom,
! [X19] :
( lhs_atom156(X19)
| ~ $true ),
file('<stdin>',to_be_clausified_156) ).
fof(c_0_157,axiom,
! [X19] :
( lhs_atom141(X19)
| ~ $true ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_158,axiom,
! [X12] :
( lhs_atom127(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_159,axiom,
! [X40] :
( lhs_atom120(X40)
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_160,axiom,
! [X40] :
( lhs_atom119(X40)
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_161,axiom,
! [X12] :
( lhs_atom103(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_162,axiom,
! [X46] :
( lhs_atom87(X46)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_163,axiom,
! [X12] :
( lhs_atom64(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_164,axiom,
! [X45] :
( lhs_atom60(X45)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_165,axiom,
! [X12] :
( lhs_atom56(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_166,axiom,
! [X12] :
( lhs_atom41(X12)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_167,axiom,
( lhs_atom182
| ~ $true ),
file('<stdin>',to_be_clausified_182) ).
fof(c_0_168,axiom,
( lhs_atom181
| ~ $true ),
file('<stdin>',to_be_clausified_181) ).
fof(c_0_169,axiom,
( lhs_atom180
| ~ $true ),
file('<stdin>',to_be_clausified_180) ).
fof(c_0_170,axiom,
( lhs_atom179
| ~ $true ),
file('<stdin>',to_be_clausified_179) ).
fof(c_0_171,axiom,
( lhs_atom178
| ~ $true ),
file('<stdin>',to_be_clausified_178) ).
fof(c_0_172,axiom,
( lhs_atom177
| ~ $true ),
file('<stdin>',to_be_clausified_177) ).
fof(c_0_173,axiom,
( lhs_atom176
| ~ $true ),
file('<stdin>',to_be_clausified_176) ).
fof(c_0_174,axiom,
( lhs_atom175
| ~ $true ),
file('<stdin>',to_be_clausified_175) ).
fof(c_0_175,axiom,
( lhs_atom174
| ~ $true ),
file('<stdin>',to_be_clausified_174) ).
fof(c_0_176,axiom,
( lhs_atom173
| ~ $true ),
file('<stdin>',to_be_clausified_173) ).
fof(c_0_177,axiom,
( lhs_atom172
| ~ $true ),
file('<stdin>',to_be_clausified_172) ).
fof(c_0_178,axiom,
( lhs_atom171
| ~ $true ),
file('<stdin>',to_be_clausified_171) ).
fof(c_0_179,axiom,
( lhs_atom170
| ~ $true ),
file('<stdin>',to_be_clausified_170) ).
fof(c_0_180,axiom,
( lhs_atom169
| ~ $true ),
file('<stdin>',to_be_clausified_169) ).
fof(c_0_181,axiom,
( lhs_atom168
| ~ $true ),
file('<stdin>',to_be_clausified_168) ).
fof(c_0_182,axiom,
( lhs_atom167
| ~ $true ),
file('<stdin>',to_be_clausified_167) ).
fof(c_0_183,axiom,
( lhs_atom163
| ~ $true ),
file('<stdin>',to_be_clausified_163) ).
fof(c_0_184,axiom,
( lhs_atom161
| ~ $true ),
file('<stdin>',to_be_clausified_161) ).
fof(c_0_185,axiom,
( lhs_atom159
| ~ $true ),
file('<stdin>',to_be_clausified_159) ).
fof(c_0_186,plain,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] : lhs_atom125(X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_187,plain,
! [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] : lhs_atom106(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_188,plain,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] : lhs_atom93(X2,X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_189,plain,
! [X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom81(X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_190,plain,
! [X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom13(X13,X26,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_191,plain,
! [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] : lhs_atom1(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_192,plain,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] : lhs_atom107(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_193,plain,
! [X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] : lhs_atom91(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_194,plain,
! [X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom89(X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_195,plain,
! [X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] : lhs_atom78(X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_196,plain,
! [X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12] : lhs_atom22(X3,X4,X5,X6,X7,X8,X9,X10,X20,X21,X12),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_197,plain,
! [X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom17(X13,X2,X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_198,plain,
! [X26,X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom155(X26,X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_199,plain,
! [X26,X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom143(X26,X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_200,plain,
! [X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom48(X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_201,plain,
! [X3,X4,X5,X6,X7,X8,X9,X10,X12] : lhs_atom3(X3,X4,X5,X6,X7,X8,X9,X10,X12),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_202,plain,
! [X30,X28,X29,X31,X16,X12] : lhs_atom166(X30,X28,X29,X31,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_203,plain,
! [X30,X28,X29,X31,X16,X12] : lhs_atom183(X30,X28,X29,X31,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_204,plain,
! [X30,X28,X29,X31,X16,X12] : lhs_atom166(X30,X28,X29,X31,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_205,plain,
! [X49,X32,X22,X31,X16,X12] : lhs_atom165(X49,X32,X22,X31,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_206,plain,
! [X18,X19,X1,X17,X2,X11] : lhs_atom128(X18,X19,X1,X17,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_207,plain,
! [X27,X23,X49,X32,X16,X12] : lhs_atom116(X27,X23,X49,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_208,plain,
! [X18,X19,X1,X17,X2,X11] : lhs_atom76(X18,X19,X1,X17,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_209,plain,
! [X44,X27,X23,X32,X16,X12] : lhs_atom57(X44,X27,X23,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_210,plain,
! [X18,X19,X17,X2,X20,X21] : lhs_atom44(X18,X19,X17,X2,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_211,plain,
! [X1,X17,X2,X14,X15,X11] : lhs_atom39(X1,X17,X2,X14,X15,X11),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_212,plain,
! [X30,X28,X29,X31,X16,X12] : lhs_atom16(X30,X28,X29,X31,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_213,plain,
! [X18,X19,X17,X2,X20,X21] : lhs_atom6(X18,X19,X17,X2,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_214,plain,
! [X1,X17,X2,X14,X15,X11] : lhs_atom5(X1,X17,X2,X14,X15,X11),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_215,plain,
! [X49,X32,X31,X16,X12] : lhs_atom162(X49,X32,X31,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_216,plain,
! [X9,X10,X24,X16,X12] : lhs_atom137(X9,X10,X24,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_217,plain,
! [X33,X23,X34,X47,X12] : lhs_atom132(X33,X23,X34,X47,X12),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_218,plain,
! [X9,X10,X24,X16,X12] : lhs_atom131(X9,X10,X24,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_219,plain,
! [X18,X13,X19,X17,X2] : lhs_atom112(X18,X13,X19,X17,X2),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_220,plain,
! [X27,X23,X32,X47,X12] : lhs_atom101(X27,X23,X32,X47,X12),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_221,plain,
! [X27,X23,X32,X16,X12] : lhs_atom99(X27,X23,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_222,plain,
! [X32,X24,X25,X16,X12] : lhs_atom95(X32,X24,X25,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_223,plain,
! [X32,X25,X22,X16,X12] : lhs_atom94(X32,X25,X22,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_224,plain,
! [X13,X17,X2,X14,X15] : lhs_atom90(X13,X17,X2,X14,X15),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_225,plain,
! [X18,X19,X17,X20,X21] : lhs_atom88(X18,X19,X17,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_226,plain,
! [X17,X2,X35,X20,X21] : lhs_atom86(X17,X2,X35,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_227,plain,
! [X1,X2,X14,X15,X11] : lhs_atom79(X1,X2,X14,X15,X11),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_228,plain,
! [X18,X19,X17,X2,X11] : lhs_atom77(X18,X19,X17,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_229,plain,
! [X18,X13,X19,X17,X2] : lhs_atom73(X18,X13,X19,X17,X2),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_230,plain,
! [X18,X19,X17,X2,X11] : lhs_atom59(X18,X19,X17,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_231,plain,
! [X13,X17,X2,X14,X15] : lhs_atom52(X13,X17,X2,X14,X15),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_232,plain,
! [X1,X17,X2,X35,X11] : lhs_atom49(X1,X17,X2,X35,X11),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_233,plain,
! [X13,X39,X17,X2,X35] : lhs_atom47(X13,X39,X17,X2,X35),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_234,plain,
! [X41,X42,X43,X16,X12] : lhs_atom46(X41,X42,X43,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_235,plain,
! [X17,X14,X20,X15,X21] : lhs_atom42(X17,X14,X20,X15,X21),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_236,plain,
! [X17,X2,X35,X20,X21] : lhs_atom37(X17,X2,X35,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_237,plain,
! [X13,X39,X17,X2,X35] : lhs_atom36(X13,X39,X17,X2,X35),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_238,plain,
! [X23,X37,X38,X16,X12] : lhs_atom34(X23,X37,X38,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_239,plain,
! [X1,X2,X14,X15,X11] : lhs_atom33(X1,X2,X14,X15,X11),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_240,plain,
! [X17,X14,X20,X15,X21] : lhs_atom31(X17,X14,X20,X15,X21),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_241,plain,
! [X1,X17,X2,X35,X11] : lhs_atom24(X1,X17,X2,X35,X11),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_242,plain,
! [X18,X19,X17,X20,X21] : lhs_atom8(X18,X19,X17,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_243,plain,
! [X18,X19,X26,X17] : lhs_atom154(X18,X19,X26,X17),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_244,plain,
! [X19,X1,X2,X11] : lhs_atom153(X19,X1,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_245,plain,
! [X18,X19,X26,X17] : lhs_atom150(X18,X19,X26,X17),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_246,plain,
! [X19,X1,X2,X11] : lhs_atom148(X19,X1,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_247,plain,
! [X19,X2,X20,X21] : lhs_atom145(X19,X2,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_248,plain,
! [X19,X2,X20,X21] : lhs_atom144(X19,X2,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_249,plain,
! [X23,X32,X16,X12] : lhs_atom140(X23,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_250,plain,
! [X17,X35,X20,X21] : lhs_atom118(X17,X35,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_251,plain,
! [X13,X17,X2,X35] : lhs_atom104(X13,X17,X2,X35),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_252,plain,
! [X23,X32,X47,X12] : lhs_atom102(X23,X32,X47,X12),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_253,plain,
! [X23,X32,X16,X12] : lhs_atom100(X23,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_254,plain,
! [X23,X32,X16,X12] : lhs_atom98(X23,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_255,plain,
! [X33,X23,X16,X12] : lhs_atom74(X33,X23,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_256,plain,
! [X36,X25,X22,X12] : lhs_atom69(X36,X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_257,plain,
! [X36,X25,X22,X12] : lhs_atom68(X36,X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_258,plain,
! [X9,X10,X16,X12] : lhs_atom66(X9,X10,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_259,plain,
! [X9,X10,X16,X12] : lhs_atom65(X9,X10,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_260,plain,
! [X13,X2,X14,X15] : lhs_atom61(X13,X2,X14,X15),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_261,plain,
! [X13,X17,X2,X35] : lhs_atom45(X13,X17,X2,X35),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_262,plain,
! [X40,X34,X16,X12] : lhs_atom38(X40,X34,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_263,plain,
! [X17,X35,X20,X21] : lhs_atom28(X17,X35,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_264,plain,
! [X24,X25,X22,X12] : lhs_atom26(X24,X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_265,plain,
! [X24,X36,X25,X12] : lhs_atom25(X24,X36,X25,X12),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_266,plain,
! [X23,X32,X16,X12] : lhs_atom18(X23,X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_267,plain,
! [X28,X29,X16,X12] : lhs_atom15(X28,X29,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_268,plain,
! [X27,X23,X22,X12] : lhs_atom14(X27,X23,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_269,plain,
! [X13,X2,X14,X15] : lhs_atom2(X13,X2,X14,X15),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_270,plain,
! [X27,X16,X12] : lhs_atom158(X27,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_271,plain,
! [X19,X20,X21] : lhs_atom152(X19,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_272,plain,
! [X19,X20,X21] : lhs_atom151(X19,X20,X21),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_273,plain,
! [X19,X2,X11] : lhs_atom149(X19,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_274,plain,
! [X13,X19,X2] : lhs_atom147(X13,X19,X2),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_275,plain,
! [X13,X19,X2] : lhs_atom146(X13,X19,X2),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_276,plain,
! [X19,X2,X11] : lhs_atom142(X19,X2,X11),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_277,plain,
! [X32,X16,X12] : lhs_atom96(X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_278,plain,
! [X18,X19,X17] : lhs_atom123(X18,X19,X17),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_279,plain,
! [X18,X19,X17] : lhs_atom117(X18,X19,X17),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_280,plain,
! [X23,X22,X12] : lhs_atom115(X23,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_281,plain,
! [X29,X48,X12] : lhs_atom114(X29,X48,X12),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_282,plain,
! [X24,X22,X12] : lhs_atom105(X24,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_283,plain,
! [X32,X16,X12] : lhs_atom96(X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_284,plain,
! [X17,X14,X15] : lhs_atom85(X17,X14,X15),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_285,plain,
! [X25,X22,X12] : lhs_atom84(X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_286,plain,
! [X32,X16,X12] : lhs_atom83(X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_287,plain,
! [X24,X22,X12] : lhs_atom82(X24,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_288,plain,
! [X25,X22,X12] : lhs_atom80(X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_289,plain,
! [X46,X16,X12] : lhs_atom75(X46,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_290,plain,
! [X17,X14,X15] : lhs_atom72(X17,X14,X15),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_291,plain,
! [X25,X22,X12] : lhs_atom71(X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_292,plain,
! [X25,X22,X12] : lhs_atom70(X25,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_293,plain,
! [X32,X16,X12] : lhs_atom67(X32,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_294,plain,
! [X39,X17,X35] : lhs_atom62(X39,X17,X35),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_295,plain,
! [X39,X17,X35] : lhs_atom55(X39,X17,X35),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_296,plain,
! [X24,X25,X12] : lhs_atom40(X24,X25,X12),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_297,plain,
! [X23,X22,X12] : lhs_atom35(X23,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_298,plain,
! [X24,X22,X12] : lhs_atom32(X24,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_299,plain,
! [X34,X16,X12] : lhs_atom21(X34,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_300,plain,
! [X34,X16,X12] : lhs_atom20(X34,X16,X12),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_301,plain,
! [X33,X23,X12] : lhs_atom19(X33,X23,X12),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_302,plain,
! [X23,X25,X12] : lhs_atom11(X23,X25,X12),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_303,plain,
! [X24,X25,X12] : lhs_atom10(X24,X25,X12),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_304,plain,
! [X23,X22,X12] : lhs_atom9(X23,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_305,plain,
! [X23,X12] : lhs_atom184(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_306,plain,
! [X23,X12] : lhs_atom164(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_307,plain,
! [X24,X52] : lhs_atom160(X24,X52),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_308,plain,
! [X48,X12] : lhs_atom157(X48,X12),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_309,plain,
! [X51,X12] : lhs_atom139(X51,X12),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_310,plain,
! [X27,X12] : lhs_atom138(X27,X12),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_311,plain,
! [X51,X12] : lhs_atom136(X51,X12),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_312,plain,
! [X33,X12] : lhs_atom135(X33,X12),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_313,plain,
! [X23,X12] : lhs_atom134(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_314,plain,
! [X22,X12] : lhs_atom133(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_315,plain,
! [X50,X12] : lhs_atom130(X50,X12),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_316,plain,
! [X14,X15] : lhs_atom129(X14,X15),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_317,plain,
! [X18,X17] : lhs_atom126(X18,X17),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_318,plain,
! [X23,X12] : lhs_atom124(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_319,plain,
! [X22,X12] : lhs_atom122(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_320,plain,
! [X23,X12] : lhs_atom121(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_321,plain,
! [X14,X15] : lhs_atom113(X14,X15),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_322,plain,
! [X22,X12] : lhs_atom111(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_323,plain,
! [X23,X12] : lhs_atom110(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_324,plain,
! [X46,X12] : lhs_atom109(X46,X12),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_325,plain,
! [X24,X12] : lhs_atom108(X24,X12),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_326,plain,
! [X18,X17] : lhs_atom97(X18,X17),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_327,plain,
! [X23,X12] : lhs_atom92(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_328,plain,
! [X45,X40] : lhs_atom63(X45,X40),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_329,plain,
! [X23,X12] : lhs_atom58(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_330,plain,
! [X23,X12] : lhs_atom54(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_331,plain,
! [X17,X35] : lhs_atom53(X17,X35),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_332,plain,
! [X22,X12] : lhs_atom51(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_333,plain,
! [X25,X12] : lhs_atom50(X25,X12),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_334,plain,
! [X23,X12] : lhs_atom43(X23,X12),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_335,plain,
! [X22,X12] : lhs_atom30(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_336,plain,
! [X25,X12] : lhs_atom29(X25,X12),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_337,plain,
! [X22,X12] : lhs_atom27(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_338,plain,
! [X17,X35] : lhs_atom23(X17,X35),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_339,plain,
! [X22,X12] : lhs_atom12(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_340,plain,
! [X22,X12] : lhs_atom7(X22,X12),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_341,plain,
! [X16,X12] : lhs_atom4(X16,X12),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_342,plain,
! [X19] : lhs_atom156(X19),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_343,plain,
! [X19] : lhs_atom141(X19),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_344,plain,
! [X12] : lhs_atom127(X12),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_345,plain,
! [X40] : lhs_atom120(X40),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_346,plain,
! [X40] : lhs_atom119(X40),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_347,plain,
! [X12] : lhs_atom103(X12),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_348,plain,
! [X46] : lhs_atom87(X46),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_349,plain,
! [X12] : lhs_atom64(X12),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_350,plain,
! [X45] : lhs_atom60(X45),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_351,plain,
! [X12] : lhs_atom56(X12),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_352,plain,
! [X12] : lhs_atom41(X12),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_353,plain,
lhs_atom182,
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_354,plain,
lhs_atom181,
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_355,plain,
lhs_atom180,
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_356,plain,
lhs_atom179,
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_357,plain,
lhs_atom178,
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_358,plain,
lhs_atom177,
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_359,plain,
lhs_atom176,
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_360,plain,
lhs_atom175,
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_361,plain,
lhs_atom174,
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_362,plain,
lhs_atom173,
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_363,plain,
lhs_atom172,
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_364,plain,
lhs_atom171,
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_365,plain,
lhs_atom170,
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_366,plain,
lhs_atom169,
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_367,plain,
lhs_atom168,
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_368,plain,
lhs_atom167,
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_369,plain,
lhs_atom163,
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_370,plain,
lhs_atom161,
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_371,plain,
lhs_atom159,
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_372,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33] : lhs_atom125(X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_373,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24] : lhs_atom106(X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_374,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33] : lhs_atom93(X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_375,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38] : lhs_atom81(X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_376,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38] : lhs_atom13(X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_377,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24] : lhs_atom1(X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_378,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23] : lhs_atom107(X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_379,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23] : lhs_atom91(X13,X14,X15,X16,X17,X18,X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_380,plain,
! [X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24] : lhs_atom89(X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_381,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32] : lhs_atom78(X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_382,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32] : lhs_atom22(X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_383,plain,
! [X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24] : lhs_atom17(X14,X15,X16,X17,X18,X19,X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_384,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36] : lhs_atom155(X27,X28,X29,X30,X31,X32,X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_385,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34,X35,X36] : lhs_atom143(X27,X28,X29,X30,X31,X32,X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_386,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21] : lhs_atom48(X13,X14,X15,X16,X17,X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_387,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21] : lhs_atom3(X13,X14,X15,X16,X17,X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_388,plain,
! [X32,X33,X34,X35,X36,X37] : lhs_atom166(X32,X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_389,plain,
! [X32,X33,X34,X35,X36,X37] : lhs_atom183(X32,X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_390,plain,
! [X32,X33,X34,X35,X36,X37] : lhs_atom166(X32,X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_391,plain,
! [X50,X51,X52,X53,X54,X55] : lhs_atom165(X50,X51,X52,X53,X54,X55),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_392,plain,
! [X20,X21,X22,X23,X24,X25] : lhs_atom128(X20,X21,X22,X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_393,plain,
! [X50,X51,X52,X53,X54,X55] : lhs_atom116(X50,X51,X52,X53,X54,X55),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_394,plain,
! [X20,X21,X22,X23,X24,X25] : lhs_atom76(X20,X21,X22,X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_395,plain,
! [X45,X46,X47,X48,X49,X50] : lhs_atom57(X45,X46,X47,X48,X49,X50),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_396,plain,
! [X22,X23,X24,X25,X26,X27] : lhs_atom44(X22,X23,X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_397,plain,
! [X18,X19,X20,X21,X22,X23] : lhs_atom39(X18,X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_398,plain,
! [X32,X33,X34,X35,X36,X37] : lhs_atom16(X32,X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_399,plain,
! [X22,X23,X24,X25,X26,X27] : lhs_atom6(X22,X23,X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_400,plain,
! [X18,X19,X20,X21,X22,X23] : lhs_atom5(X18,X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_401,plain,
! [X50,X51,X52,X53,X54] : lhs_atom162(X50,X51,X52,X53,X54),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_402,plain,
! [X25,X26,X27,X28,X29] : lhs_atom137(X25,X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_403,plain,
! [X48,X49,X50,X51,X52] : lhs_atom132(X48,X49,X50,X51,X52),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_404,plain,
! [X25,X26,X27,X28,X29] : lhs_atom131(X25,X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_405,plain,
! [X20,X21,X22,X23,X24] : lhs_atom112(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_406,plain,
! [X48,X49,X50,X51,X52] : lhs_atom101(X48,X49,X50,X51,X52),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_407,plain,
! [X33,X34,X35,X36,X37] : lhs_atom99(X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_408,plain,
! [X33,X34,X35,X36,X37] : lhs_atom95(X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_409,plain,
! [X33,X34,X35,X36,X37] : lhs_atom94(X33,X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_410,plain,
! [X18,X19,X20,X21,X22] : lhs_atom90(X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_411,plain,
! [X22,X23,X24,X25,X26] : lhs_atom88(X22,X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_412,plain,
! [X36,X37,X38,X39,X40] : lhs_atom86(X36,X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_413,plain,
! [X16,X17,X18,X19,X20] : lhs_atom79(X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_414,plain,
! [X20,X21,X22,X23,X24] : lhs_atom77(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_415,plain,
! [X20,X21,X22,X23,X24] : lhs_atom73(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_416,plain,
! [X20,X21,X22,X23,X24] : lhs_atom59(X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_417,plain,
! [X18,X19,X20,X21,X22] : lhs_atom52(X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_418,plain,
! [X36,X37,X38,X39,X40] : lhs_atom49(X36,X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_419,plain,
! [X40,X41,X42,X43,X44] : lhs_atom47(X40,X41,X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_420,plain,
! [X44,X45,X46,X47,X48] : lhs_atom46(X44,X45,X46,X47,X48),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_421,plain,
! [X22,X23,X24,X25,X26] : lhs_atom42(X22,X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_422,plain,
! [X36,X37,X38,X39,X40] : lhs_atom37(X36,X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_423,plain,
! [X40,X41,X42,X43,X44] : lhs_atom36(X40,X41,X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_424,plain,
! [X39,X40,X41,X42,X43] : lhs_atom34(X39,X40,X41,X42,X43),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_425,plain,
! [X16,X17,X18,X19,X20] : lhs_atom33(X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_426,plain,
! [X22,X23,X24,X25,X26] : lhs_atom31(X22,X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_427,plain,
! [X36,X37,X38,X39,X40] : lhs_atom24(X36,X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_428,plain,
! [X22,X23,X24,X25,X26] : lhs_atom8(X22,X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_429,plain,
! [X27,X28,X29,X30] : lhs_atom154(X27,X28,X29,X30),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_430,plain,
! [X20,X21,X22,X23] : lhs_atom153(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_431,plain,
! [X27,X28,X29,X30] : lhs_atom150(X27,X28,X29,X30),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_432,plain,
! [X20,X21,X22,X23] : lhs_atom148(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_433,plain,
! [X22,X23,X24,X25] : lhs_atom145(X22,X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_434,plain,
! [X22,X23,X24,X25] : lhs_atom144(X22,X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_435,plain,
! [X33,X34,X35,X36] : lhs_atom140(X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_436,plain,
! [X36,X37,X38,X39] : lhs_atom118(X36,X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_437,plain,
! [X36,X37,X38,X39] : lhs_atom104(X36,X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_438,plain,
! [X48,X49,X50,X51] : lhs_atom102(X48,X49,X50,X51),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_439,plain,
! [X33,X34,X35,X36] : lhs_atom100(X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_440,plain,
! [X33,X34,X35,X36] : lhs_atom98(X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_441,plain,
! [X34,X35,X36,X37] : lhs_atom74(X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_442,plain,
! [X37,X38,X39,X40] : lhs_atom69(X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_443,plain,
! [X37,X38,X39,X40] : lhs_atom68(X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_444,plain,
! [X17,X18,X19,X20] : lhs_atom66(X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_445,plain,
! [X17,X18,X19,X20] : lhs_atom65(X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_446,plain,
! [X16,X17,X18,X19] : lhs_atom61(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_447,plain,
! [X36,X37,X38,X39] : lhs_atom45(X36,X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_448,plain,
! [X41,X42,X43,X44] : lhs_atom38(X41,X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_449,plain,
! [X36,X37,X38,X39] : lhs_atom28(X36,X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_450,plain,
! [X26,X27,X28,X29] : lhs_atom26(X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_451,plain,
! [X37,X38,X39,X40] : lhs_atom25(X37,X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_452,plain,
! [X33,X34,X35,X36] : lhs_atom18(X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_453,plain,
! [X30,X31,X32,X33] : lhs_atom15(X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_454,plain,
! [X28,X29,X30,X31] : lhs_atom14(X28,X29,X30,X31),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_455,plain,
! [X16,X17,X18,X19] : lhs_atom2(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_456,plain,
! [X28,X29,X30] : lhs_atom158(X28,X29,X30),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_457,plain,
! [X22,X23,X24] : lhs_atom152(X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_458,plain,
! [X22,X23,X24] : lhs_atom151(X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_459,plain,
! [X20,X21,X22] : lhs_atom149(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_273]) ).
fof(c_0_460,plain,
! [X20,X21,X22] : lhs_atom147(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_461,plain,
! [X20,X21,X22] : lhs_atom146(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_462,plain,
! [X20,X21,X22] : lhs_atom142(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_463,plain,
! [X33,X34,X35] : lhs_atom96(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_464,plain,
! [X20,X21,X22] : lhs_atom123(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_465,plain,
! [X20,X21,X22] : lhs_atom117(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_466,plain,
! [X24,X25,X26] : lhs_atom115(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_467,plain,
! [X49,X50,X51] : lhs_atom114(X49,X50,X51),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_468,plain,
! [X25,X26,X27] : lhs_atom105(X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_469,plain,
! [X33,X34,X35] : lhs_atom96(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_470,plain,
! [X18,X19,X20] : lhs_atom85(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_471,plain,
! [X26,X27,X28] : lhs_atom84(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_472,plain,
! [X33,X34,X35] : lhs_atom83(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_473,plain,
! [X25,X26,X27] : lhs_atom82(X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_287]) ).
fof(c_0_474,plain,
! [X26,X27,X28] : lhs_atom80(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_475,plain,
! [X47,X48,X49] : lhs_atom75(X47,X48,X49),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_476,plain,
! [X18,X19,X20] : lhs_atom72(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_477,plain,
! [X26,X27,X28] : lhs_atom71(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_478,plain,
! [X26,X27,X28] : lhs_atom70(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_479,plain,
! [X33,X34,X35] : lhs_atom67(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_480,plain,
! [X40,X41,X42] : lhs_atom62(X40,X41,X42),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_481,plain,
! [X40,X41,X42] : lhs_atom55(X40,X41,X42),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_482,plain,
! [X26,X27,X28] : lhs_atom40(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_483,plain,
! [X24,X25,X26] : lhs_atom35(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_484,plain,
! [X25,X26,X27] : lhs_atom32(X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_485,plain,
! [X35,X36,X37] : lhs_atom21(X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_486,plain,
! [X35,X36,X37] : lhs_atom20(X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_300]) ).
fof(c_0_487,plain,
! [X34,X35,X36] : lhs_atom19(X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_488,plain,
! [X26,X27,X28] : lhs_atom11(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_302]) ).
fof(c_0_489,plain,
! [X26,X27,X28] : lhs_atom10(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_303]) ).
fof(c_0_490,plain,
! [X24,X25,X26] : lhs_atom9(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_491,plain,
! [X24,X25] : lhs_atom184(X24,X25),
inference(variable_rename,[status(thm)],[c_0_305]) ).
fof(c_0_492,plain,
! [X24,X25] : lhs_atom164(X24,X25),
inference(variable_rename,[status(thm)],[c_0_306]) ).
fof(c_0_493,plain,
! [X53,X54] : lhs_atom160(X53,X54),
inference(variable_rename,[status(thm)],[c_0_307]) ).
fof(c_0_494,plain,
! [X49,X50] : lhs_atom157(X49,X50),
inference(variable_rename,[status(thm)],[c_0_308]) ).
fof(c_0_495,plain,
! [X52,X53] : lhs_atom139(X52,X53),
inference(variable_rename,[status(thm)],[c_0_309]) ).
fof(c_0_496,plain,
! [X28,X29] : lhs_atom138(X28,X29),
inference(variable_rename,[status(thm)],[c_0_310]) ).
fof(c_0_497,plain,
! [X52,X53] : lhs_atom136(X52,X53),
inference(variable_rename,[status(thm)],[c_0_311]) ).
fof(c_0_498,plain,
! [X34,X35] : lhs_atom135(X34,X35),
inference(variable_rename,[status(thm)],[c_0_312]) ).
fof(c_0_499,plain,
! [X24,X25] : lhs_atom134(X24,X25),
inference(variable_rename,[status(thm)],[c_0_313]) ).
fof(c_0_500,plain,
! [X23,X24] : lhs_atom133(X23,X24),
inference(variable_rename,[status(thm)],[c_0_314]) ).
fof(c_0_501,plain,
! [X51,X52] : lhs_atom130(X51,X52),
inference(variable_rename,[status(thm)],[c_0_315]) ).
fof(c_0_502,plain,
! [X16,X17] : lhs_atom129(X16,X17),
inference(variable_rename,[status(thm)],[c_0_316]) ).
fof(c_0_503,plain,
! [X19,X20] : lhs_atom126(X19,X20),
inference(variable_rename,[status(thm)],[c_0_317]) ).
fof(c_0_504,plain,
! [X24,X25] : lhs_atom124(X24,X25),
inference(variable_rename,[status(thm)],[c_0_318]) ).
fof(c_0_505,plain,
! [X23,X24] : lhs_atom122(X23,X24),
inference(variable_rename,[status(thm)],[c_0_319]) ).
fof(c_0_506,plain,
! [X24,X25] : lhs_atom121(X24,X25),
inference(variable_rename,[status(thm)],[c_0_320]) ).
fof(c_0_507,plain,
! [X16,X17] : lhs_atom113(X16,X17),
inference(variable_rename,[status(thm)],[c_0_321]) ).
fof(c_0_508,plain,
! [X23,X24] : lhs_atom111(X23,X24),
inference(variable_rename,[status(thm)],[c_0_322]) ).
fof(c_0_509,plain,
! [X24,X25] : lhs_atom110(X24,X25),
inference(variable_rename,[status(thm)],[c_0_323]) ).
fof(c_0_510,plain,
! [X47,X48] : lhs_atom109(X47,X48),
inference(variable_rename,[status(thm)],[c_0_324]) ).
fof(c_0_511,plain,
! [X25,X26] : lhs_atom108(X25,X26),
inference(variable_rename,[status(thm)],[c_0_325]) ).
fof(c_0_512,plain,
! [X19,X20] : lhs_atom97(X19,X20),
inference(variable_rename,[status(thm)],[c_0_326]) ).
fof(c_0_513,plain,
! [X24,X25] : lhs_atom92(X24,X25),
inference(variable_rename,[status(thm)],[c_0_327]) ).
fof(c_0_514,plain,
! [X46,X47] : lhs_atom63(X46,X47),
inference(variable_rename,[status(thm)],[c_0_328]) ).
fof(c_0_515,plain,
! [X24,X25] : lhs_atom58(X24,X25),
inference(variable_rename,[status(thm)],[c_0_329]) ).
fof(c_0_516,plain,
! [X24,X25] : lhs_atom54(X24,X25),
inference(variable_rename,[status(thm)],[c_0_330]) ).
fof(c_0_517,plain,
! [X36,X37] : lhs_atom53(X36,X37),
inference(variable_rename,[status(thm)],[c_0_331]) ).
fof(c_0_518,plain,
! [X23,X24] : lhs_atom51(X23,X24),
inference(variable_rename,[status(thm)],[c_0_332]) ).
fof(c_0_519,plain,
! [X26,X27] : lhs_atom50(X26,X27),
inference(variable_rename,[status(thm)],[c_0_333]) ).
fof(c_0_520,plain,
! [X24,X25] : lhs_atom43(X24,X25),
inference(variable_rename,[status(thm)],[c_0_334]) ).
fof(c_0_521,plain,
! [X23,X24] : lhs_atom30(X23,X24),
inference(variable_rename,[status(thm)],[c_0_335]) ).
fof(c_0_522,plain,
! [X26,X27] : lhs_atom29(X26,X27),
inference(variable_rename,[status(thm)],[c_0_336]) ).
fof(c_0_523,plain,
! [X23,X24] : lhs_atom27(X23,X24),
inference(variable_rename,[status(thm)],[c_0_337]) ).
fof(c_0_524,plain,
! [X36,X37] : lhs_atom23(X36,X37),
inference(variable_rename,[status(thm)],[c_0_338]) ).
fof(c_0_525,plain,
! [X23,X24] : lhs_atom12(X23,X24),
inference(variable_rename,[status(thm)],[c_0_339]) ).
fof(c_0_526,plain,
! [X23,X24] : lhs_atom7(X23,X24),
inference(variable_rename,[status(thm)],[c_0_340]) ).
fof(c_0_527,plain,
! [X17,X18] : lhs_atom4(X17,X18),
inference(variable_rename,[status(thm)],[c_0_341]) ).
fof(c_0_528,plain,
! [X20] : lhs_atom156(X20),
inference(variable_rename,[status(thm)],[c_0_342]) ).
fof(c_0_529,plain,
! [X20] : lhs_atom141(X20),
inference(variable_rename,[status(thm)],[c_0_343]) ).
fof(c_0_530,plain,
! [X13] : lhs_atom127(X13),
inference(variable_rename,[status(thm)],[c_0_344]) ).
fof(c_0_531,plain,
! [X41] : lhs_atom120(X41),
inference(variable_rename,[status(thm)],[c_0_345]) ).
fof(c_0_532,plain,
! [X41] : lhs_atom119(X41),
inference(variable_rename,[status(thm)],[c_0_346]) ).
fof(c_0_533,plain,
! [X13] : lhs_atom103(X13),
inference(variable_rename,[status(thm)],[c_0_347]) ).
fof(c_0_534,plain,
! [X47] : lhs_atom87(X47),
inference(variable_rename,[status(thm)],[c_0_348]) ).
fof(c_0_535,plain,
! [X13] : lhs_atom64(X13),
inference(variable_rename,[status(thm)],[c_0_349]) ).
fof(c_0_536,plain,
! [X46] : lhs_atom60(X46),
inference(variable_rename,[status(thm)],[c_0_350]) ).
fof(c_0_537,plain,
! [X13] : lhs_atom56(X13),
inference(variable_rename,[status(thm)],[c_0_351]) ).
fof(c_0_538,plain,
! [X13] : lhs_atom41(X13),
inference(variable_rename,[status(thm)],[c_0_352]) ).
fof(c_0_539,plain,
lhs_atom182,
c_0_353 ).
fof(c_0_540,plain,
lhs_atom181,
c_0_354 ).
fof(c_0_541,plain,
lhs_atom180,
c_0_355 ).
fof(c_0_542,plain,
lhs_atom179,
c_0_356 ).
fof(c_0_543,plain,
lhs_atom178,
c_0_357 ).
fof(c_0_544,plain,
lhs_atom177,
c_0_358 ).
fof(c_0_545,plain,
lhs_atom176,
c_0_359 ).
fof(c_0_546,plain,
lhs_atom175,
c_0_360 ).
fof(c_0_547,plain,
lhs_atom174,
c_0_361 ).
fof(c_0_548,plain,
lhs_atom173,
c_0_362 ).
fof(c_0_549,plain,
lhs_atom172,
c_0_363 ).
fof(c_0_550,plain,
lhs_atom171,
c_0_364 ).
fof(c_0_551,plain,
lhs_atom170,
c_0_365 ).
fof(c_0_552,plain,
lhs_atom169,
c_0_366 ).
fof(c_0_553,plain,
lhs_atom168,
c_0_367 ).
fof(c_0_554,plain,
lhs_atom167,
c_0_368 ).
fof(c_0_555,plain,
lhs_atom163,
c_0_369 ).
fof(c_0_556,plain,
lhs_atom161,
c_0_370 ).
fof(c_0_557,plain,
lhs_atom159,
c_0_371 ).
cnf(c_0_558,plain,
lhs_atom125(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_559,plain,
lhs_atom106(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_560,plain,
lhs_atom93(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_561,plain,
lhs_atom81(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_562,plain,
lhs_atom13(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_563,plain,
lhs_atom1(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_564,plain,
lhs_atom107(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_565,plain,
lhs_atom91(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_566,plain,
lhs_atom89(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_567,plain,
lhs_atom78(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_568,plain,
lhs_atom22(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_569,plain,
lhs_atom17(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_570,plain,
lhs_atom155(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_571,plain,
lhs_atom143(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_572,plain,
lhs_atom48(X1,X2,X3,X4,X5,X6,X7,X8,X9),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_573,plain,
lhs_atom3(X1,X2,X3,X4,X5,X6,X7,X8,X9),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_574,plain,
lhs_atom166(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_575,plain,
lhs_atom183(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_576,plain,
lhs_atom166(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_577,plain,
lhs_atom165(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_578,plain,
lhs_atom128(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_579,plain,
lhs_atom116(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_580,plain,
lhs_atom76(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_581,plain,
lhs_atom57(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_582,plain,
lhs_atom44(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_583,plain,
lhs_atom39(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_584,plain,
lhs_atom16(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_585,plain,
lhs_atom6(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_586,plain,
lhs_atom5(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_587,plain,
lhs_atom162(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_588,plain,
lhs_atom137(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_589,plain,
lhs_atom132(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_590,plain,
lhs_atom131(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_591,plain,
lhs_atom112(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_592,plain,
lhs_atom101(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_593,plain,
lhs_atom99(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_594,plain,
lhs_atom95(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_595,plain,
lhs_atom94(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_596,plain,
lhs_atom90(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_597,plain,
lhs_atom88(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_598,plain,
lhs_atom86(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_599,plain,
lhs_atom79(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_600,plain,
lhs_atom77(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_601,plain,
lhs_atom73(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_602,plain,
lhs_atom59(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_603,plain,
lhs_atom52(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_604,plain,
lhs_atom49(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_605,plain,
lhs_atom47(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_606,plain,
lhs_atom46(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_607,plain,
lhs_atom42(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_608,plain,
lhs_atom37(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_609,plain,
lhs_atom36(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_610,plain,
lhs_atom34(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_611,plain,
lhs_atom33(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_612,plain,
lhs_atom31(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_613,plain,
lhs_atom24(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_614,plain,
lhs_atom8(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_615,plain,
lhs_atom154(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_616,plain,
lhs_atom153(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_617,plain,
lhs_atom150(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_618,plain,
lhs_atom148(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_619,plain,
lhs_atom145(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_620,plain,
lhs_atom144(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_621,plain,
lhs_atom140(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_622,plain,
lhs_atom118(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_623,plain,
lhs_atom104(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_624,plain,
lhs_atom102(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_625,plain,
lhs_atom100(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_626,plain,
lhs_atom98(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_627,plain,
lhs_atom74(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_628,plain,
lhs_atom69(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_629,plain,
lhs_atom68(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_630,plain,
lhs_atom66(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_631,plain,
lhs_atom65(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_632,plain,
lhs_atom61(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_633,plain,
lhs_atom45(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_634,plain,
lhs_atom38(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_635,plain,
lhs_atom28(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_636,plain,
lhs_atom26(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_637,plain,
lhs_atom25(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_638,plain,
lhs_atom18(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_639,plain,
lhs_atom15(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_640,plain,
lhs_atom14(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_641,plain,
lhs_atom2(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_642,plain,
lhs_atom158(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_643,plain,
lhs_atom152(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_644,plain,
lhs_atom151(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_645,plain,
lhs_atom149(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_646,plain,
lhs_atom147(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_647,plain,
lhs_atom146(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_648,plain,
lhs_atom142(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_649,plain,
lhs_atom96(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_650,plain,
lhs_atom123(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_651,plain,
lhs_atom117(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_652,plain,
lhs_atom115(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_653,plain,
lhs_atom114(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_654,plain,
lhs_atom105(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_655,plain,
lhs_atom96(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_656,plain,
lhs_atom85(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_657,plain,
lhs_atom84(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_658,plain,
lhs_atom83(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_659,plain,
lhs_atom82(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_660,plain,
lhs_atom80(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_661,plain,
lhs_atom75(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_662,plain,
lhs_atom72(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_663,plain,
lhs_atom71(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_664,plain,
lhs_atom70(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_665,plain,
lhs_atom67(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_666,plain,
lhs_atom62(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_667,plain,
lhs_atom55(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_668,plain,
lhs_atom40(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_669,plain,
lhs_atom35(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_670,plain,
lhs_atom32(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_671,plain,
lhs_atom21(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_672,plain,
lhs_atom20(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_673,plain,
lhs_atom19(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_674,plain,
lhs_atom11(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_675,plain,
lhs_atom10(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_676,plain,
lhs_atom9(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_677,plain,
lhs_atom184(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_678,plain,
lhs_atom164(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_679,plain,
lhs_atom160(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_680,plain,
lhs_atom157(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_681,plain,
lhs_atom139(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_682,plain,
lhs_atom138(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_683,plain,
lhs_atom136(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_684,plain,
lhs_atom135(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_685,plain,
lhs_atom134(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_686,plain,
lhs_atom133(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_687,plain,
lhs_atom130(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_688,plain,
lhs_atom129(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_689,plain,
lhs_atom126(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_690,plain,
lhs_atom124(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_691,plain,
lhs_atom122(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_692,plain,
lhs_atom121(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_693,plain,
lhs_atom113(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_694,plain,
lhs_atom111(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_695,plain,
lhs_atom110(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_696,plain,
lhs_atom109(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_510]) ).
cnf(c_0_697,plain,
lhs_atom108(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_698,plain,
lhs_atom97(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_512]) ).
cnf(c_0_699,plain,
lhs_atom92(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_700,plain,
lhs_atom63(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_701,plain,
lhs_atom58(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_702,plain,
lhs_atom54(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_703,plain,
lhs_atom53(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_704,plain,
lhs_atom51(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_518]) ).
cnf(c_0_705,plain,
lhs_atom50(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_706,plain,
lhs_atom43(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_707,plain,
lhs_atom30(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_521]) ).
cnf(c_0_708,plain,
lhs_atom29(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_522]) ).
cnf(c_0_709,plain,
lhs_atom27(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_710,plain,
lhs_atom23(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_711,plain,
lhs_atom12(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_712,plain,
lhs_atom7(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_713,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_714,plain,
lhs_atom156(X1),
inference(split_conjunct,[status(thm)],[c_0_528]) ).
cnf(c_0_715,plain,
lhs_atom141(X1),
inference(split_conjunct,[status(thm)],[c_0_529]) ).
cnf(c_0_716,plain,
lhs_atom127(X1),
inference(split_conjunct,[status(thm)],[c_0_530]) ).
cnf(c_0_717,plain,
lhs_atom120(X1),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_718,plain,
lhs_atom119(X1),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_719,plain,
lhs_atom103(X1),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_720,plain,
lhs_atom87(X1),
inference(split_conjunct,[status(thm)],[c_0_534]) ).
cnf(c_0_721,plain,
lhs_atom64(X1),
inference(split_conjunct,[status(thm)],[c_0_535]) ).
cnf(c_0_722,plain,
lhs_atom60(X1),
inference(split_conjunct,[status(thm)],[c_0_536]) ).
cnf(c_0_723,plain,
lhs_atom56(X1),
inference(split_conjunct,[status(thm)],[c_0_537]) ).
cnf(c_0_724,plain,
lhs_atom41(X1),
inference(split_conjunct,[status(thm)],[c_0_538]) ).
cnf(c_0_725,plain,
lhs_atom182,
inference(split_conjunct,[status(thm)],[c_0_539]) ).
cnf(c_0_726,plain,
lhs_atom181,
inference(split_conjunct,[status(thm)],[c_0_540]) ).
cnf(c_0_727,plain,
lhs_atom180,
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_728,plain,
lhs_atom179,
inference(split_conjunct,[status(thm)],[c_0_542]) ).
cnf(c_0_729,plain,
lhs_atom178,
inference(split_conjunct,[status(thm)],[c_0_543]) ).
cnf(c_0_730,plain,
lhs_atom177,
inference(split_conjunct,[status(thm)],[c_0_544]) ).
cnf(c_0_731,plain,
lhs_atom176,
inference(split_conjunct,[status(thm)],[c_0_545]) ).
cnf(c_0_732,plain,
lhs_atom175,
inference(split_conjunct,[status(thm)],[c_0_546]) ).
cnf(c_0_733,plain,
lhs_atom174,
inference(split_conjunct,[status(thm)],[c_0_547]) ).
cnf(c_0_734,plain,
lhs_atom173,
inference(split_conjunct,[status(thm)],[c_0_548]) ).
cnf(c_0_735,plain,
lhs_atom172,
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_736,plain,
lhs_atom171,
inference(split_conjunct,[status(thm)],[c_0_550]) ).
cnf(c_0_737,plain,
lhs_atom170,
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_738,plain,
lhs_atom169,
inference(split_conjunct,[status(thm)],[c_0_552]) ).
cnf(c_0_739,plain,
lhs_atom168,
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_740,plain,
lhs_atom167,
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_741,plain,
lhs_atom163,
inference(split_conjunct,[status(thm)],[c_0_555]) ).
cnf(c_0_742,plain,
lhs_atom161,
inference(split_conjunct,[status(thm)],[c_0_556]) ).
cnf(c_0_743,plain,
lhs_atom159,
inference(split_conjunct,[status(thm)],[c_0_557]) ).
cnf(c_0_744,plain,
lhs_atom125(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
c_0_558,
[final] ).
cnf(c_0_745,plain,
lhs_atom106(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
c_0_559,
[final] ).
cnf(c_0_746,plain,
lhs_atom93(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
c_0_560,
[final] ).
cnf(c_0_747,plain,
lhs_atom81(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
c_0_561,
[final] ).
cnf(c_0_748,plain,
lhs_atom13(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
c_0_562,
[final] ).
cnf(c_0_749,plain,
lhs_atom1(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12),
c_0_563,
[final] ).
cnf(c_0_750,plain,
lhs_atom107(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
c_0_564,
[final] ).
cnf(c_0_751,plain,
lhs_atom91(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
c_0_565,
[final] ).
cnf(c_0_752,plain,
lhs_atom89(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
c_0_566,
[final] ).
cnf(c_0_753,plain,
lhs_atom78(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
c_0_567,
[final] ).
cnf(c_0_754,plain,
lhs_atom22(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
c_0_568,
[final] ).
cnf(c_0_755,plain,
lhs_atom17(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11),
c_0_569,
[final] ).
cnf(c_0_756,plain,
lhs_atom155(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10),
c_0_570,
[final] ).
cnf(c_0_757,plain,
lhs_atom143(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10),
c_0_571,
[final] ).
cnf(c_0_758,plain,
lhs_atom48(X1,X2,X3,X4,X5,X6,X7,X8,X9),
c_0_572,
[final] ).
cnf(c_0_759,plain,
lhs_atom3(X1,X2,X3,X4,X5,X6,X7,X8,X9),
c_0_573,
[final] ).
cnf(c_0_760,plain,
lhs_atom166(X1,X2,X3,X4,X5,X6),
c_0_574,
[final] ).
cnf(c_0_761,plain,
lhs_atom183(X1,X2,X3,X4,X5,X6),
c_0_575,
[final] ).
cnf(c_0_762,plain,
lhs_atom166(X1,X2,X3,X4,X5,X6),
c_0_576,
[final] ).
cnf(c_0_763,plain,
lhs_atom165(X1,X2,X3,X4,X5,X6),
c_0_577,
[final] ).
cnf(c_0_764,plain,
lhs_atom128(X1,X2,X3,X4,X5,X6),
c_0_578,
[final] ).
cnf(c_0_765,plain,
lhs_atom116(X1,X2,X3,X4,X5,X6),
c_0_579,
[final] ).
cnf(c_0_766,plain,
lhs_atom76(X1,X2,X3,X4,X5,X6),
c_0_580,
[final] ).
cnf(c_0_767,plain,
lhs_atom57(X1,X2,X3,X4,X5,X6),
c_0_581,
[final] ).
cnf(c_0_768,plain,
lhs_atom44(X1,X2,X3,X4,X5,X6),
c_0_582,
[final] ).
cnf(c_0_769,plain,
lhs_atom39(X1,X2,X3,X4,X5,X6),
c_0_583,
[final] ).
cnf(c_0_770,plain,
lhs_atom16(X1,X2,X3,X4,X5,X6),
c_0_584,
[final] ).
cnf(c_0_771,plain,
lhs_atom6(X1,X2,X3,X4,X5,X6),
c_0_585,
[final] ).
cnf(c_0_772,plain,
lhs_atom5(X1,X2,X3,X4,X5,X6),
c_0_586,
[final] ).
cnf(c_0_773,plain,
lhs_atom162(X1,X2,X3,X4,X5),
c_0_587,
[final] ).
cnf(c_0_774,plain,
lhs_atom137(X1,X2,X3,X4,X5),
c_0_588,
[final] ).
cnf(c_0_775,plain,
lhs_atom132(X1,X2,X3,X4,X5),
c_0_589,
[final] ).
cnf(c_0_776,plain,
lhs_atom131(X1,X2,X3,X4,X5),
c_0_590,
[final] ).
cnf(c_0_777,plain,
lhs_atom112(X1,X2,X3,X4,X5),
c_0_591,
[final] ).
cnf(c_0_778,plain,
lhs_atom101(X1,X2,X3,X4,X5),
c_0_592,
[final] ).
cnf(c_0_779,plain,
lhs_atom99(X1,X2,X3,X4,X5),
c_0_593,
[final] ).
cnf(c_0_780,plain,
lhs_atom95(X1,X2,X3,X4,X5),
c_0_594,
[final] ).
cnf(c_0_781,plain,
lhs_atom94(X1,X2,X3,X4,X5),
c_0_595,
[final] ).
cnf(c_0_782,plain,
lhs_atom90(X1,X2,X3,X4,X5),
c_0_596,
[final] ).
cnf(c_0_783,plain,
lhs_atom88(X1,X2,X3,X4,X5),
c_0_597,
[final] ).
cnf(c_0_784,plain,
lhs_atom86(X1,X2,X3,X4,X5),
c_0_598,
[final] ).
cnf(c_0_785,plain,
lhs_atom79(X1,X2,X3,X4,X5),
c_0_599,
[final] ).
cnf(c_0_786,plain,
lhs_atom77(X1,X2,X3,X4,X5),
c_0_600,
[final] ).
cnf(c_0_787,plain,
lhs_atom73(X1,X2,X3,X4,X5),
c_0_601,
[final] ).
cnf(c_0_788,plain,
lhs_atom59(X1,X2,X3,X4,X5),
c_0_602,
[final] ).
cnf(c_0_789,plain,
lhs_atom52(X1,X2,X3,X4,X5),
c_0_603,
[final] ).
cnf(c_0_790,plain,
lhs_atom49(X1,X2,X3,X4,X5),
c_0_604,
[final] ).
cnf(c_0_791,plain,
lhs_atom47(X1,X2,X3,X4,X5),
c_0_605,
[final] ).
cnf(c_0_792,plain,
lhs_atom46(X1,X2,X3,X4,X5),
c_0_606,
[final] ).
cnf(c_0_793,plain,
lhs_atom42(X1,X2,X3,X4,X5),
c_0_607,
[final] ).
cnf(c_0_794,plain,
lhs_atom37(X1,X2,X3,X4,X5),
c_0_608,
[final] ).
cnf(c_0_795,plain,
lhs_atom36(X1,X2,X3,X4,X5),
c_0_609,
[final] ).
cnf(c_0_796,plain,
lhs_atom34(X1,X2,X3,X4,X5),
c_0_610,
[final] ).
cnf(c_0_797,plain,
lhs_atom33(X1,X2,X3,X4,X5),
c_0_611,
[final] ).
cnf(c_0_798,plain,
lhs_atom31(X1,X2,X3,X4,X5),
c_0_612,
[final] ).
cnf(c_0_799,plain,
lhs_atom24(X1,X2,X3,X4,X5),
c_0_613,
[final] ).
cnf(c_0_800,plain,
lhs_atom8(X1,X2,X3,X4,X5),
c_0_614,
[final] ).
cnf(c_0_801,plain,
lhs_atom154(X1,X2,X3,X4),
c_0_615,
[final] ).
cnf(c_0_802,plain,
lhs_atom153(X1,X2,X3,X4),
c_0_616,
[final] ).
cnf(c_0_803,plain,
lhs_atom150(X1,X2,X3,X4),
c_0_617,
[final] ).
cnf(c_0_804,plain,
lhs_atom148(X1,X2,X3,X4),
c_0_618,
[final] ).
cnf(c_0_805,plain,
lhs_atom145(X1,X2,X3,X4),
c_0_619,
[final] ).
cnf(c_0_806,plain,
lhs_atom144(X1,X2,X3,X4),
c_0_620,
[final] ).
cnf(c_0_807,plain,
lhs_atom140(X1,X2,X3,X4),
c_0_621,
[final] ).
cnf(c_0_808,plain,
lhs_atom118(X1,X2,X3,X4),
c_0_622,
[final] ).
cnf(c_0_809,plain,
lhs_atom104(X1,X2,X3,X4),
c_0_623,
[final] ).
cnf(c_0_810,plain,
lhs_atom102(X1,X2,X3,X4),
c_0_624,
[final] ).
cnf(c_0_811,plain,
lhs_atom100(X1,X2,X3,X4),
c_0_625,
[final] ).
cnf(c_0_812,plain,
lhs_atom98(X1,X2,X3,X4),
c_0_626,
[final] ).
cnf(c_0_813,plain,
lhs_atom74(X1,X2,X3,X4),
c_0_627,
[final] ).
cnf(c_0_814,plain,
lhs_atom69(X1,X2,X3,X4),
c_0_628,
[final] ).
cnf(c_0_815,plain,
lhs_atom68(X1,X2,X3,X4),
c_0_629,
[final] ).
cnf(c_0_816,plain,
lhs_atom66(X1,X2,X3,X4),
c_0_630,
[final] ).
cnf(c_0_817,plain,
lhs_atom65(X1,X2,X3,X4),
c_0_631,
[final] ).
cnf(c_0_818,plain,
lhs_atom61(X1,X2,X3,X4),
c_0_632,
[final] ).
cnf(c_0_819,plain,
lhs_atom45(X1,X2,X3,X4),
c_0_633,
[final] ).
cnf(c_0_820,plain,
lhs_atom38(X1,X2,X3,X4),
c_0_634,
[final] ).
cnf(c_0_821,plain,
lhs_atom28(X1,X2,X3,X4),
c_0_635,
[final] ).
cnf(c_0_822,plain,
lhs_atom26(X1,X2,X3,X4),
c_0_636,
[final] ).
cnf(c_0_823,plain,
lhs_atom25(X1,X2,X3,X4),
c_0_637,
[final] ).
cnf(c_0_824,plain,
lhs_atom18(X1,X2,X3,X4),
c_0_638,
[final] ).
cnf(c_0_825,plain,
lhs_atom15(X1,X2,X3,X4),
c_0_639,
[final] ).
cnf(c_0_826,plain,
lhs_atom14(X1,X2,X3,X4),
c_0_640,
[final] ).
cnf(c_0_827,plain,
lhs_atom2(X1,X2,X3,X4),
c_0_641,
[final] ).
cnf(c_0_828,plain,
lhs_atom158(X1,X2,X3),
c_0_642,
[final] ).
cnf(c_0_829,plain,
lhs_atom152(X1,X2,X3),
c_0_643,
[final] ).
cnf(c_0_830,plain,
lhs_atom151(X1,X2,X3),
c_0_644,
[final] ).
cnf(c_0_831,plain,
lhs_atom149(X1,X2,X3),
c_0_645,
[final] ).
cnf(c_0_832,plain,
lhs_atom147(X1,X2,X3),
c_0_646,
[final] ).
cnf(c_0_833,plain,
lhs_atom146(X1,X2,X3),
c_0_647,
[final] ).
cnf(c_0_834,plain,
lhs_atom142(X1,X2,X3),
c_0_648,
[final] ).
cnf(c_0_835,plain,
lhs_atom96(X1,X2,X3),
c_0_649,
[final] ).
cnf(c_0_836,plain,
lhs_atom123(X1,X2,X3),
c_0_650,
[final] ).
cnf(c_0_837,plain,
lhs_atom117(X1,X2,X3),
c_0_651,
[final] ).
cnf(c_0_838,plain,
lhs_atom115(X1,X2,X3),
c_0_652,
[final] ).
cnf(c_0_839,plain,
lhs_atom114(X1,X2,X3),
c_0_653,
[final] ).
cnf(c_0_840,plain,
lhs_atom105(X1,X2,X3),
c_0_654,
[final] ).
cnf(c_0_841,plain,
lhs_atom96(X1,X2,X3),
c_0_655,
[final] ).
cnf(c_0_842,plain,
lhs_atom85(X1,X2,X3),
c_0_656,
[final] ).
cnf(c_0_843,plain,
lhs_atom84(X1,X2,X3),
c_0_657,
[final] ).
cnf(c_0_844,plain,
lhs_atom83(X1,X2,X3),
c_0_658,
[final] ).
cnf(c_0_845,plain,
lhs_atom82(X1,X2,X3),
c_0_659,
[final] ).
cnf(c_0_846,plain,
lhs_atom80(X1,X2,X3),
c_0_660,
[final] ).
cnf(c_0_847,plain,
lhs_atom75(X1,X2,X3),
c_0_661,
[final] ).
cnf(c_0_848,plain,
lhs_atom72(X1,X2,X3),
c_0_662,
[final] ).
cnf(c_0_849,plain,
lhs_atom71(X1,X2,X3),
c_0_663,
[final] ).
cnf(c_0_850,plain,
lhs_atom70(X1,X2,X3),
c_0_664,
[final] ).
cnf(c_0_851,plain,
lhs_atom67(X1,X2,X3),
c_0_665,
[final] ).
cnf(c_0_852,plain,
lhs_atom62(X1,X2,X3),
c_0_666,
[final] ).
cnf(c_0_853,plain,
lhs_atom55(X1,X2,X3),
c_0_667,
[final] ).
cnf(c_0_854,plain,
lhs_atom40(X1,X2,X3),
c_0_668,
[final] ).
cnf(c_0_855,plain,
lhs_atom35(X1,X2,X3),
c_0_669,
[final] ).
cnf(c_0_856,plain,
lhs_atom32(X1,X2,X3),
c_0_670,
[final] ).
cnf(c_0_857,plain,
lhs_atom21(X1,X2,X3),
c_0_671,
[final] ).
cnf(c_0_858,plain,
lhs_atom20(X1,X2,X3),
c_0_672,
[final] ).
cnf(c_0_859,plain,
lhs_atom19(X1,X2,X3),
c_0_673,
[final] ).
cnf(c_0_860,plain,
lhs_atom11(X1,X2,X3),
c_0_674,
[final] ).
cnf(c_0_861,plain,
lhs_atom10(X1,X2,X3),
c_0_675,
[final] ).
cnf(c_0_862,plain,
lhs_atom9(X1,X2,X3),
c_0_676,
[final] ).
cnf(c_0_863,plain,
lhs_atom184(X1,X2),
c_0_677,
[final] ).
cnf(c_0_864,plain,
lhs_atom164(X1,X2),
c_0_678,
[final] ).
cnf(c_0_865,plain,
lhs_atom160(X1,X2),
c_0_679,
[final] ).
cnf(c_0_866,plain,
lhs_atom157(X1,X2),
c_0_680,
[final] ).
cnf(c_0_867,plain,
lhs_atom139(X1,X2),
c_0_681,
[final] ).
cnf(c_0_868,plain,
lhs_atom138(X1,X2),
c_0_682,
[final] ).
cnf(c_0_869,plain,
lhs_atom136(X1,X2),
c_0_683,
[final] ).
cnf(c_0_870,plain,
lhs_atom135(X1,X2),
c_0_684,
[final] ).
cnf(c_0_871,plain,
lhs_atom134(X1,X2),
c_0_685,
[final] ).
cnf(c_0_872,plain,
lhs_atom133(X1,X2),
c_0_686,
[final] ).
cnf(c_0_873,plain,
lhs_atom130(X1,X2),
c_0_687,
[final] ).
cnf(c_0_874,plain,
lhs_atom129(X1,X2),
c_0_688,
[final] ).
cnf(c_0_875,plain,
lhs_atom126(X1,X2),
c_0_689,
[final] ).
cnf(c_0_876,plain,
lhs_atom124(X1,X2),
c_0_690,
[final] ).
cnf(c_0_877,plain,
lhs_atom122(X1,X2),
c_0_691,
[final] ).
cnf(c_0_878,plain,
lhs_atom121(X1,X2),
c_0_692,
[final] ).
cnf(c_0_879,plain,
lhs_atom113(X1,X2),
c_0_693,
[final] ).
cnf(c_0_880,plain,
lhs_atom111(X1,X2),
c_0_694,
[final] ).
cnf(c_0_881,plain,
lhs_atom110(X1,X2),
c_0_695,
[final] ).
cnf(c_0_882,plain,
lhs_atom109(X1,X2),
c_0_696,
[final] ).
cnf(c_0_883,plain,
lhs_atom108(X1,X2),
c_0_697,
[final] ).
cnf(c_0_884,plain,
lhs_atom97(X1,X2),
c_0_698,
[final] ).
cnf(c_0_885,plain,
lhs_atom92(X1,X2),
c_0_699,
[final] ).
cnf(c_0_886,plain,
lhs_atom63(X1,X2),
c_0_700,
[final] ).
cnf(c_0_887,plain,
lhs_atom58(X1,X2),
c_0_701,
[final] ).
cnf(c_0_888,plain,
lhs_atom54(X1,X2),
c_0_702,
[final] ).
cnf(c_0_889,plain,
lhs_atom53(X1,X2),
c_0_703,
[final] ).
cnf(c_0_890,plain,
lhs_atom51(X1,X2),
c_0_704,
[final] ).
cnf(c_0_891,plain,
lhs_atom50(X1,X2),
c_0_705,
[final] ).
cnf(c_0_892,plain,
lhs_atom43(X1,X2),
c_0_706,
[final] ).
cnf(c_0_893,plain,
lhs_atom30(X1,X2),
c_0_707,
[final] ).
cnf(c_0_894,plain,
lhs_atom29(X1,X2),
c_0_708,
[final] ).
cnf(c_0_895,plain,
lhs_atom27(X1,X2),
c_0_709,
[final] ).
cnf(c_0_896,plain,
lhs_atom23(X1,X2),
c_0_710,
[final] ).
cnf(c_0_897,plain,
lhs_atom12(X1,X2),
c_0_711,
[final] ).
cnf(c_0_898,plain,
lhs_atom7(X1,X2),
c_0_712,
[final] ).
cnf(c_0_899,plain,
lhs_atom4(X1,X2),
c_0_713,
[final] ).
cnf(c_0_900,plain,
lhs_atom156(X1),
c_0_714,
[final] ).
cnf(c_0_901,plain,
lhs_atom141(X1),
c_0_715,
[final] ).
cnf(c_0_902,plain,
lhs_atom127(X1),
c_0_716,
[final] ).
cnf(c_0_903,plain,
lhs_atom120(X1),
c_0_717,
[final] ).
cnf(c_0_904,plain,
lhs_atom119(X1),
c_0_718,
[final] ).
cnf(c_0_905,plain,
lhs_atom103(X1),
c_0_719,
[final] ).
cnf(c_0_906,plain,
lhs_atom87(X1),
c_0_720,
[final] ).
cnf(c_0_907,plain,
lhs_atom64(X1),
c_0_721,
[final] ).
cnf(c_0_908,plain,
lhs_atom60(X1),
c_0_722,
[final] ).
cnf(c_0_909,plain,
lhs_atom56(X1),
c_0_723,
[final] ).
cnf(c_0_910,plain,
lhs_atom41(X1),
c_0_724,
[final] ).
cnf(c_0_911,plain,
lhs_atom182,
c_0_725,
[final] ).
cnf(c_0_912,plain,
lhs_atom181,
c_0_726,
[final] ).
cnf(c_0_913,plain,
lhs_atom180,
c_0_727,
[final] ).
cnf(c_0_914,plain,
lhs_atom179,
c_0_728,
[final] ).
cnf(c_0_915,plain,
lhs_atom178,
c_0_729,
[final] ).
cnf(c_0_916,plain,
lhs_atom177,
c_0_730,
[final] ).
cnf(c_0_917,plain,
lhs_atom176,
c_0_731,
[final] ).
cnf(c_0_918,plain,
lhs_atom175,
c_0_732,
[final] ).
cnf(c_0_919,plain,
lhs_atom174,
c_0_733,
[final] ).
cnf(c_0_920,plain,
lhs_atom173,
c_0_734,
[final] ).
cnf(c_0_921,plain,
lhs_atom172,
c_0_735,
[final] ).
cnf(c_0_922,plain,
lhs_atom171,
c_0_736,
[final] ).
cnf(c_0_923,plain,
lhs_atom170,
c_0_737,
[final] ).
cnf(c_0_924,plain,
lhs_atom169,
c_0_738,
[final] ).
cnf(c_0_925,plain,
lhs_atom168,
c_0_739,
[final] ).
cnf(c_0_926,plain,
lhs_atom167,
c_0_740,
[final] ).
cnf(c_0_927,plain,
lhs_atom163,
c_0_741,
[final] ).
cnf(c_0_928,plain,
lhs_atom161,
c_0_742,
[final] ).
cnf(c_0_929,plain,
lhs_atom159,
c_0_743,
[final] ).
% End CNF derivation
cnf(c_0_744_0,axiom,
c_Com_Ocom_Ocom__case(X9,X8,X7,X6,X5,X4,X3,X2,c_Com_Ocom_OCond(X1,X11,X10),X12) = hAPP(hAPP(hAPP(X5,X1),X11),X10),
inference(unfold_definition,[status(thm)],[c_0_744,def_lhs_atom125]) ).
cnf(c_0_745_0,axiom,
c_Com_Ocom_Ocom__case(X10,X9,X8,X7,X6,X5,X4,X3,c_Com_Ocom_OLocal(X1,X2,X11),X12) = hAPP(hAPP(hAPP(X8,X1),X2),X11),
inference(unfold_definition,[status(thm)],[c_0_745,def_lhs_atom106]) ).
cnf(c_0_746_0,axiom,
c_Com_Ocom_Ocom__rec(X9,X8,X7,X6,X5,X4,X3,X2,c_Com_Ocom_OCond(X1,X11,X10),X12) = hAPP(hAPP(hAPP(hAPP(hAPP(X5,X1),X11),X10),c_Com_Ocom_Ocom__rec(X9,X8,X7,X6,X5,X4,X3,X2,X11,X12)),c_Com_Ocom_Ocom__rec(X9,X8,X7,X6,X5,X4,X3,X2,X10,X12)),
inference(unfold_definition,[status(thm)],[c_0_746,def_lhs_atom93]) ).
cnf(c_0_747_0,axiom,
c_Com_Ocom_Ocom__rec(X11,X10,X9,X8,X7,X6,X5,X4,c_Com_Ocom_OCall(X1,X2,X3),X12) = hAPP(hAPP(hAPP(X4,X1),X2),X3),
inference(unfold_definition,[status(thm)],[c_0_747,def_lhs_atom81]) ).
cnf(c_0_748_0,axiom,
c_Com_Ocom_Ocom__case(X11,X10,X9,X8,X7,X6,X5,X4,c_Com_Ocom_OCall(X1,X2,X3),X12) = hAPP(hAPP(hAPP(X4,X1),X2),X3),
inference(unfold_definition,[status(thm)],[c_0_748,def_lhs_atom13]) ).
cnf(c_0_749_0,axiom,
c_Com_Ocom_Ocom__rec(X10,X9,X8,X7,X6,X5,X4,X3,c_Com_Ocom_OLocal(X1,X2,X11),X12) = hAPP(hAPP(hAPP(hAPP(X8,X1),X2),X11),c_Com_Ocom_Ocom__rec(X10,X9,X8,X7,X6,X5,X4,X3,X11,X12)),
inference(unfold_definition,[status(thm)],[c_0_749,def_lhs_atom1]) ).
cnf(c_0_750_0,axiom,
c_Com_Ocom_Ocom__case(X9,X8,X7,X6,X5,X4,X3,X2,c_Com_Ocom_OWhile(X1,X10),X11) = hAPP(hAPP(X4,X1),X10),
inference(unfold_definition,[status(thm)],[c_0_750,def_lhs_atom107]) ).
cnf(c_0_751_0,axiom,
c_Com_Ocom_Ocom__rec(X9,X8,X7,X6,X5,X4,X3,X2,c_Com_Ocom_OWhile(X1,X10),X11) = hAPP(hAPP(hAPP(X4,X1),X10),c_Com_Ocom_Ocom__rec(X9,X8,X7,X6,X5,X4,X3,X2,X10,X11)),
inference(unfold_definition,[status(thm)],[c_0_751,def_lhs_atom91]) ).
cnf(c_0_752_0,axiom,
c_Com_Ocom_Ocom__rec(X10,X9,X8,X7,X6,X5,X4,X3,c_Com_Ocom_OAss(X1,X2),X11) = hAPP(hAPP(X9,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_752,def_lhs_atom89]) ).
cnf(c_0_753_0,axiom,
c_Com_Ocom_Ocom__case(X8,X7,X6,X5,X4,X3,X2,X1,c_Com_Ocom_OSemi(X10,X9),X11) = hAPP(hAPP(X5,X10),X9),
inference(unfold_definition,[status(thm)],[c_0_753,def_lhs_atom78]) ).
cnf(c_0_754_0,axiom,
c_Com_Ocom_Ocom__rec(X8,X7,X6,X5,X4,X3,X2,X1,c_Com_Ocom_OSemi(X10,X9),X11) = hAPP(hAPP(hAPP(hAPP(X5,X10),X9),c_Com_Ocom_Ocom__rec(X8,X7,X6,X5,X4,X3,X2,X1,X10,X11)),c_Com_Ocom_Ocom__rec(X8,X7,X6,X5,X4,X3,X2,X1,X9,X11)),
inference(unfold_definition,[status(thm)],[c_0_754,def_lhs_atom22]) ).
cnf(c_0_755_0,axiom,
c_Com_Ocom_Ocom__case(X10,X9,X8,X7,X6,X5,X4,X3,c_Com_Ocom_OAss(X1,X2),X11) = hAPP(hAPP(X9,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_755,def_lhs_atom17]) ).
cnf(c_0_756_0,axiom,
c_Com_Ocom_Ocom__case(X9,X8,X7,X6,X5,X4,X3,X2,hAPP(c_Com_Ocom_OBODY,X1),X10) = hAPP(X3,X1),
inference(unfold_definition,[status(thm)],[c_0_756,def_lhs_atom155]) ).
cnf(c_0_757_0,axiom,
c_Com_Ocom_Ocom__rec(X9,X8,X7,X6,X5,X4,X3,X2,hAPP(c_Com_Ocom_OBODY,X1),X10) = hAPP(X3,X1),
inference(unfold_definition,[status(thm)],[c_0_757,def_lhs_atom143]) ).
cnf(c_0_758_0,axiom,
c_Com_Ocom_Ocom__case(X8,X7,X6,X5,X4,X3,X2,X1,c_Com_Ocom_OSKIP,X9) = X8,
inference(unfold_definition,[status(thm)],[c_0_758,def_lhs_atom48]) ).
cnf(c_0_759_0,axiom,
c_Com_Ocom_Ocom__rec(X8,X7,X6,X5,X4,X3,X2,X1,c_Com_Ocom_OSKIP,X9) = X8,
inference(unfold_definition,[status(thm)],[c_0_759,def_lhs_atom3]) ).
cnf(c_0_760_0,axiom,
hAPP(c_COMBB(X3,X2,X5,X6,X4),X1) = hAPP(X3,hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_760,def_lhs_atom166]) ).
cnf(c_0_761_0,axiom,
c_COMBC(X3,X2,X1,X5,X4,X6) = hAPP(hAPP(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_761,def_lhs_atom183]) ).
cnf(c_0_762_0,axiom,
hAPP(c_COMBB(X3,X2,X5,X6,X4),X1) = hAPP(X3,hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_762,def_lhs_atom166]) ).
cnf(c_0_763_0,axiom,
c_Set_Oimage(X2,c_Set_Oimage(X1,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X2,X1,X5,X6,X4),X3,X4,X6),
inference(unfold_definition,[status(thm)],[c_0_763,def_lhs_atom165]) ).
cnf(c_0_764_0,axiom,
c_Com_Ocom_OLocal(X3,X5,X6) != c_Com_Ocom_OCall(X1,X2,X4),
inference(unfold_definition,[status(thm)],[c_0_764,def_lhs_atom128]) ).
cnf(c_0_765_0,axiom,
c_Map_Omap__add(X4,c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)),X6,X5) = c_Fun_Ofun__upd(c_Map_Omap__add(X4,X3,X6,X5),X2,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)),
inference(unfold_definition,[status(thm)],[c_0_765,def_lhs_atom116]) ).
cnf(c_0_766_0,axiom,
c_Com_Ocom_OCall(X1,X2,X4) != c_Com_Ocom_OLocal(X3,X5,X6),
inference(unfold_definition,[status(thm)],[c_0_766,def_lhs_atom76]) ).
cnf(c_0_767_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X3,X2,X6,X5),X3,X1,X6,X5) = c_Fun_Ofun__upd(X4,X3,X1,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_767,def_lhs_atom57]) ).
cnf(c_0_768_0,axiom,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCond(X4,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_768,def_lhs_atom44]) ).
cnf(c_0_769_0,axiom,
c_Com_Ocom_OCond(X2,X5,X4) != c_Com_Ocom_OLocal(X1,X3,X6),
inference(unfold_definition,[status(thm)],[c_0_769,def_lhs_atom39]) ).
cnf(c_0_770_0,axiom,
hAPP(c_COMBS(X3,X2,X5,X4,X6),X1) = hAPP(hAPP(X3,X1),hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_770,def_lhs_atom16]) ).
cnf(c_0_771_0,axiom,
c_Com_Ocom_OCond(X4,X6,X5) != c_Com_Ocom_OCall(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_771,def_lhs_atom6]) ).
cnf(c_0_772_0,axiom,
c_Com_Ocom_OLocal(X1,X3,X6) != c_Com_Ocom_OCond(X2,X5,X4),
inference(unfold_definition,[status(thm)],[c_0_772,def_lhs_atom5]) ).
cnf(c_0_773_0,axiom,
c_Set_Oimage(c_COMBB(X2,X1,X3,X5,X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) = c_Set_Oimage(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),X3,X5),
inference(unfold_definition,[status(thm)],[c_0_773,def_lhs_atom162]) ).
cnf(c_0_774_0,axiom,
c_Option_Ooption_Ooption__case(X2,X1,hAPP(c_Option_Ooption_OSome(X4),X3),X5,X4) = hAPP(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_774,def_lhs_atom137]) ).
cnf(c_0_775_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X1,hAPP(c_Option_Ooption_OSome(X5),X2),X4,tc_Option_Ooption(X5)),X1) = hAPP(c_Option_Ooption_OSome(X5),X2),
inference(unfold_definition,[status(thm)],[c_0_775,def_lhs_atom132]) ).
cnf(c_0_776_0,axiom,
c_Option_Ooption_Ooption__rec(X2,X1,hAPP(c_Option_Ooption_OSome(X4),X3),X5,X4) = hAPP(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_776,def_lhs_atom131]) ).
cnf(c_0_777_0,axiom,
c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OAss(X2,X5),
inference(unfold_definition,[status(thm)],[c_0_777,def_lhs_atom112]) ).
cnf(c_0_778_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X2,X1,X5,X4),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_778,def_lhs_atom101]) ).
cnf(c_0_779_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X5),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_779,def_lhs_atom99]) ).
cnf(c_0_780_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_780,def_lhs_atom95]) ).
cnf(c_0_781_0,axiom,
c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X3,X4,X5),c_Set_Oimage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_781,def_lhs_atom94]) ).
cnf(c_0_782_0,axiom,
c_Com_Ocom_OCond(X2,X5,X4) != c_Com_Ocom_OAss(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_782,def_lhs_atom90]) ).
cnf(c_0_783_0,axiom,
c_Com_Ocom_OSemi(X5,X4) != c_Com_Ocom_OCall(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_783,def_lhs_atom88]) ).
cnf(c_0_784_0,axiom,
c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OCond(X2,X5,X4),
inference(unfold_definition,[status(thm)],[c_0_784,def_lhs_atom86]) ).
cnf(c_0_785_0,axiom,
c_Com_Ocom_OLocal(X1,X2,X5) != c_Com_Ocom_OSemi(X4,X3),
inference(unfold_definition,[status(thm)],[c_0_785,def_lhs_atom79]) ).
cnf(c_0_786_0,axiom,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(unfold_definition,[status(thm)],[c_0_786,def_lhs_atom77]) ).
cnf(c_0_787_0,axiom,
c_Com_Ocom_OAss(X2,X5) != c_Com_Ocom_OCall(X1,X3,X4),
inference(unfold_definition,[status(thm)],[c_0_787,def_lhs_atom73]) ).
cnf(c_0_788_0,axiom,
c_Com_Ocom_OWhile(X4,X5) != c_Com_Ocom_OCall(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_788,def_lhs_atom59]) ).
cnf(c_0_789_0,axiom,
c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OCond(X2,X5,X4),
inference(unfold_definition,[status(thm)],[c_0_789,def_lhs_atom52]) ).
cnf(c_0_790_0,axiom,
c_Com_Ocom_OLocal(X1,X3,X5) != c_Com_Ocom_OWhile(X2,X4),
inference(unfold_definition,[status(thm)],[c_0_790,def_lhs_atom49]) ).
cnf(c_0_791_0,axiom,
c_Com_Ocom_OAss(X1,X4) != c_Com_Ocom_OLocal(X2,X3,X5),
inference(unfold_definition,[status(thm)],[c_0_791,def_lhs_atom47]) ).
cnf(c_0_792_0,axiom,
c_Map_Omap__add(X3,c_Map_Omap__add(X2,X1,X5,X4),X5,X4) = c_Map_Omap__add(c_Map_Omap__add(X3,X2,X5,X4),X1,X5,X4),
inference(unfold_definition,[status(thm)],[c_0_792,def_lhs_atom46]) ).
cnf(c_0_793_0,axiom,
c_Com_Ocom_OCond(X1,X4,X2) != c_Com_Ocom_OSemi(X5,X3),
inference(unfold_definition,[status(thm)],[c_0_793,def_lhs_atom42]) ).
cnf(c_0_794_0,axiom,
c_Com_Ocom_OCond(X2,X5,X4) != c_Com_Ocom_OWhile(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_794,def_lhs_atom37]) ).
cnf(c_0_795_0,axiom,
c_Com_Ocom_OLocal(X2,X3,X5) != c_Com_Ocom_OAss(X1,X4),
inference(unfold_definition,[status(thm)],[c_0_795,def_lhs_atom36]) ).
cnf(c_0_796_0,axiom,
c_Fun_Ofun__upd(X2,X3,hAPP(c_Option_Ooption_OSome(X4),X1),X5,tc_Option_Ooption(X4)) != c_COMBK(c_Option_Ooption_ONone(X4),tc_Option_Ooption(X4),X5),
inference(unfold_definition,[status(thm)],[c_0_796,def_lhs_atom34]) ).
cnf(c_0_797_0,axiom,
c_Com_Ocom_OSemi(X4,X3) != c_Com_Ocom_OLocal(X1,X2,X5),
inference(unfold_definition,[status(thm)],[c_0_797,def_lhs_atom33]) ).
cnf(c_0_798_0,axiom,
c_Com_Ocom_OSemi(X5,X3) != c_Com_Ocom_OCond(X1,X4,X2),
inference(unfold_definition,[status(thm)],[c_0_798,def_lhs_atom31]) ).
cnf(c_0_799_0,axiom,
c_Com_Ocom_OWhile(X2,X4) != c_Com_Ocom_OLocal(X1,X3,X5),
inference(unfold_definition,[status(thm)],[c_0_799,def_lhs_atom24]) ).
cnf(c_0_800_0,axiom,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSemi(X5,X4),
inference(unfold_definition,[status(thm)],[c_0_800,def_lhs_atom8]) ).
cnf(c_0_801_0,axiom,
hAPP(c_Com_Ocom_OBODY,X3) != c_Com_Ocom_OCall(X1,X2,X4),
inference(unfold_definition,[status(thm)],[c_0_801,def_lhs_atom154]) ).
cnf(c_0_802_0,axiom,
c_Com_Ocom_OLocal(X2,X3,X4) != hAPP(c_Com_Ocom_OBODY,X1),
inference(unfold_definition,[status(thm)],[c_0_802,def_lhs_atom153]) ).
cnf(c_0_803_0,axiom,
c_Com_Ocom_OCall(X1,X2,X4) != hAPP(c_Com_Ocom_OBODY,X3),
inference(unfold_definition,[status(thm)],[c_0_803,def_lhs_atom150]) ).
cnf(c_0_804_0,axiom,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OLocal(X2,X3,X4),
inference(unfold_definition,[status(thm)],[c_0_804,def_lhs_atom148]) ).
cnf(c_0_805_0,axiom,
c_Com_Ocom_OCond(X2,X4,X3) != hAPP(c_Com_Ocom_OBODY,X1),
inference(unfold_definition,[status(thm)],[c_0_805,def_lhs_atom145]) ).
cnf(c_0_806_0,axiom,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCond(X2,X4,X3),
inference(unfold_definition,[status(thm)],[c_0_806,def_lhs_atom144]) ).
cnf(c_0_807_0,axiom,
c_Option_Omap(X2,hAPP(c_Option_Ooption_OSome(X3),X1),X3,X4) = hAPP(c_Option_Ooption_OSome(X4),hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_807,def_lhs_atom140]) ).
cnf(c_0_808_0,axiom,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X4,X3),
inference(unfold_definition,[status(thm)],[c_0_808,def_lhs_atom118]) ).
cnf(c_0_809_0,axiom,
c_Com_Ocom_OWhile(X2,X4) != c_Com_Ocom_OAss(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_809,def_lhs_atom104]) ).
cnf(c_0_810_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_810,def_lhs_atom102]) ).
cnf(c_0_811_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_811,def_lhs_atom100]) ).
cnf(c_0_812_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_812,def_lhs_atom98]) ).
cnf(c_0_813_0,axiom,
c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X3),tc_Option_Ooption(X3),X4),X2,hAPP(c_Option_Ooption_OSome(X3),X1),X4,tc_Option_Ooption(X3)),X4,X3) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_813,def_lhs_atom74]) ).
cnf(c_0_814_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_814,def_lhs_atom69]) ).
cnf(c_0_815_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_815,def_lhs_atom68]) ).
cnf(c_0_816_0,axiom,
c_Option_Ooption_Ooption__rec(X2,X1,c_Option_Ooption_ONone(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_816,def_lhs_atom66]) ).
cnf(c_0_817_0,axiom,
c_Option_Ooption_Ooption__case(X2,X1,c_Option_Ooption_ONone(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_817,def_lhs_atom65]) ).
cnf(c_0_818_0,axiom,
c_Com_Ocom_OSemi(X4,X3) != c_Com_Ocom_OAss(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_818,def_lhs_atom61]) ).
cnf(c_0_819_0,axiom,
c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OWhile(X2,X4),
inference(unfold_definition,[status(thm)],[c_0_819,def_lhs_atom45]) ).
cnf(c_0_820_0,axiom,
c_Map_Odom(c_Map_Omap__add(X2,X1,X4,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(X1,X4,X3),c_Map_Odom(X2,X4,X3),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_820,def_lhs_atom38]) ).
cnf(c_0_821_0,axiom,
c_Com_Ocom_OSemi(X4,X3) != c_Com_Ocom_OWhile(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_821,def_lhs_atom28]) ).
cnf(c_0_822_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_822,def_lhs_atom26]) ).
cnf(c_0_823_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X3,X4),X2,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_823,def_lhs_atom25]) ).
cnf(c_0_824_0,axiom,
c_in(hAPP(X2,X1),c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_824,def_lhs_atom18]) ).
cnf(c_0_825_0,axiom,
hAPP(c_COMBK(X2,X4,X3),X1) = X2,
inference(unfold_definition,[status(thm)],[c_0_825,def_lhs_atom15]) ).
cnf(c_0_826_0,axiom,
c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4) = c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_826,def_lhs_atom14]) ).
cnf(c_0_827_0,axiom,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSemi(X4,X3),
inference(unfold_definition,[status(thm)],[c_0_827,def_lhs_atom2]) ).
cnf(c_0_828_0,axiom,
c_Map_Odom(c_COMBK(hAPP(c_Option_Ooption_OSome(X2),X1),tc_Option_Ooption(X2),X3),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_828,def_lhs_atom158]) ).
cnf(c_0_829_0,axiom,
c_Com_Ocom_OSemi(X3,X2) != hAPP(c_Com_Ocom_OBODY,X1),
inference(unfold_definition,[status(thm)],[c_0_829,def_lhs_atom152]) ).
cnf(c_0_830_0,axiom,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSemi(X3,X2),
inference(unfold_definition,[status(thm)],[c_0_830,def_lhs_atom151]) ).
cnf(c_0_831_0,axiom,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OWhile(X2,X3),
inference(unfold_definition,[status(thm)],[c_0_831,def_lhs_atom149]) ).
cnf(c_0_832_0,axiom,
c_Com_Ocom_OAss(X1,X3) != hAPP(c_Com_Ocom_OBODY,X2),
inference(unfold_definition,[status(thm)],[c_0_832,def_lhs_atom147]) ).
cnf(c_0_833_0,axiom,
hAPP(c_Com_Ocom_OBODY,X2) != c_Com_Ocom_OAss(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_833,def_lhs_atom146]) ).
cnf(c_0_834_0,axiom,
c_Com_Ocom_OWhile(X2,X3) != hAPP(c_Com_Ocom_OBODY,X1),
inference(unfold_definition,[status(thm)],[c_0_834,def_lhs_atom142]) ).
cnf(c_0_835_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_835,def_lhs_atom96]) ).
cnf(c_0_836_0,axiom,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_836,def_lhs_atom123]) ).
cnf(c_0_837_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_837,def_lhs_atom117]) ).
cnf(c_0_838_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_838,def_lhs_atom115]) ).
cnf(c_0_839_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),c_Com_Ocom_OSKIP),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3),
inference(unfold_definition,[status(thm)],[c_0_839,def_lhs_atom114]) ).
cnf(c_0_840_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oinsert(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_840,def_lhs_atom105]) ).
cnf(c_0_841_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_841,def_lhs_atom96]) ).
cnf(c_0_842_0,axiom,
c_Com_Ocom_OCond(X1,X3,X2) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_842,def_lhs_atom85]) ).
cnf(c_0_843_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_843,def_lhs_atom84]) ).
cnf(c_0_844_0,axiom,
c_Option_Omap(X1,c_Option_Ooption_ONone(X2),X2,X3) = c_Option_Ooption_ONone(X3),
inference(unfold_definition,[status(thm)],[c_0_844,def_lhs_atom83]) ).
cnf(c_0_845_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_845,def_lhs_atom82]) ).
cnf(c_0_846_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_846,def_lhs_atom80]) ).
cnf(c_0_847_0,axiom,
c_Set_Oimage(c_COMBK(X1,X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_847,def_lhs_atom75]) ).
cnf(c_0_848_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_848,def_lhs_atom72]) ).
cnf(c_0_849_0,axiom,
c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_849,def_lhs_atom71]) ).
cnf(c_0_850_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_850,def_lhs_atom70]) ).
cnf(c_0_851_0,axiom,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2),
inference(unfold_definition,[status(thm)],[c_0_851,def_lhs_atom67]) ).
cnf(c_0_852_0,axiom,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_852,def_lhs_atom62]) ).
cnf(c_0_853_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_853,def_lhs_atom55]) ).
cnf(c_0_854_0,axiom,
c_lessequals(X2,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_854,def_lhs_atom40]) ).
cnf(c_0_855_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_855,def_lhs_atom35]) ).
cnf(c_0_856_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_856,def_lhs_atom32]) ).
cnf(c_0_857_0,axiom,
c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X1,X3,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_857,def_lhs_atom21]) ).
cnf(c_0_858_0,axiom,
c_Map_Omap__add(X1,c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X3,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_858,def_lhs_atom20]) ).
cnf(c_0_859_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(unfold_definition,[status(thm)],[c_0_859,def_lhs_atom19]) ).
cnf(c_0_860_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_860,def_lhs_atom11]) ).
cnf(c_0_861_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_861,def_lhs_atom10]) ).
cnf(c_0_862_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_862,def_lhs_atom9]) ).
cnf(c_0_863_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_863,def_lhs_atom184]) ).
cnf(c_0_864_0,axiom,
hAPP(c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X1)) = X1,
inference(unfold_definition,[status(thm)],[c_0_864,def_lhs_atom164]) ).
cnf(c_0_865_0,axiom,
c_Com_OWT(c_Com_Ocom_OAss(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_865,def_lhs_atom160]) ).
cnf(c_0_866_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_866,def_lhs_atom157]) ).
cnf(c_0_867_0,axiom,
c_Option_Ooption_ONone(X2) != hAPP(c_Option_Ooption_OSome(X2),X1),
inference(unfold_definition,[status(thm)],[c_0_867,def_lhs_atom139]) ).
cnf(c_0_868_0,axiom,
c_Option_Ooption_ONone(X2) != hAPP(c_Option_Ooption_OSome(X2),X1),
inference(unfold_definition,[status(thm)],[c_0_868,def_lhs_atom138]) ).
cnf(c_0_869_0,axiom,
hAPP(c_Option_Ooption_OSome(X2),X1) != c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_869,def_lhs_atom136]) ).
cnf(c_0_870_0,axiom,
hAPP(c_Option_Ooption_OSome(X2),X1) != c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_870,def_lhs_atom135]) ).
cnf(c_0_871_0,axiom,
~ c_Option_Ois__none(hAPP(c_Option_Ooption_OSome(X2),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_871,def_lhs_atom134]) ).
cnf(c_0_872_0,axiom,
c_Fun_Oinj__on(c_Option_Ooption_OSome(X2),X1,X2,tc_Option_Ooption(X2)),
inference(unfold_definition,[status(thm)],[c_0_872,def_lhs_atom133]) ).
cnf(c_0_873_0,axiom,
c_Set_Oimage(c_Fun_Oid(X2),X1,X2,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_873,def_lhs_atom130]) ).
cnf(c_0_874_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_874,def_lhs_atom129]) ).
cnf(c_0_875_0,axiom,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_875,def_lhs_atom126]) ).
cnf(c_0_876_0,axiom,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
inference(unfold_definition,[status(thm)],[c_0_876,def_lhs_atom124]) ).
cnf(c_0_877_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_877,def_lhs_atom122]) ).
cnf(c_0_878_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_878,def_lhs_atom121]) ).
cnf(c_0_879_0,axiom,
c_Com_Ocom_OSemi(X2,X1) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_879,def_lhs_atom113]) ).
cnf(c_0_880_0,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_880,def_lhs_atom111]) ).
cnf(c_0_881_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_881,def_lhs_atom110]) ).
cnf(c_0_882_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_882,def_lhs_atom109]) ).
cnf(c_0_883_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_883,def_lhs_atom108]) ).
cnf(c_0_884_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_884,def_lhs_atom97]) ).
cnf(c_0_885_0,axiom,
hAPP(c_Fun_Oid(X2),X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_885,def_lhs_atom92]) ).
cnf(c_0_886_0,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
inference(unfold_definition,[status(thm)],[c_0_886,def_lhs_atom63]) ).
cnf(c_0_887_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1)),
inference(unfold_definition,[status(thm)],[c_0_887,def_lhs_atom58]) ).
cnf(c_0_888_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1)),
inference(unfold_definition,[status(thm)],[c_0_888,def_lhs_atom54]) ).
cnf(c_0_889_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_889,def_lhs_atom53]) ).
cnf(c_0_890_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_890,def_lhs_atom51]) ).
cnf(c_0_891_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_891,def_lhs_atom50]) ).
cnf(c_0_892_0,axiom,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_892,def_lhs_atom43]) ).
cnf(c_0_893_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_893,def_lhs_atom30]) ).
cnf(c_0_894_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_894,def_lhs_atom29]) ).
cnf(c_0_895_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_895,def_lhs_atom27]) ).
cnf(c_0_896_0,axiom,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_896,def_lhs_atom23]) ).
cnf(c_0_897_0,axiom,
c_Fun_Oinj__on(c_Fun_Oid(X2),X1,X2,X2),
inference(unfold_definition,[status(thm)],[c_0_897,def_lhs_atom12]) ).
cnf(c_0_898_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_898,def_lhs_atom7]) ).
cnf(c_0_899_0,axiom,
c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(X1),tc_Option_Ooption(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_899,def_lhs_atom4]) ).
cnf(c_0_900_0,axiom,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X1),
inference(unfold_definition,[status(thm)],[c_0_900,def_lhs_atom156]) ).
cnf(c_0_901_0,axiom,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_901,def_lhs_atom141]) ).
cnf(c_0_902_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_902,def_lhs_atom127]) ).
cnf(c_0_903_0,axiom,
X1 != c_Suc(X1),
inference(unfold_definition,[status(thm)],[c_0_903,def_lhs_atom120]) ).
cnf(c_0_904_0,axiom,
c_Suc(X1) != X1,
inference(unfold_definition,[status(thm)],[c_0_904,def_lhs_atom119]) ).
cnf(c_0_905_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_905,def_lhs_atom103]) ).
cnf(c_0_906_0,axiom,
hAPP(c_Hoare__Mirabelle_OMGT,X1) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),X1),c_Natural_Oevalc(X1)),
inference(unfold_definition,[status(thm)],[c_0_906,def_lhs_atom87]) ).
cnf(c_0_907_0,axiom,
c_Option_Ois__none(c_Option_Ooption_ONone(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_907,def_lhs_atom64]) ).
cnf(c_0_908_0,axiom,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_908,def_lhs_atom60]) ).
cnf(c_0_909_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_909,def_lhs_atom56]) ).
cnf(c_0_910_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(unfold_definition,[status(thm)],[c_0_910,def_lhs_atom41]) ).
cnf(c_0_911_0,axiom,
class_HOL_Oord(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_911,def_lhs_atom182]) ).
cnf(c_0_912_0,axiom,
class_Orderings_Obot(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_912,def_lhs_atom181]) ).
cnf(c_0_913_0,axiom,
class_Orderings_Otop(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_913,def_lhs_atom180]) ).
cnf(c_0_914_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_914,def_lhs_atom179]) ).
cnf(c_0_915_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_915,def_lhs_atom178]) ).
cnf(c_0_916_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_916,def_lhs_atom177]) ).
cnf(c_0_917_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_917,def_lhs_atom176]) ).
cnf(c_0_918_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_918,def_lhs_atom175]) ).
cnf(c_0_919_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_919,def_lhs_atom174]) ).
cnf(c_0_920_0,axiom,
class_HOL_Oord(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_920,def_lhs_atom173]) ).
cnf(c_0_921_0,axiom,
class_Orderings_Obot(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_921,def_lhs_atom172]) ).
cnf(c_0_922_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_922,def_lhs_atom171]) ).
cnf(c_0_923_0,axiom,
class_Lattices_Olattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_923,def_lhs_atom170]) ).
cnf(c_0_924_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_924,def_lhs_atom169]) ).
cnf(c_0_925_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_925,def_lhs_atom168]) ).
cnf(c_0_926_0,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_926,def_lhs_atom167]) ).
cnf(c_0_927_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
inference(unfold_definition,[status(thm)],[c_0_927,def_lhs_atom163]) ).
cnf(c_0_928_0,axiom,
hAPP(c_Hoare__Mirabelle_OMGT,v_c) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal(tc_Com_Ostate)),v_c),c_Natural_Oevalc(v_c)),
inference(unfold_definition,[status(thm)],[c_0_928,def_lhs_atom161]) ).
cnf(c_0_929_0,axiom,
c_Com_OWT(c_Com_Ocom_OSKIP),
inference(unfold_definition,[status(thm)],[c_0_929,def_lhs_atom159]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X32,X83,X84,X29,X85,X18,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X18,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X29,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X85,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X84,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X18,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X32,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X29,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X83,t_a) ),
file('<stdin>',cls_finite__pointwise_1) ).
fof(c_0_1_002,axiom,
! [X32,X83,X84,X29,X85,X18,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X18,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X29,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X85,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X84,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X85,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X32,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X84,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X83,t_a) ),
file('<stdin>',cls_finite__pointwise_0) ).
fof(c_0_2_003,axiom,
! [X29,X19,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_Body__sound__lemma_0) ).
fof(c_0_3_004,axiom,
! [X29,X19,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_hoare__derivs_OBody_0) ).
fof(c_0_4_005,axiom,
! [X15,X29,X19,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),hAPP(X18,X15)),hAPP(c_Com_Ocom_OBODY,X15)),hAPP(X29,X15)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_in(X15,X19,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_Body1_0) ).
fof(c_0_5_006,axiom,
! [X19,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X19,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('<stdin>',cls_MGT__Body_0) ).
fof(c_0_6_007,axiom,
! [X17] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X17,tc_Com_Ostate)
| ~ c_lessequals(X17,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF__lemma2__simult_0) ).
fof(c_0_7_008,axiom,
! [X8,X42,X43,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X43,X42,hAPP(c_Option_Ooption_OSome(t_b),X8),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X42,X8))) ),
file('<stdin>',cls_option_Osplit__asm_1) ).
fof(c_0_8_009,axiom,
! [X42,X43,X11,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X43,X42,hAPP(c_Option_Ooption_OSome(t_b),X11),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X42,X11))) ),
file('<stdin>',cls_option_Osplit_1) ).
fof(c_0_9_010,axiom,
! [X42,X43,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X43,X42,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X18,X43)) ),
file('<stdin>',cls_option_Osplit_0) ).
fof(c_0_10_011,axiom,
! [X27,X67,X23,X16,X11,X26,X3] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X27,X11,X16,X3,X26),X23,X67,X3,X26) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X27,X23,X67,X3,X26),X11,X16,X3,X26)
| X11 = X23 ),
file('<stdin>',cls_fun__upd__twist_0) ).
fof(c_0_11_012,axiom,
! [X69,X25,X40,X26,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X25,X69,X3,X40,X26),c_Orderings_Otop__class_Otop(tc_fun(X26,tc_bool)),X26,X40),X40)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X69,c_Orderings_Otop__class_Otop(tc_fun(X26,tc_bool)),X26,X3),X3) ),
file('<stdin>',cls_finite__range__imageI_0) ).
fof(c_0_12_013,axiom,
! [X9,X44,X37,X38,X35,X40,X26,X3] :
( hAPP(X38,X9) != hAPP(c_Option_Ooption_OSome(X3),X44)
| hAPP(X37,X35) != hAPP(c_Option_Ooption_OSome(X26),X9)
| c_Map_Omap__comp(X38,X37,X35,X26,X3,X40) = hAPP(c_Option_Ooption_OSome(X3),X44) ),
file('<stdin>',cls_map__comp__Some__iff_2) ).
fof(c_0_13_014,axiom,
! [X9,X37,X38,X35,X40,X26,X3] :
( hAPP(X38,X9) != c_Option_Ooption_ONone(X3)
| hAPP(X37,X35) != hAPP(c_Option_Ooption_OSome(X26),X9)
| c_Map_Omap__comp(X38,X37,X35,X26,X3,X40) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__comp__None__iff_3) ).
fof(c_0_14_015,axiom,
! [X37,X38,X39,X35,X40,X26,X3] :
( hAPP(X37,X35) != hAPP(c_Option_Ooption_OSome(X3),X39)
| c_Map_Omap__comp(X38,X37,X35,X3,X40,X26) = hAPP(X38,X39) ),
file('<stdin>',cls_map__comp__simps_I2_J_0) ).
fof(c_0_15_016,axiom,
! [X37,X38,X35,X40,X26,X3] :
( hAPP(X37,X35) != c_Option_Ooption_ONone(X26)
| c_Map_Omap__comp(X38,X37,X35,X26,X3,X40) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__comp__None__iff_2) ).
fof(c_0_16_017,axiom,
! [X37,X38,X35,X40,X26,X3] :
( hAPP(X37,X35) != c_Option_Ooption_ONone(X3)
| c_Map_Omap__comp(X38,X37,X35,X3,X40,X26) = c_Option_Ooption_ONone(X40) ),
file('<stdin>',cls_map__comp__simps_I1_J_0) ).
fof(c_0_17_018,axiom,
! [X80,X27,X81,X82,X26,X3] :
( c_Map_Omap__add(c_Fun_Ofun__upd(X82,X27,hAPP(c_Option_Ooption_OSome(X26),X80),X3,tc_Option_Ooption(X26)),X81,X3,X26) = c_Fun_Ofun__upd(c_Map_Omap__add(X82,X81,X3,X26),X27,hAPP(c_Option_Ooption_OSome(X26),X80),X3,tc_Option_Ooption(X26))
| c_in(X27,c_Map_Odom(X81,X3,X26),X3) ),
file('<stdin>',cls_map__add__upd__left_0) ).
fof(c_0_18_019,axiom,
! [X15,X29,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),X14,tc_Hoare__Mirabelle_Otriple(X3)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_BodyN_0) ).
fof(c_0_19_020,axiom,
! [X24,X9,X27,X16,X11,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X3),X16),X26,tc_Option_Ooption(X3)),X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| hAPP(X27,X9) = hAPP(c_Option_Ooption_OSome(X3),X24)
| X16 = X24 ),
file('<stdin>',cls_map__upd__Some__unfold_2) ).
fof(c_0_20_021,axiom,
! [X24,X9,X27,X16,X11,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X3),X16),X26,tc_Option_Ooption(X3)),X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| hAPP(X27,X9) = hAPP(c_Option_Ooption_OSome(X3),X24)
| X9 = X11 ),
file('<stdin>',cls_map__upd__Some__unfold_0) ).
fof(c_0_21_022,axiom,
! [X24,X9,X27,X16,X41,X3] :
( X16 = X24
| hAPP(c_Fun_Ofun__upd(X27,X9,hAPP(c_Option_Ooption_OSome(X41),X16),X3,tc_Option_Ooption(X41)),X9) != hAPP(c_Option_Ooption_OSome(X41),X24) ),
file('<stdin>',cls_map__upd__Some__unfold_1) ).
fof(c_0_22_023,axiom,
! [X24,X9,X28,X27,X11,X26,X3] :
( c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X26),X9),X3,tc_Option_Ooption(X26)) != c_Fun_Ofun__upd(X28,X11,hAPP(c_Option_Ooption_OSome(X26),X24),X3,tc_Option_Ooption(X26))
| X9 = X24 ),
file('<stdin>',cls_map__upd__eqD1_0) ).
fof(c_0_23_024,axiom,
! [X24,X9,X25,X45,X26,X3] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X25,X9,X24,X3,X26),X45,X3,X26)
| c_in(X24,c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26) ),
file('<stdin>',cls_inj__on__fun__updI_0) ).
fof(c_0_24_025,axiom,
! [X67,X23,X72,X29,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),c_Com_Ocom_OSemi(X23,X67)),X72),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X29),X67),X72),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),X23),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_Comp_0) ).
fof(c_0_25_026,axiom,
! [X15,X29,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_weak__Body_0) ).
fof(c_0_26_027,axiom,
! [X24,X9,X25,X45,X26,X3] :
( c_Set_Oimage(c_Fun_Ofun__upd(X25,X9,X24,X26,X3),X45,X26,X3) = c_Set_Oimage(X25,X45,X26,X3)
| c_in(X9,X45,X26) ),
file('<stdin>',cls_fun__upd__image_1) ).
fof(c_0_27_028,axiom,
! [X24,X9,X25,X26,X3] :
( c_Map_Odom(c_Fun_Ofun__upd(X25,X9,X24,X3,tc_Option_Ooption(X26)),X3,X26) = c_Set_Oinsert(X9,c_Map_Odom(X25,X3,X26),X3)
| X24 = c_Option_Ooption_ONone(X26) ),
file('<stdin>',cls_dom__fun__upd_1) ).
fof(c_0_28_029,axiom,
! [X9,X25,X26,X3] :
( c_Map_Odom(X25,X3,X26) != c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X25 = c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X26),tc_Option_Ooption(X26),X3),X9,hAPP(c_Option_Ooption_OSome(X26),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X25,X9,X3,X26)),X3,tc_Option_Ooption(X26)) ),
file('<stdin>',cls_dom__eq__singleton__conv_0) ).
fof(c_0_29_030,axiom,
! [X23,X29,X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X18),X23),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X18),X23),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('<stdin>',cls_MGF__complete_0) ).
fof(c_0_30_031,axiom,
! [X24,X9,X27,X16,X11,X26,X3] :
( hAPP(X27,X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| X9 = X11
| hAPP(c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X3),X16),X26,tc_Option_Ooption(X3)),X9) = hAPP(c_Option_Ooption_OSome(X3),X24) ),
file('<stdin>',cls_map__upd__Some__unfold_4) ).
fof(c_0_31_032,axiom,
! [X50,X24,X9,X25,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X25,X9,X24,X26,X3),X50) = hAPP(X25,X50)
| X50 = X9 ),
file('<stdin>',cls_fun__upd__apply_1) ).
fof(c_0_32_033,axiom,
! [X50,X24,X9,X25,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X25,X9,X24,X3,X26),X50) = hAPP(X25,X50)
| X50 = X9 ),
file('<stdin>',cls_fun__upd__other_0) ).
fof(c_0_33_034,axiom,
! [X25,X51,X45,X26,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X25,X45,X3,X26),c_Set_Oimage(X25,X51,X3,X26),tc_fun(X26,tc_bool))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
file('<stdin>',cls_inj__image__subset__iff_0) ).
fof(c_0_34_035,axiom,
! [X24,X9,X25,X26,X3] :
( c_Fun_Ofun__upd(X25,X9,X24,X3,X26) != X25
| hAPP(X25,X9) = X24 ),
file('<stdin>',cls_fun__upd__idem__iff_0) ).
fof(c_0_35_036,axiom,
! [X15,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X15)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X15)),X14,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('<stdin>',cls_MGT__BodyN_0) ).
fof(c_0_36_037,axiom,
! [X30,X21,X33,X31,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X33),X21),X30))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X21),X30))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X31,X33)),X21),X30)) ),
file('<stdin>',cls_evalc__elim__cases_I5_J_2) ).
fof(c_0_37_038,axiom,
! [X58,X27,X26,X3] :
( c_Fun_Oinj__on(X58,c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26))
| ~ c_Fun_Oinj__on(c_Map_Omap__add(X27,X58,X3,X26),c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26)) ),
file('<stdin>',cls_inj__on__map__add__dom_0) ).
fof(c_0_38_039,axiom,
! [X30,X21,X33,X31,X16] :
( ~ hBOOL(hAPP(X16,X21))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X21),X30))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X31,X33)),X21),X30)) ),
file('<stdin>',cls_evalc__elim__cases_I5_J_1) ).
fof(c_0_39_040,axiom,
! [X25,X51,X45,X26,X3] :
( c_lessequals(c_Set_Oimage(X25,X45,X3,X26),c_Set_Oimage(X25,X51,X3,X26),tc_fun(X26,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
file('<stdin>',cls_inj__image__subset__iff_1) ).
fof(c_0_40_041,axiom,
! [X30,X21,X33,X31,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X33),X21),X30))
| hBOOL(hAPP(X16,X21))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X31,X33)),X21),X30)) ),
file('<stdin>',cls_evalc__elim__cases_I5_J_0) ).
fof(c_0_41_042,axiom,
! [X25,X45,X3] :
( c_Set_Oimage(X25,X45,X3,X3) = X45
| ~ c_Fun_Oinj__on(X25,X45,X3,X3)
| ~ c_lessequals(c_Set_Oimage(X25,X45,X3,X3),X45,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X45,X3) ),
file('<stdin>',cls_endo__inj__surj_0) ).
fof(c_0_42_043,axiom,
! [X20,X22,X15] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X15)),X22),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X22),X20)) ),
file('<stdin>',cls_evalc_OBody_0) ).
fof(c_0_43_044,axiom,
! [X25,X11,X45,X26,X3] :
( c_in(X11,X45,X3)
| ~ c_in(hAPP(X25,X11),c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
file('<stdin>',cls_inj__image__mem__iff_0) ).
fof(c_0_44_045,axiom,
! [X58,X27,X26,X3] :
( c_Fun_Oinj__on(c_Map_Omap__add(X27,X58,X3,X26),c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26))
| ~ c_Fun_Oinj__on(X58,c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26)) ),
file('<stdin>',cls_inj__on__map__add__dom_1) ).
fof(c_0_45_046,axiom,
! [X25,X51,X45,X26,X3] :
( c_Set_Oimage(X25,X45,X3,X26) != c_Set_Oimage(X25,X51,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3,X26)
| X45 = X51 ),
file('<stdin>',cls_inj__on__Un__image__eq__iff_0) ).
fof(c_0_46_047,axiom,
! [X15,X28,X29,X18,X3] :
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X28),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),X3) ),
file('<stdin>',cls_Body__triple__valid__Suc_0) ).
fof(c_0_47_048,axiom,
! [X9,X30,X35,X26,X3] :
( hAPP(X30,X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| c_Fun_Ofun__upd(X30,X35,hAPP(c_Option_Ooption_OSome(X3),X9),X26,tc_Option_Ooption(X3)) = X30 ),
file('<stdin>',cls_map__upd__triv_0) ).
fof(c_0_48_049,axiom,
! [X25,X51,X45,X26,X3] :
( c_Set_Oimage(X25,X45,X3,X26) != c_Set_Oimage(X25,X51,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26)
| X45 = X51 ),
file('<stdin>',cls_inj__image__eq__iff_0) ).
fof(c_0_49_050,axiom,
! [X20,X21,X28,X18] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X18)),X21,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X18,X28,X21,X20),X20)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X18),X21,X28,X20) ),
file('<stdin>',cls_evaln__elim__cases_I6_J_1) ).
fof(c_0_50_051,axiom,
! [X25,X45,X26,X3] :
( c_Finite__Set_Ofinite(X45,X26)
| ~ c_Fun_Oinj__on(X25,X45,X26,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X45,X26,X3),X3) ),
file('<stdin>',cls_finite__imageD_0) ).
fof(c_0_51_052,axiom,
! [X15,X28,X29,X18,X3] :
( c_Hoare__Mirabelle_Otriple__valid(X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X28),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),X3) ),
file('<stdin>',cls_Body__triple__valid__Suc_1) ).
fof(c_0_52_053,axiom,
! [X9,X25,X45,X26,X3] :
( ~ c_lessequals(X9,X45,tc_fun(X26,tc_bool))
| c_lessequals(c_Set_Oimage(X25,X9,X26,X3),c_Set_Oimage(X25,X45,X26,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_53_054,axiom,
! [X25,X51,X45,X26,X3] :
( c_lessequals(c_Set_Oimage(X25,X45,X3,X26),c_Set_Oimage(X25,X51,X3,X26),tc_fun(X26,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_54_055,axiom,
! [X20,X21,X18] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X18))),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X18)),X21),X20)) ),
file('<stdin>',cls_evalc__elim__cases_I6_J_0) ).
fof(c_0_55_056,axiom,
! [X20,X21,X31,X32,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X32,X31)),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X32),X21),X20))
| ~ hBOOL(hAPP(X16,X21)) ),
file('<stdin>',cls_evalc_OIfTrue_0) ).
fof(c_0_56_057,axiom,
! [X25,X45,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X3)
| ~ c_lessequals(X45,c_Set_Oimage(X25,X45,X3,X3),tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X45,X3) ),
file('<stdin>',cls_finite__surj__inj_0) ).
fof(c_0_57_058,axiom,
! [X20,X21,X31,X32,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X32,X31)),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X21),X20))
| hBOOL(hAPP(X16,X21)) ),
file('<stdin>',cls_evalc_OIfFalse_0) ).
fof(c_0_58_059,axiom,
! [X70,X20,X22,X28,X23,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X22,X28,X70)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X20,X28,X70)
| ~ c_Natural_Oevaln(X23,X22,X28,X20)
| ~ hBOOL(hAPP(X16,X22)) ),
file('<stdin>',cls_evaln_OWhileTrue_0) ).
fof(c_0_59_060,axiom,
! [X25,X11,X45,X26,X3] :
( c_in(hAPP(X25,X11),c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_in(X11,X45,X3)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
file('<stdin>',cls_inj__image__mem__iff_1) ).
fof(c_0_60_061,axiom,
! [X23,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X14))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF__lemma1_1) ).
fof(c_0_61_062,axiom,
! [X9,X25,X51,X45,X26,X3] :
( c_in(hAPP(X25,X9),X51,X3)
| ~ c_in(X9,X45,X26)
| ~ c_lessequals(c_Set_Oimage(X25,X45,X26,X3),X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_62_063,axiom,
! [X30,X21,X28,X33,X31,X16] :
( c_Natural_Oevaln(X33,X21,X28,X30)
| c_Natural_Oevaln(X31,X21,X28,X30)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X31,X33),X21,X28,X30) ),
file('<stdin>',cls_evaln__elim__cases_I5_J_2) ).
fof(c_0_63_064,axiom,
! [X70,X20,X22,X28,X31,X32] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X32,X31),X22,X28,X70)
| ~ c_Natural_Oevaln(X31,X20,X28,X70)
| ~ c_Natural_Oevaln(X32,X22,X28,X20) ),
file('<stdin>',cls_evaln_OSemi_0) ).
fof(c_0_64_065,axiom,
! [X70,X20,X22,X23,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X22),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X20),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X22),X20))
| ~ hBOOL(hAPP(X16,X22)) ),
file('<stdin>',cls_evalc_OWhileTrue_0) ).
fof(c_0_65_066,axiom,
! [X65,X21,X28,X23,X66,X29,X18] :
( hBOOL(hAPP(hAPP(X29,X66),X65))
| ~ c_Natural_Oevaln(X23,X21,X28,X65)
| ~ hBOOL(hAPP(hAPP(X18,X66),X21))
| ~ c_Hoare__Mirabelle_Otriple__valid(X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X18),X23),X29),t_a) ),
file('<stdin>',cls_triple__valid__def2_0) ).
fof(c_0_66_067,axiom,
! [X25,X51,X45,X26,X3] :
( c_Finite__Set_Ofinite(X51,X26)
| ~ c_lessequals(X51,c_Set_Oimage(X25,X45,X3,X26),tc_fun(X26,tc_bool))
| ~ c_Finite__Set_Ofinite(X45,X3) ),
file('<stdin>',cls_finite__surj_0) ).
fof(c_0_67_068,axiom,
! [X20,X21,X28,X18] :
( X28 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X18,X28,X21,X20))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X18),X21,X28,X20) ),
file('<stdin>',cls_evaln__elim__cases_I6_J_0) ).
fof(c_0_68_069,axiom,
! [X9,X25,X45,X26,X3] :
( c_Set_Oinsert(hAPP(X25,X9),c_Set_Oimage(X25,X45,X3,X26),X26) = c_Set_Oimage(X25,X45,X3,X26)
| ~ c_in(X9,X45,X3) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_69_070,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X27,X35) = hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X28,X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
file('<stdin>',cls_map__add__SomeD_1) ).
fof(c_0_70_071,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X28,X35) = c_Option_Ooption_ONone(X3)
| hAPP(X28,X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
file('<stdin>',cls_map__add__SomeD_0) ).
fof(c_0_71_072,axiom,
! [X25,X51,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X51,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3,X26) ),
file('<stdin>',cls_inj__on__Un_1) ).
fof(c_0_72_073,axiom,
! [X25,X51,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3,X26) ),
file('<stdin>',cls_inj__on__Un_0) ).
fof(c_0_73_074,axiom,
! [X30,X21,X28,X33,X31,X16] :
( ~ hBOOL(hAPP(X16,X21))
| c_Natural_Oevaln(X31,X21,X28,X30)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X31,X33),X21,X28,X30) ),
file('<stdin>',cls_evaln__elim__cases_I5_J_1) ).
fof(c_0_74_075,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X11 = X67
| X11 = X23 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_75_076,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X23
| X11 = X23 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_76_077,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X11 = X67
| X16 = X67 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_77_078,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X23
| X16 = X67 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_78_079,axiom,
! [X30,X21,X28,X33,X31,X16] :
( c_Natural_Oevaln(X33,X21,X28,X30)
| hBOOL(hAPP(X16,X21))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X31,X33),X21,X28,X30) ),
file('<stdin>',cls_evaln__elim__cases_I5_J_0) ).
fof(c_0_79_080,axiom,
! [X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != c_Option_Ooption_ONone(X3)
| hAPP(X27,X35) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_1) ).
fof(c_0_80_081,axiom,
! [X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != c_Option_Ooption_ONone(X3)
| hAPP(X28,X35) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_0) ).
fof(c_0_81_082,axiom,
! [X25,X11,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X11,X45,X3),X3,X26) ),
file('<stdin>',cls_inj__on__insert_0) ).
fof(c_0_82_083,axiom,
! [X20,X21,X28,X31,X32,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X32,X31),X21,X28,X20)
| ~ c_Natural_Oevaln(X32,X21,X28,X20)
| ~ hBOOL(hAPP(X16,X21)) ),
file('<stdin>',cls_evaln_OIfTrue_0) ).
fof(c_0_83_084,axiom,
! [X20,X22,X15,X28] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X15),X22,c_Suc(X28),X20)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15)),X22,X28,X20) ),
file('<stdin>',cls_evaln_OBody_0) ).
fof(c_0_84_085,axiom,
! [X27,X11,X26,X3] :
( hAPP(X27,X11) = hAPP(c_Option_Ooption_OSome(X26),c_Map_Osko__Map__XdomD__1__1(X11,X27,X3,X26))
| ~ c_in(X11,c_Map_Odom(X27,X3,X26),X3) ),
file('<stdin>',cls_domD_0) ).
fof(c_0_85_086,axiom,
! [X27,X46,X47,X26,X3] :
( hAPP(c_Map_Omap__add(X47,X46,X3,X26),X27) = hAPP(X46,X27)
| ~ c_in(X27,c_Map_Odom(X46,X3,X26),X3) ),
file('<stdin>',cls_map__add__dom__app__simps_I1_J_0) ).
fof(c_0_86_087,axiom,
! [X20,X21,X28,X31,X32,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X32,X31),X21,X28,X20)
| ~ c_Natural_Oevaln(X31,X21,X28,X20)
| hBOOL(hAPP(X16,X21)) ),
file('<stdin>',cls_evaln_OIfFalse_0) ).
fof(c_0_87_088,axiom,
! [X12,X30,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,X12,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_hoare__derivs_Oinsert_0) ).
fof(c_0_88_089,axiom,
! [X25,X51,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X26)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X25,X51,X3,X26) ),
file('<stdin>',cls_subset__inj__on_0) ).
fof(c_0_89_090,axiom,
! [X27,X46,X47,X26,X3] :
( hAPP(c_Map_Omap__add(X47,X46,X3,X26),X27) = hAPP(X46,X27)
| c_in(X27,c_Map_Odom(X47,X3,X26),X3) ),
file('<stdin>',cls_map__add__dom__app__simps_I2_J_0) ).
fof(c_0_90_091,axiom,
! [X27,X46,X47,X26,X3] :
( hAPP(c_Map_Omap__add(X47,X46,X3,X26),X27) = hAPP(X47,X27)
| c_in(X27,c_Map_Odom(X46,X3,X26),X3) ),
file('<stdin>',cls_map__add__dom__app__simps_I3_J_0) ).
fof(c_0_91_092,axiom,
! [X9,X25,X45,X41,X3] :
( ~ c_in(X9,X45,X41)
| c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X41,X3),X3) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_92_093,axiom,
! [X9,X25,X45,X26,X3] :
( ~ c_in(X9,X45,X26)
| c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X26,X3),X3) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_93_094,axiom,
! [X9,X25,X45,X26,X3] :
( c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X26,X3),X3)
| ~ c_in(X9,X45,X26) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_94_095,axiom,
! [X9,X25,X45,X26,X3] :
( c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_in(X9,X45,X3) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_95_096,axiom,
! [X9,X18,X3] :
( ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X3),X9),X18,X3)))
| hBOOL(hAPP(X18,X9)) ),
file('<stdin>',cls_ospec_1) ).
fof(c_0_96_097,axiom,
! [X70,X20,X22,X31,X32] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X32,X31)),X22),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X20),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X32),X22),X20)) ),
file('<stdin>',cls_evalc_OSemi_0) ).
fof(c_0_97_098,axiom,
! [X65,X21,X28,X23] :
( c_Natural_Oevaln(X23,X21,c_Suc(X28),X65)
| ~ c_Natural_Oevaln(X23,X21,X28,X65) ),
file('<stdin>',cls_evaln__Suc_0) ).
fof(c_0_98_099,axiom,
! [X48,X49,X51,X45,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X49,X48,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X48,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X49,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_99_100,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(X27,X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X28,X35) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
file('<stdin>',cls_map__add__Some__iff_3) ).
fof(c_0_100_101,axiom,
! [X24,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_in(X24,X45,X3)
| ~ c_in(X9,X45,X3)
| X9 = X24
| ~ c_Fun_Oinj__on(X25,X45,X3,X26) ),
file('<stdin>',cls_inj__on__contraD_0) ).
fof(c_0_101_102,axiom,
! [X24,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_in(X24,X45,X3)
| ~ c_in(X9,X45,X3)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26)
| X9 = X24 ),
file('<stdin>',cls_inj__on__iff_0) ).
fof(c_0_102_103,axiom,
! [X8,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X8)
| ~ c_in(X8,X45,X3)
| ~ c_in(X9,X45,X3)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26)
| X9 = X8 ),
file('<stdin>',cls_inj__on__def_0) ).
fof(c_0_103_104,axiom,
! [X24,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26)
| X9 = X24
| ~ c_in(X24,X45,X3)
| ~ c_in(X9,X45,X3) ),
file('<stdin>',cls_inj__onD_0) ).
fof(c_0_104_105,axiom,
! [X12,X30,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,X12,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_derivs__insertD_0) ).
fof(c_0_105_106,axiom,
! [X9,X45,X3] :
( X45 = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_106_107,axiom,
! [X9,X51,X45,X3] :
( hBOOL(hAPP(X51,X9))
| hBOOL(hAPP(X45,X9))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X9)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_107_108,axiom,
! [X36,X28,X27,X35,X26,X3] :
( hAPP(X28,X35) != hAPP(c_Option_Ooption_OSome(X3),X36)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = hAPP(c_Option_Ooption_OSome(X3),X36) ),
file('<stdin>',cls_map__add__find__right_0) ).
fof(c_0_108_109,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(X28,X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
file('<stdin>',cls_map__add__Some__iff_2) ).
fof(c_0_109_110,axiom,
! [X28,X27,X35,X26,X3] :
( hAPP(X27,X35) != c_Option_Ooption_ONone(X3)
| hAPP(X28,X35) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_2) ).
fof(c_0_110_111,axiom,
! [X9,X23,X45,X26,X3] :
( c_Set_Oimage(c_COMBK(X23,X26,X3),X45,X3,X26) = c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26)
| ~ c_in(X9,X45,X3) ),
file('<stdin>',cls_image__constant_0) ).
fof(c_0_111_112,axiom,
! [X68,X17,X26,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X68,X17,X3,X26),X26)
| ~ c_Finite__Set_Ofinite(X17,X3) ),
file('<stdin>',cls_finite__imageI_0) ).
fof(c_0_112_113,axiom,
! [X30,X21,X23,X16] :
( hBOOL(hAPP(X16,X21))
| X30 = X21
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X21),X30)) ),
file('<stdin>',cls_evalc__WHILE__case_0) ).
fof(c_0_113_114,axiom,
! [X24,X9,X25,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26)
| X9 = X24 ),
file('<stdin>',cls_injD_0) ).
fof(c_0_114_115,axiom,
! [X23,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X14),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF__lemma1_0) ).
fof(c_0_115_116,axiom,
! [X30,X21,X28,X23] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X30))
| ~ c_Natural_Oevaln(X23,X21,X28,X30) ),
file('<stdin>',cls_evaln__evalc_0) ).
fof(c_0_116_117,axiom,
! [X9,X30,X21,X23] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X30))
| ~ c_Natural_Oevaln(X23,X21,X9,X30) ),
file('<stdin>',cls_eval__eq_1) ).
fof(c_0_117_118,axiom,
! [X23,X45,X26,X3] :
( c_Set_Oimage(c_COMBK(X23,X3,X26),X45,X26,X3) = c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)) ),
file('<stdin>',cls_image__constant__conv_1) ).
fof(c_0_118_119,axiom,
! [X49,X51,X45,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X49,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_119_120,axiom,
! [X49,X51,X45,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X49,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_120_121,axiom,
! [X30,X21,X28,X23,X16] :
( hBOOL(hAPP(X16,X21))
| X30 = X21
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X21,X28,X30) ),
file('<stdin>',cls_evaln__WHILE__case_0) ).
fof(c_0_121_122,axiom,
! [X25,X45,X26,X3] :
( c_Set_Oimage(X25,X45,X26,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)) ),
file('<stdin>',cls_image__is__empty_0) ).
fof(c_0_122_123,axiom,
! [X25,X45,X26,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X25,X45,X26,X3)
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)) ),
file('<stdin>',cls_empty__is__image_0) ).
fof(c_0_123_124,axiom,
! [X49,X51,X45,X3] :
( c_lessequals(X45,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_124_125,axiom,
! [X49,X51,X45,X3] :
( c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_125_126,axiom,
! [X23,X51,X45,X3] :
( c_in(X23,X51,X3)
| c_in(X23,X45,X3)
| ~ c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_126_127,axiom,
! [X9,X51,X45,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| c_in(X9,X45,X3)
| ~ c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_127_128,axiom,
! [X9,X51,X45,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool))
| c_in(X9,X45,X3) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_128_129,axiom,
! [X16,X11,X3] :
( X16 = X11
| ~ c_in(X16,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_129_130,axiom,
! [X24,X9,X45,X3] :
( hBOOL(hAPP(X45,X9))
| X24 = X9
| ~ hBOOL(hAPP(c_Set_Oinsert(X24,X45,X3),X9)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_130_131,axiom,
! [X23] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_MGF_0) ).
fof(c_0_131_132,axiom,
! [X11,X48,X49,X3] :
( c_lessequals(c_Set_Oinsert(X11,X49,X3),c_Set_Oinsert(X11,X48,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X49,X48,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_132_133,axiom,
! [X73,X25,X26,X3] :
( c_Option_Omap(X25,X73,X26,X3) != c_Option_Ooption_ONone(X3)
| X73 = c_Option_Ooption_ONone(X26) ),
file('<stdin>',cls_option__map__is__None_0) ).
fof(c_0_133_134,axiom,
! [X9,X51,X45,X3] :
( c_lessequals(c_Set_Oinsert(X9,X45,X3),X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_in(X9,X51,X3) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_134_135,axiom,
! [X30,X21,X28] :
( X30 = X21
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X21,X28,X30) ),
file('<stdin>',cls_evaln__elim__cases_I1_J_0) ).
fof(c_0_135_136,axiom,
! [X9,X51,X45,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X9))
| ~ hBOOL(hAPP(X51,X9)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_136_137,axiom,
! [X9,X51,X45,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X9))
| ~ hBOOL(hAPP(X45,X9)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_137_138,axiom,
! [X9,X51,X45,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X9,X45,X3),X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_138_139,axiom,
! [X61,X62,X63,X64,X56,X57,X3] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X64),X57),X62) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X63),X56),X61)
| X64 = X63 ),
file('<stdin>',cls_triple_Oinject_0) ).
fof(c_0_139_140,axiom,
! [X61,X62,X63,X64,X56,X57,X3] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X64),X57),X62) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X63),X56),X61)
| X57 = X56 ),
file('<stdin>',cls_triple_Oinject_1) ).
fof(c_0_140_141,axiom,
! [X61,X62,X63,X64,X56,X57,X3] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X64),X57),X62) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X63),X56),X61)
| X62 = X61 ),
file('<stdin>',cls_triple_Oinject_2) ).
fof(c_0_141_142,axiom,
! [X9,X51,X45,X3] :
( c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| c_in(X9,X45,X3) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_142_143,axiom,
! [X9,X51,X45,X3] :
( c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| c_in(X9,X45,X3) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_143_144,axiom,
! [X9,X51,X45,X3] :
( c_in(X9,X51,X3)
| ~ c_lessequals(c_Set_Oinsert(X9,X45,X3),X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_144_145,axiom,
! [X21,X23,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X21),X21))
| hBOOL(hAPP(X16,X21)) ),
file('<stdin>',cls_evalc_OWhileFalse_0) ).
fof(c_0_145_146,axiom,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X9,X3)
| ~ c_lessequals(X16,X9,X3)
| ~ c_lessequals(X11,X9,X3) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_146_147,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X9,X3)
| ~ c_lessequals(X50,X9,X3)
| ~ c_lessequals(X24,X9,X3) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_147_148,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3)
| ~ c_lessequals(X24,X50,X3)
| ~ c_lessequals(X9,X50,X3) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_148_149,axiom,
! [X71,X30,X21,X23] :
( X71 = X30
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X71))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X30)) ),
file('<stdin>',cls_com__det_0) ).
fof(c_0_149_150,axiom,
! [X16,X11,X3] :
( c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X11 = X16 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_150_151,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_151_152,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X50,X3),X3) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_152_153,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X50,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_153_154,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_154_155,axiom,
! [X12,X30,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,X12,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('<stdin>',cls_derivs__insertD_1) ).
fof(c_0_155_156,axiom,
! [X49,X51,X45,X3] :
( c_lessequals(X45,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_156_157,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X24,X50,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_157_158,axiom,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,X50,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_158_159,axiom,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X16,X9,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X9,X3) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_159_160,axiom,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X11,X9,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X9,X3) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_160_161,axiom,
! [X16,X11,X45,X3] :
( c_in(X11,X45,X3)
| X11 = X16
| ~ c_in(X11,c_Set_Oinsert(X16,X45,X3),X3) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_161_162,axiom,
! [X16,X51,X45,X3] :
( c_lessequals(X45,c_Set_Oinsert(X16,X51,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_162_163,axiom,
! [X21,X28,X23,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X21,X28,X21)
| hBOOL(hAPP(X16,X21)) ),
file('<stdin>',cls_evaln_OWhileFalse_0) ).
fof(c_0_163_164,axiom,
! [X23,X51,X45,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X51,X3) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_164_165,axiom,
! [X23,X51,X45,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X45,X3) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_165_166,axiom,
! [X24,X9,X45,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X24,X45,X3),X9))
| ~ hBOOL(hAPP(X45,X9)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_166_167,axiom,
! [X9,X51,X45,X3] :
( c_Set_Oinsert(X9,X45,X3) != c_Set_Oinsert(X9,X51,X3)
| c_in(X9,X51,X3)
| c_in(X9,X45,X3)
| X45 = X51 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_167_168,axiom,
! [X27,X11,X26,X3] :
( hAPP(X27,X11) != c_Option_Ooption_ONone(X26)
| ~ c_in(X11,c_Map_Odom(X27,X3,X26),X3) ),
file('<stdin>',cls_domIff_0) ).
fof(c_0_168_169,axiom,
! [X34,X12,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_lessequals(X12,X34,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X34,X3) ),
file('<stdin>',cls_weaken_0) ).
fof(c_0_169_170,axiom,
! [X12,X13,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_lessequals(X13,X14,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X12,X3) ),
file('<stdin>',cls_thin_0) ).
fof(c_0_170_171,axiom,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(X17,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_0) ).
fof(c_0_171_172,axiom,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(X14,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_1) ).
fof(c_0_172_173,axiom,
! [X24,X9,X25,X26,X3] :
( hAPP(X25,X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| c_Set_Oinsert(X9,c_Map_Odom(X25,X26,X3),X26) = c_Map_Odom(X25,X26,X3) ),
file('<stdin>',cls_insert__dom_0) ).
fof(c_0_173_174,axiom,
! [X9,X51,X45,X3] :
( c_in(X9,X51,X3)
| ~ c_in(X9,X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_174_175,axiom,
! [X23,X51,X45,X3] :
( c_in(X23,X51,X3)
| ~ c_in(X23,X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_175_176,axiom,
! [X9,X51,X45,X3] :
( c_in(X9,X51,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_in(X9,X45,X3) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_176_177,axiom,
! [X30,X51,X45,X3] :
( c_in(X30,X51,X3)
| ~ c_in(X30,X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_177_178,axiom,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X3)
| ~ c_lessequals(X9,X16,X3) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_178_179,axiom,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X3)
| ~ c_lessequals(X9,X11,X3) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_179_180,axiom,
! [X16,X11,X51,X3] :
( c_in(X11,c_Set_Oinsert(X16,X51,X3),X3)
| ~ c_in(X11,X51,X3) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_180_181,axiom,
! [X16,X11,X45,X3] :
( c_in(X11,c_Set_Oinsert(X16,X45,X3),X3)
| ~ c_in(X11,X45,X3) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_181_182,axiom,
! [X51,X45,X3] :
( X45 = X51
| ~ c_lessequals(X51,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_182_183,axiom,
! [X51,X45,X3] :
( X45 = X51
| ~ c_lessequals(X51,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_183_184,axiom,
! [X9,X69,X25,X26,X3] :
( ~ class_HOL_Oord(X26)
| c_lessequals(hAPP(X25,X9),hAPP(X69,X9),X26)
| ~ c_lessequals(X25,X69,tc_fun(X3,X26)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_184_185,axiom,
! [X50,X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X50,X9,X3)
| ~ c_lessequals(X50,X24,X3)
| ~ c_lessequals(X24,X9,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_185_186,axiom,
! [X50,X24,X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X50,X3)
| ~ c_lessequals(X24,X50,X3)
| ~ c_lessequals(X9,X24,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_186_187,axiom,
! [X45,X3] :
( X45 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_187_188,axiom,
! [X12,X13,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X12,X3) ),
file('<stdin>',cls_cut_0) ).
fof(c_0_188_189,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_189_190,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_190_191,axiom,
! [X9,X18,X3] :
( ~ hBOOL(hAPP(X18,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_191_192,axiom,
! [X27,X16,X11,X26,X3] :
( hAPP(X27,X11) != hAPP(c_Option_Ooption_OSome(X3),X16)
| c_in(X11,c_Map_Odom(X27,X26,X3),X26) ),
file('<stdin>',cls_domI_0) ).
fof(c_0_192_193,axiom,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X14,X3)
| ~ c_Finite__Set_Ofinite(X17,X3) ),
file('<stdin>',cls_finite__Un_2) ).
fof(c_0_193_194,axiom,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X14,X3)
| ~ c_Finite__Set_Ofinite(X17,X3) ),
file('<stdin>',cls_finite__UnI_0) ).
fof(c_0_194_195,axiom,
! [X11,X45,X3] :
( c_Finite__Set_Ofinite(X45,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X11,X45,X3),X3) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_195_196,axiom,
! [X11,X2,X18] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X18))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X18,X11)) ),
file('<stdin>',cls_WTs__elim__cases_I8_J_0) ).
fof(c_0_196_197,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) != X51
| c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_197_198,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) = X51
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_198_199,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) = X45
| ~ c_lessequals(X51,X45,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_199_200,axiom,
! [X9,X29,X18,X3] :
( hBOOL(hAPP(X29,X9))
| ~ hBOOL(hAPP(X18,X9))
| ~ c_lessequals(X18,X29,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_200_201,axiom,
! [X9,X29,X18,X3] :
( hBOOL(hAPP(X29,X9))
| ~ c_lessequals(X18,X29,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X18,X9)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_201_202,axiom,
! [X9,X18,X3] :
( hBOOL(hAPP(X18,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_202_203,axiom,
! [X12,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_lessequals(X12,X14,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
file('<stdin>',cls_asm_0) ).
fof(c_0_203_204,axiom,
! [X25,X26,X3] :
( c_Map_Odom(X25,X3,X26) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X25 = c_COMBK(c_Option_Ooption_ONone(X26),tc_Option_Ooption(X26),X3) ),
file('<stdin>',cls_dom__eq__empty__conv_0) ).
fof(c_0_204_205,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X51 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_205_206,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_206_207,axiom,
! [X8,X9,X3] :
( c_Set_Oinsert(X9,X8,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_in(X9,X8,X3) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_207_208,axiom,
! [X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X24
| ~ c_lessequals(X24,X9,X3)
| ~ c_lessequals(X9,X24,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_208_209,axiom,
! [X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X24
| ~ c_lessequals(X24,X9,X3)
| ~ c_lessequals(X9,X24,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_209_210,axiom,
! [X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X24
| ~ c_lessequals(X9,X24,X3)
| ~ c_lessequals(X24,X9,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_210_211,axiom,
! [X27,X11,X26,X3] :
( c_in(X11,c_Map_Odom(X27,X3,X26),X3)
| hAPP(X27,X11) = c_Option_Ooption_ONone(X26) ),
file('<stdin>',cls_domIff_1) ).
fof(c_0_211_212,axiom,
! [X33,X31,X16] :
( c_Com_OWT(X31)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X16,X31,X33)) ),
file('<stdin>',cls_WTs__elim__cases_I5_J_0) ).
fof(c_0_212_213,axiom,
! [X33,X31,X16] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X16,X31,X33)) ),
file('<stdin>',cls_WTs__elim__cases_I5_J_1) ).
fof(c_0_213_214,axiom,
! [X23,X11,X1] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X1,X11,X23)) ),
file('<stdin>',cls_WTs__elim__cases_I3_J_0) ).
fof(c_0_214_215,axiom,
! [X59,X60,X6,X7,X54,X55] :
( c_Com_Ocom_OCall(X60,X7,X55) != c_Com_Ocom_OCall(X59,X6,X54)
| X55 = X54 ),
file('<stdin>',cls_com_Osimps_I7_J_2) ).
fof(c_0_215_216,axiom,
! [X59,X60,X6,X7,X54,X55] :
( c_Com_Ocom_OCall(X60,X7,X55) != c_Com_Ocom_OCall(X59,X6,X54)
| X7 = X6 ),
file('<stdin>',cls_com_Osimps_I7_J_1) ).
fof(c_0_216_217,axiom,
! [X59,X60,X6,X7,X54,X55] :
( c_Com_Ocom_OCall(X60,X7,X55) != c_Com_Ocom_OCall(X59,X6,X54)
| X60 = X59 ),
file('<stdin>',cls_com_Osimps_I7_J_0) ).
fof(c_0_217_218,axiom,
! [X54,X55,X76,X77,X78,X79] :
( c_Com_Ocom_OCond(X55,X79,X77) != c_Com_Ocom_OCond(X54,X78,X76)
| X77 = X76 ),
file('<stdin>',cls_com_Osimps_I4_J_2) ).
fof(c_0_218_219,axiom,
! [X54,X55,X76,X77,X78,X79] :
( c_Com_Ocom_OCond(X55,X79,X77) != c_Com_Ocom_OCond(X54,X78,X76)
| X79 = X78 ),
file('<stdin>',cls_com_Osimps_I4_J_1) ).
fof(c_0_219_220,axiom,
! [X54,X55,X76,X77,X78,X79] :
( c_Com_Ocom_OCond(X55,X79,X77) != c_Com_Ocom_OCond(X54,X78,X76)
| X55 = X54 ),
file('<stdin>',cls_com_Osimps_I4_J_0) ).
fof(c_0_220_221,axiom,
! [X52,X53,X54,X55,X56,X57] :
( c_Com_Ocom_OLocal(X53,X55,X57) != c_Com_Ocom_OLocal(X52,X54,X56)
| X57 = X56 ),
file('<stdin>',cls_com_Osimps_I2_J_2) ).
fof(c_0_221_222,axiom,
! [X52,X53,X54,X55,X56,X57] :
( c_Com_Ocom_OLocal(X53,X55,X57) != c_Com_Ocom_OLocal(X52,X54,X56)
| X55 = X54 ),
file('<stdin>',cls_com_Osimps_I2_J_1) ).
fof(c_0_222_223,axiom,
! [X52,X53,X54,X55,X56,X57] :
( c_Com_Ocom_OLocal(X53,X55,X57) != c_Com_Ocom_OLocal(X52,X54,X56)
| X53 = X52 ),
file('<stdin>',cls_com_Osimps_I2_J_0) ).
fof(c_0_223_224,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_224_225,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_225_226,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_226_227,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_227_228,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_228_229,axiom,
! [X51,X45,X3] :
( c_Finite__Set_Ofinite(X45,X3)
| ~ c_Finite__Set_Ofinite(X51,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_229_230,axiom,
! [X51,X45,X3] :
( c_Finite__Set_Ofinite(X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X51,X3) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_230_231,axiom,
! [X15,X11,X2] :
( c_Com_OWT(c_Com_Ocom_OCall(X2,X15,X11))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X15)) ),
file('<stdin>',cls_WT_OCall_0) ).
fof(c_0_231_232,axiom,
! [X30,X21] :
( X30 = X21
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X21),X30)) ),
file('<stdin>',cls_evalc__elim__cases_I1_J_0) ).
fof(c_0_232_233,axiom,
! [X30,X28,X3] :
( c_Hoare__Mirabelle_Otriple__valid(X28,X30,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X28),X30,X3) ),
file('<stdin>',cls_triple__valid__Suc_0) ).
fof(c_0_233_234,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) != X24
| c_lessequals(X9,X24,X3) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_234_235,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = X9
| ~ c_lessequals(X24,X9,X3) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_235_236,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = X24
| ~ c_lessequals(X9,X24,X3) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_236_237,axiom,
! [X11,X45,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X11,X45,X3),X3)
| ~ c_Finite__Set_Ofinite(X45,X3) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_237_238,axiom,
! [X11,X45,X3] :
( c_Set_Oinsert(X11,X45,X3) = X45
| ~ c_in(X11,X45,X3) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_238_239,axiom,
! [X12,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3) ),
file('<stdin>',cls_hoare__sound_0) ).
fof(c_0_239_240,axiom,
! [X31,X32,X16] :
( c_Com_OWT(c_Com_Ocom_OCond(X16,X32,X31))
| ~ c_Com_OWT(X31)
| ~ c_Com_OWT(X32) ),
file('<stdin>',cls_WT_OIf_0) ).
fof(c_0_240_241,axiom,
! [X23,X11,X1] :
( c_Com_OWT(c_Com_Ocom_OLocal(X1,X11,X23))
| ~ c_Com_OWT(X23) ),
file('<stdin>',cls_WT_OLocal_0) ).
fof(c_0_241_242,axiom,
! [X24,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,X9,X3)
| c_lessequals(X9,X24,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_242_243,axiom,
! [X9,X86,X3] :
( hBOOL(hAPP(X86,X9))
| ~ c_in(X9,X86,X3) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_243_244,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,X9,X3) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_244_245,axiom,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,X9,X3) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_245_246,axiom,
! [X51,X45,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X45,X51,X3) != c_Orderings_Obot__class_Obot(X3)
| X45 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_246_247,axiom,
! [X51,X45,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X45,X51,X3) != c_Orderings_Obot__class_Obot(X3)
| X51 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_247_248,axiom,
! [X9,X86,X3] :
( c_in(X9,X86,X3)
| ~ hBOOL(hAPP(X86,X9)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_248_249,axiom,
! [X18] :
( hAPP(c_Com_Obody,X18) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X18))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X18)) ),
file('<stdin>',cls_WTs__elim__cases_I7_J_0) ).
fof(c_0_249_250,axiom,
! [X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__UNIV_0) ).
fof(c_0_250_251,axiom,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Orderings_Otop__class_Otop(X3),X3) = c_Orderings_Otop__class_Otop(X3) ),
file('<stdin>',cls_sup__top__right_0) ).
fof(c_0_251_252,axiom,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X3),X9,X3) = c_Orderings_Otop__class_Otop(X3) ),
file('<stdin>',cls_sup__top__left_0) ).
fof(c_0_252_253,axiom,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Orderings_Obot__class_Obot(X3),X3) = X9 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_253_254,axiom,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X9,X3) = X9 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_254_255,axiom,
! [X9,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X9,X3) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_255_256,axiom,
! [X9,X3] :
( ~ class_Orderings_Otop(X3)
| c_lessequals(X9,c_Orderings_Otop__class_Otop(X3),X3) ),
file('<stdin>',cls_top__greatest_0) ).
fof(c_0_256_257,axiom,
! [X10,X11,X3] :
( hAPP(c_Option_Ooption_OSome(X3),X11) != hAPP(c_Option_Ooption_OSome(X3),X10)
| X11 = X10 ),
file('<stdin>',cls_option_Oinject_0) ).
fof(c_0_257_258,axiom,
! [X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X9,X3) = X9 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_258_259,axiom,
! [X9,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X9,X9,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_259_260,axiom,
! [X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X9,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_260_261,axiom,
! [X33,X31] :
( c_Com_OWT(X31)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X31,X33)) ),
file('<stdin>',cls_WTs__elim__cases_I4_J_0) ).
fof(c_0_261_262,axiom,
! [X33,X31] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X31,X33)) ),
file('<stdin>',cls_WTs__elim__cases_I4_J_1) ).
fof(c_0_262_263,axiom,
! [X23,X16] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X16,X23)) ),
file('<stdin>',cls_WTs__elim__cases_I6_J_0) ).
fof(c_0_263_264,axiom,
! [X15,X16] :
( hAPP(c_Com_Obody,X15) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X16)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X16) ),
file('<stdin>',cls_WT__bodiesD_0) ).
fof(c_0_264_265,axiom,
! [X76,X77,X78,X79] :
( c_Com_Ocom_OSemi(X79,X77) != c_Com_Ocom_OSemi(X78,X76)
| X77 = X76 ),
file('<stdin>',cls_com_Osimps_I3_J_1) ).
fof(c_0_265_266,axiom,
! [X76,X77,X78,X79] :
( c_Com_Ocom_OSemi(X79,X77) != c_Com_Ocom_OSemi(X78,X76)
| X79 = X78 ),
file('<stdin>',cls_com_Osimps_I3_J_0) ).
fof(c_0_266_267,axiom,
! [X54,X55,X56,X57] :
( c_Com_Ocom_OWhile(X55,X57) != c_Com_Ocom_OWhile(X54,X56)
| X55 = X54 ),
file('<stdin>',cls_com_Osimps_I5_J_0) ).
fof(c_0_267_268,axiom,
! [X54,X55,X56,X57] :
( c_Com_Ocom_OWhile(X55,X57) != c_Com_Ocom_OWhile(X54,X56)
| X57 = X56 ),
file('<stdin>',cls_com_Osimps_I5_J_1) ).
fof(c_0_268_269,axiom,
! [X59,X60,X54,X55] :
( c_Com_Ocom_OAss(X60,X55) != c_Com_Ocom_OAss(X59,X54)
| X55 = X54 ),
file('<stdin>',cls_com_Osimps_I1_J_1) ).
fof(c_0_269_270,axiom,
! [X59,X60,X54,X55] :
( c_Com_Ocom_OAss(X60,X55) != c_Com_Ocom_OAss(X59,X54)
| X60 = X59 ),
file('<stdin>',cls_com_Osimps_I1_J_0) ).
fof(c_0_270_271,axiom,
! [X31,X32] :
( c_Com_OWT(c_Com_Ocom_OSemi(X32,X31))
| ~ c_Com_OWT(X31)
| ~ c_Com_OWT(X32) ),
file('<stdin>',cls_WT_OSemi_0) ).
fof(c_0_271_272,axiom,
! [X5,X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X5,X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4)
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_272_273,axiom,
! [X15] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X15))
| hAPP(c_Com_Obody,X15) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
file('<stdin>',cls_WT_OBody_0) ).
fof(c_0_273_274,axiom,
! [X6,X7] :
( hAPP(c_Com_Ocom_OBODY,X7) != hAPP(c_Com_Ocom_OBODY,X6)
| X7 = X6 ),
file('<stdin>',cls_com_Osimps_I6_J_0) ).
fof(c_0_274_275,axiom,
! [X23,X16] :
( c_Com_OWT(c_Com_Ocom_OWhile(X16,X23))
| ~ c_Com_OWT(X23) ),
file('<stdin>',cls_While_0) ).
fof(c_0_275_276,axiom,
! [X5,X4] :
( class_Lattices_Oupper__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_276_277,axiom,
! [X5,X4] :
( class_Lattices_Obounded__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Obounded__lattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_277_278,axiom,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_278_279,axiom,
! [X5,X4] :
( class_Lattices_Olattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_279_280,axiom,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_280_281,axiom,
! [X5,X4] :
( class_Orderings_Otop(tc_fun(X5,X4))
| ~ class_Orderings_Otop(X4) ),
file('<stdin>',clsarity_fun__Orderings_Otop) ).
fof(c_0_281_282,axiom,
! [X5,X4] :
( class_Orderings_Obot(tc_fun(X5,X4))
| ~ class_Orderings_Obot(X4) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_282_283,axiom,
! [X5,X4] :
( class_HOL_Oord(tc_fun(X5,X4))
| ~ class_HOL_Oord(X4) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_283_284,axiom,
! [X9,X3] :
( X9 = c_Option_Ooption_ONone(X3)
| ~ c_Option_Ois__none(X9,X3) ),
file('<stdin>',cls_is__none__def_0) ).
fof(c_0_284_285,axiom,
! [X45,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X45,X3) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_285_286,axiom,
! [X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
file('<stdin>',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_286_287,axiom,
! [X24,X9] :
( c_Suc(X9) != c_Suc(X24)
| X9 = X24 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_287_288,axiom,
! [X74,X75] :
( c_Suc(X75) != c_Suc(X74)
| X75 = X74 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_288_289,axiom,
! [X30] :
( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X30) != X30
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('<stdin>',cls_single__stateE_0) ).
fof(c_0_289_290,axiom,
! [X8,X9] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| X9 = X8 ),
file('<stdin>',cls_state__not__singleton__def_1) ).
fof(c_0_290_291,plain,
! [X32,X83,X84,X29,X85,X18,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X18,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X29,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X85,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X84,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X18,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X32,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X29,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X83,t_a) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_291_292,plain,
! [X32,X83,X84,X29,X85,X18,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X18,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X29,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X85,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X32,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X84,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X83,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X85,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X32,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),hAPP(X84,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X14,X18,X85,X29,X84,X32))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X83,t_a) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_292_293,plain,
! [X29,X19,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_293_294,plain,
! [X29,X19,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_294_295,plain,
! [X15,X29,X19,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),hAPP(X18,X15)),hAPP(c_Com_Ocom_OBODY,X15)),hAPP(X29,X15)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_in(X15,X19,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3))),X29,tc_Com_Opname,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_295_296,plain,
! [X19,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X19,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X14,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X19,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_296_297,plain,
! [X17] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X17,tc_Com_Ostate)
| ~ c_lessequals(X17,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_297_298,plain,
! [X8,X42,X43,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X43,X42,hAPP(c_Option_Ooption_OSome(t_b),X8),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X42,X8))) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_298_299,plain,
! [X42,X43,X11,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X43,X42,hAPP(c_Option_Ooption_OSome(t_b),X11),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X42,X11))) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_299_300,plain,
! [X42,X43,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X43,X42,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X18,X43)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_300_301,axiom,
! [X27,X67,X23,X16,X11,X26,X3] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X27,X11,X16,X3,X26),X23,X67,X3,X26) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X27,X23,X67,X3,X26),X11,X16,X3,X26)
| X11 = X23 ),
c_0_10 ).
fof(c_0_301_302,plain,
! [X69,X25,X40,X26,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X25,X69,X3,X40,X26),c_Orderings_Otop__class_Otop(tc_fun(X26,tc_bool)),X26,X40),X40)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X69,c_Orderings_Otop__class_Otop(tc_fun(X26,tc_bool)),X26,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_302_303,axiom,
! [X9,X44,X37,X38,X35,X40,X26,X3] :
( hAPP(X38,X9) != hAPP(c_Option_Ooption_OSome(X3),X44)
| hAPP(X37,X35) != hAPP(c_Option_Ooption_OSome(X26),X9)
| c_Map_Omap__comp(X38,X37,X35,X26,X3,X40) = hAPP(c_Option_Ooption_OSome(X3),X44) ),
c_0_12 ).
fof(c_0_303_304,axiom,
! [X9,X37,X38,X35,X40,X26,X3] :
( hAPP(X38,X9) != c_Option_Ooption_ONone(X3)
| hAPP(X37,X35) != hAPP(c_Option_Ooption_OSome(X26),X9)
| c_Map_Omap__comp(X38,X37,X35,X26,X3,X40) = c_Option_Ooption_ONone(X3) ),
c_0_13 ).
fof(c_0_304_305,axiom,
! [X37,X38,X39,X35,X40,X26,X3] :
( hAPP(X37,X35) != hAPP(c_Option_Ooption_OSome(X3),X39)
| c_Map_Omap__comp(X38,X37,X35,X3,X40,X26) = hAPP(X38,X39) ),
c_0_14 ).
fof(c_0_305_306,axiom,
! [X37,X38,X35,X40,X26,X3] :
( hAPP(X37,X35) != c_Option_Ooption_ONone(X26)
| c_Map_Omap__comp(X38,X37,X35,X26,X3,X40) = c_Option_Ooption_ONone(X3) ),
c_0_15 ).
fof(c_0_306_307,axiom,
! [X37,X38,X35,X40,X26,X3] :
( hAPP(X37,X35) != c_Option_Ooption_ONone(X3)
| c_Map_Omap__comp(X38,X37,X35,X3,X40,X26) = c_Option_Ooption_ONone(X40) ),
c_0_16 ).
fof(c_0_307_308,axiom,
! [X80,X27,X81,X82,X26,X3] :
( c_Map_Omap__add(c_Fun_Ofun__upd(X82,X27,hAPP(c_Option_Ooption_OSome(X26),X80),X3,tc_Option_Ooption(X26)),X81,X3,X26) = c_Fun_Ofun__upd(c_Map_Omap__add(X82,X81,X3,X26),X27,hAPP(c_Option_Ooption_OSome(X26),X80),X3,tc_Option_Ooption(X26))
| c_in(X27,c_Map_Odom(X81,X3,X26),X3) ),
c_0_17 ).
fof(c_0_308_309,plain,
! [X15,X29,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),X14,tc_Hoare__Mirabelle_Otriple(X3)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_309_310,axiom,
! [X24,X9,X27,X16,X11,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X3),X16),X26,tc_Option_Ooption(X3)),X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| hAPP(X27,X9) = hAPP(c_Option_Ooption_OSome(X3),X24)
| X16 = X24 ),
c_0_19 ).
fof(c_0_310_311,axiom,
! [X24,X9,X27,X16,X11,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X3),X16),X26,tc_Option_Ooption(X3)),X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| hAPP(X27,X9) = hAPP(c_Option_Ooption_OSome(X3),X24)
| X9 = X11 ),
c_0_20 ).
fof(c_0_311_312,axiom,
! [X24,X9,X27,X16,X41,X3] :
( X16 = X24
| hAPP(c_Fun_Ofun__upd(X27,X9,hAPP(c_Option_Ooption_OSome(X41),X16),X3,tc_Option_Ooption(X41)),X9) != hAPP(c_Option_Ooption_OSome(X41),X24) ),
c_0_21 ).
fof(c_0_312_313,axiom,
! [X24,X9,X28,X27,X11,X26,X3] :
( c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X26),X9),X3,tc_Option_Ooption(X26)) != c_Fun_Ofun__upd(X28,X11,hAPP(c_Option_Ooption_OSome(X26),X24),X3,tc_Option_Ooption(X26))
| X9 = X24 ),
c_0_22 ).
fof(c_0_313_314,plain,
! [X24,X9,X25,X45,X26,X3] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X25,X9,X24,X3,X26),X45,X3,X26)
| c_in(X24,c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_314_315,plain,
! [X67,X23,X72,X29,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),c_Com_Ocom_OSemi(X23,X67)),X72),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X29),X67),X72),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),X23),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_315_316,plain,
! [X15,X29,X18,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_316_317,axiom,
! [X24,X9,X25,X45,X26,X3] :
( c_Set_Oimage(c_Fun_Ofun__upd(X25,X9,X24,X26,X3),X45,X26,X3) = c_Set_Oimage(X25,X45,X26,X3)
| c_in(X9,X45,X26) ),
c_0_26 ).
fof(c_0_317_318,axiom,
! [X24,X9,X25,X26,X3] :
( c_Map_Odom(c_Fun_Ofun__upd(X25,X9,X24,X3,tc_Option_Ooption(X26)),X3,X26) = c_Set_Oinsert(X9,c_Map_Odom(X25,X3,X26),X3)
| X24 = c_Option_Ooption_ONone(X26) ),
c_0_27 ).
fof(c_0_318_319,axiom,
! [X9,X25,X26,X3] :
( c_Map_Odom(X25,X3,X26) != c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X25 = c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X26),tc_Option_Ooption(X26),X3),X9,hAPP(c_Option_Ooption_OSome(X26),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X25,X9,X3,X26)),X3,tc_Option_Ooption(X26)) ),
c_0_28 ).
fof(c_0_319_320,plain,
! [X23,X29,X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X18),X23),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X18),X23),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_320_321,axiom,
! [X24,X9,X27,X16,X11,X26,X3] :
( hAPP(X27,X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| X9 = X11
| hAPP(c_Fun_Ofun__upd(X27,X11,hAPP(c_Option_Ooption_OSome(X3),X16),X26,tc_Option_Ooption(X3)),X9) = hAPP(c_Option_Ooption_OSome(X3),X24) ),
c_0_30 ).
fof(c_0_321_322,axiom,
! [X50,X24,X9,X25,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X25,X9,X24,X26,X3),X50) = hAPP(X25,X50)
| X50 = X9 ),
c_0_31 ).
fof(c_0_322_323,axiom,
! [X50,X24,X9,X25,X26,X3] :
( hAPP(c_Fun_Ofun__upd(X25,X9,X24,X3,X26),X50) = hAPP(X25,X50)
| X50 = X9 ),
c_0_32 ).
fof(c_0_323_324,plain,
! [X25,X51,X45,X26,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X25,X45,X3,X26),c_Set_Oimage(X25,X51,X3,X26),tc_fun(X26,tc_bool))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_324_325,axiom,
! [X24,X9,X25,X26,X3] :
( c_Fun_Ofun__upd(X25,X9,X24,X3,X26) != X25
| hAPP(X25,X9) = X24 ),
c_0_34 ).
fof(c_0_325_326,plain,
! [X15,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X15)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X15)),X14,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_326_327,plain,
! [X30,X21,X33,X31,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X33),X21),X30))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X21),X30))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X31,X33)),X21),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_327_328,plain,
! [X58,X27,X26,X3] :
( c_Fun_Oinj__on(X58,c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26))
| ~ c_Fun_Oinj__on(c_Map_Omap__add(X27,X58,X3,X26),c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26)) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_328_329,plain,
! [X30,X21,X33,X31,X16] :
( ~ hBOOL(hAPP(X16,X21))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X21),X30))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X31,X33)),X21),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_329_330,plain,
! [X25,X51,X45,X26,X3] :
( c_lessequals(c_Set_Oimage(X25,X45,X3,X26),c_Set_Oimage(X25,X51,X3,X26),tc_fun(X26,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_330_331,plain,
! [X30,X21,X33,X31,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X33),X21),X30))
| hBOOL(hAPP(X16,X21))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X31,X33)),X21),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_331_332,plain,
! [X25,X45,X3] :
( c_Set_Oimage(X25,X45,X3,X3) = X45
| ~ c_Fun_Oinj__on(X25,X45,X3,X3)
| ~ c_lessequals(c_Set_Oimage(X25,X45,X3,X3),X45,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_332_333,plain,
! [X20,X22,X15] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X15)),X22),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X22),X20)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_333_334,plain,
! [X25,X11,X45,X26,X3] :
( c_in(X11,X45,X3)
| ~ c_in(hAPP(X25,X11),c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_334_335,plain,
! [X58,X27,X26,X3] :
( c_Fun_Oinj__on(c_Map_Omap__add(X27,X58,X3,X26),c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26))
| ~ c_Fun_Oinj__on(X58,c_Map_Odom(X58,X3,X26),X3,tc_Option_Ooption(X26)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_335_336,plain,
! [X25,X51,X45,X26,X3] :
( c_Set_Oimage(X25,X45,X3,X26) != c_Set_Oimage(X25,X51,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3,X26)
| X45 = X51 ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_336_337,plain,
! [X15,X28,X29,X18,X3] :
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X28),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),X3) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_337_338,axiom,
! [X9,X30,X35,X26,X3] :
( hAPP(X30,X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| c_Fun_Ofun__upd(X30,X35,hAPP(c_Option_Ooption_OSome(X3),X9),X26,tc_Option_Ooption(X3)) = X30 ),
c_0_47 ).
fof(c_0_338_339,plain,
! [X25,X51,X45,X26,X3] :
( c_Set_Oimage(X25,X45,X3,X26) != c_Set_Oimage(X25,X51,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26)
| X45 = X51 ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_339_340,plain,
! [X20,X21,X28,X18] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X18)),X21,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X18,X28,X21,X20),X20)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X18),X21,X28,X20) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_340_341,plain,
! [X25,X45,X26,X3] :
( c_Finite__Set_Ofinite(X45,X26)
| ~ c_Fun_Oinj__on(X25,X45,X26,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X45,X26,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_341_342,plain,
! [X15,X28,X29,X18,X3] :
( c_Hoare__Mirabelle_Otriple__valid(X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15))),X29),X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X28),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X18),hAPP(c_Com_Ocom_OBODY,X15)),X29),X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_342_343,plain,
! [X9,X25,X45,X26,X3] :
( ~ c_lessequals(X9,X45,tc_fun(X26,tc_bool))
| c_lessequals(c_Set_Oimage(X25,X9,X26,X3),c_Set_Oimage(X25,X45,X26,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_343_344,plain,
! [X25,X51,X45,X26,X3] :
( c_lessequals(c_Set_Oimage(X25,X45,X3,X26),c_Set_Oimage(X25,X51,X3,X26),tc_fun(X26,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_344_345,plain,
! [X20,X21,X18] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X18))),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X18)),X21),X20)) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_345_346,plain,
! [X20,X21,X31,X32,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X32,X31)),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X32),X21),X20))
| ~ hBOOL(hAPP(X16,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_346_347,plain,
! [X25,X45,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X3)
| ~ c_lessequals(X45,c_Set_Oimage(X25,X45,X3,X3),tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_347_348,plain,
! [X20,X21,X31,X32,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X16,X32,X31)),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X21),X20))
| hBOOL(hAPP(X16,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_348_349,plain,
! [X70,X20,X22,X28,X23,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X22,X28,X70)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X20,X28,X70)
| ~ c_Natural_Oevaln(X23,X22,X28,X20)
| ~ hBOOL(hAPP(X16,X22)) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_349_350,plain,
! [X25,X11,X45,X26,X3] :
( c_in(hAPP(X25,X11),c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_in(X11,X45,X3)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_350_351,plain,
! [X23,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X14))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_351_352,plain,
! [X9,X25,X51,X45,X26,X3] :
( c_in(hAPP(X25,X9),X51,X3)
| ~ c_in(X9,X45,X26)
| ~ c_lessequals(c_Set_Oimage(X25,X45,X26,X3),X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_352_353,plain,
! [X30,X21,X28,X33,X31,X16] :
( c_Natural_Oevaln(X33,X21,X28,X30)
| c_Natural_Oevaln(X31,X21,X28,X30)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X31,X33),X21,X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_353_354,plain,
! [X70,X20,X22,X28,X31,X32] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X32,X31),X22,X28,X70)
| ~ c_Natural_Oevaln(X31,X20,X28,X70)
| ~ c_Natural_Oevaln(X32,X22,X28,X20) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_354_355,plain,
! [X70,X20,X22,X23,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X22),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X20),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X22),X20))
| ~ hBOOL(hAPP(X16,X22)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_355_356,plain,
! [X65,X21,X28,X23,X66,X29,X18] :
( hBOOL(hAPP(hAPP(X29,X66),X65))
| ~ c_Natural_Oevaln(X23,X21,X28,X65)
| ~ hBOOL(hAPP(hAPP(X18,X66),X21))
| ~ c_Hoare__Mirabelle_Otriple__valid(X28,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X18),X23),X29),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_356_357,plain,
! [X25,X51,X45,X26,X3] :
( c_Finite__Set_Ofinite(X51,X26)
| ~ c_lessequals(X51,c_Set_Oimage(X25,X45,X3,X26),tc_fun(X26,tc_bool))
| ~ c_Finite__Set_Ofinite(X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_357_358,plain,
! [X20,X21,X28,X18] :
( X28 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X18,X28,X21,X20))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X18),X21,X28,X20) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_358_359,plain,
! [X9,X25,X45,X26,X3] :
( c_Set_Oinsert(hAPP(X25,X9),c_Set_Oimage(X25,X45,X3,X26),X26) = c_Set_Oimage(X25,X45,X3,X26)
| ~ c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_359_360,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X27,X35) = hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X28,X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
c_0_69 ).
fof(c_0_360_361,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X28,X35) = c_Option_Ooption_ONone(X3)
| hAPP(X28,X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
c_0_70 ).
fof(c_0_361_362,plain,
! [X25,X51,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X51,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_362_363,plain,
! [X25,X51,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_363_364,plain,
! [X30,X21,X28,X33,X31,X16] :
( ~ hBOOL(hAPP(X16,X21))
| c_Natural_Oevaln(X31,X21,X28,X30)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X31,X33),X21,X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_364_365,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X11 = X67
| X11 = X23 ),
c_0_74 ).
fof(c_0_365_366,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X23
| X11 = X23 ),
c_0_75 ).
fof(c_0_366_367,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X11 = X67
| X16 = X67 ),
c_0_76 ).
fof(c_0_367_368,axiom,
! [X67,X23,X16,X11,X3] :
( c_Set_Oinsert(X11,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X23,c_Set_Oinsert(X67,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X16 = X23
| X16 = X67 ),
c_0_77 ).
fof(c_0_368_369,plain,
! [X30,X21,X28,X33,X31,X16] :
( c_Natural_Oevaln(X33,X21,X28,X30)
| hBOOL(hAPP(X16,X21))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X31,X33),X21,X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_369_370,axiom,
! [X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != c_Option_Ooption_ONone(X3)
| hAPP(X27,X35) = c_Option_Ooption_ONone(X3) ),
c_0_79 ).
fof(c_0_370_371,axiom,
! [X28,X27,X35,X26,X3] :
( hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) != c_Option_Ooption_ONone(X3)
| hAPP(X28,X35) = c_Option_Ooption_ONone(X3) ),
c_0_80 ).
fof(c_0_371_372,plain,
! [X25,X11,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X26)
| ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X11,X45,X3),X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_372_373,plain,
! [X20,X21,X28,X31,X32,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X32,X31),X21,X28,X20)
| ~ c_Natural_Oevaln(X32,X21,X28,X20)
| ~ hBOOL(hAPP(X16,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_373_374,plain,
! [X20,X22,X15,X28] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X15),X22,c_Suc(X28),X20)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X15)),X22,X28,X20) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_374_375,plain,
! [X27,X11,X26,X3] :
( hAPP(X27,X11) = hAPP(c_Option_Ooption_OSome(X26),c_Map_Osko__Map__XdomD__1__1(X11,X27,X3,X26))
| ~ c_in(X11,c_Map_Odom(X27,X3,X26),X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_375_376,plain,
! [X27,X46,X47,X26,X3] :
( hAPP(c_Map_Omap__add(X47,X46,X3,X26),X27) = hAPP(X46,X27)
| ~ c_in(X27,c_Map_Odom(X46,X3,X26),X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_376_377,plain,
! [X20,X21,X28,X31,X32,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X16,X32,X31),X21,X28,X20)
| ~ c_Natural_Oevaln(X31,X21,X28,X20)
| hBOOL(hAPP(X16,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_377_378,plain,
! [X12,X30,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,X12,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_378_379,plain,
! [X25,X51,X45,X26,X3] :
( c_Fun_Oinj__on(X25,X45,X3,X26)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X25,X51,X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_379_380,axiom,
! [X27,X46,X47,X26,X3] :
( hAPP(c_Map_Omap__add(X47,X46,X3,X26),X27) = hAPP(X46,X27)
| c_in(X27,c_Map_Odom(X47,X3,X26),X3) ),
c_0_89 ).
fof(c_0_380_381,axiom,
! [X27,X46,X47,X26,X3] :
( hAPP(c_Map_Omap__add(X47,X46,X3,X26),X27) = hAPP(X47,X27)
| c_in(X27,c_Map_Odom(X46,X3,X26),X3) ),
c_0_90 ).
fof(c_0_381_382,plain,
! [X9,X25,X45,X41,X3] :
( ~ c_in(X9,X45,X41)
| c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X41,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_382_383,plain,
! [X9,X25,X45,X26,X3] :
( ~ c_in(X9,X45,X26)
| c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X26,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_383_384,plain,
! [X9,X25,X45,X26,X3] :
( c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X26,X3),X3)
| ~ c_in(X9,X45,X26) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_384_385,plain,
! [X9,X25,X45,X26,X3] :
( c_in(hAPP(X25,X9),c_Set_Oimage(X25,X45,X3,X26),X26)
| ~ c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_385_386,plain,
! [X9,X18,X3] :
( ~ hBOOL(hAPP(X18,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X3),X9),X18,X3)))
| hBOOL(hAPP(X18,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_386_387,plain,
! [X70,X20,X22,X31,X32] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X32,X31)),X22),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X31),X20),X70))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X32),X22),X20)) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_387_388,plain,
! [X65,X21,X28,X23] :
( c_Natural_Oevaln(X23,X21,c_Suc(X28),X65)
| ~ c_Natural_Oevaln(X23,X21,X28,X65) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_388_389,plain,
! [X48,X49,X51,X45,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X49,X48,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X48,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X49,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_389_390,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(X27,X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(X28,X35) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
c_0_99 ).
fof(c_0_390_391,plain,
! [X24,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_in(X24,X45,X3)
| ~ c_in(X9,X45,X3)
| X9 = X24
| ~ c_Fun_Oinj__on(X25,X45,X3,X26) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_391_392,plain,
! [X24,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_in(X24,X45,X3)
| ~ c_in(X9,X45,X3)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26)
| X9 = X24 ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_392_393,plain,
! [X8,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X8)
| ~ c_in(X8,X45,X3)
| ~ c_in(X9,X45,X3)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26)
| X9 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_393_394,plain,
! [X24,X9,X25,X45,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_Fun_Oinj__on(X25,X45,X3,X26)
| X9 = X24
| ~ c_in(X24,X45,X3)
| ~ c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_394_395,plain,
! [X12,X30,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,X12,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_395_396,plain,
! [X9,X45,X3] :
( X45 = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_396_397,plain,
! [X9,X51,X45,X3] :
( hBOOL(hAPP(X51,X9))
| hBOOL(hAPP(X45,X9))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_397_398,axiom,
! [X36,X28,X27,X35,X26,X3] :
( hAPP(X28,X35) != hAPP(c_Option_Ooption_OSome(X3),X36)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = hAPP(c_Option_Ooption_OSome(X3),X36) ),
c_0_107 ).
fof(c_0_398_399,axiom,
! [X9,X28,X27,X35,X26,X3] :
( hAPP(X28,X35) != hAPP(c_Option_Ooption_OSome(X3),X9)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = hAPP(c_Option_Ooption_OSome(X3),X9) ),
c_0_108 ).
fof(c_0_399_400,axiom,
! [X28,X27,X35,X26,X3] :
( hAPP(X27,X35) != c_Option_Ooption_ONone(X3)
| hAPP(X28,X35) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X27,X28,X26,X3),X35) = c_Option_Ooption_ONone(X3) ),
c_0_109 ).
fof(c_0_400_401,plain,
! [X9,X23,X45,X26,X3] :
( c_Set_Oimage(c_COMBK(X23,X26,X3),X45,X3,X26) = c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26)
| ~ c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_401_402,plain,
! [X68,X17,X26,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X68,X17,X3,X26),X26)
| ~ c_Finite__Set_Ofinite(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_402_403,plain,
! [X30,X21,X23,X16] :
( hBOOL(hAPP(X16,X21))
| X30 = X21
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X21),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_403_404,plain,
! [X24,X9,X25,X26,X3] :
( hAPP(X25,X9) != hAPP(X25,X24)
| ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X26)
| X9 = X24 ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_404_405,plain,
! [X23,X14] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X14),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_405_406,plain,
! [X30,X21,X28,X23] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X30))
| ~ c_Natural_Oevaln(X23,X21,X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_406_407,plain,
! [X9,X30,X21,X23] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X30))
| ~ c_Natural_Oevaln(X23,X21,X9,X30) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_407_408,axiom,
! [X23,X45,X26,X3] :
( c_Set_Oimage(c_COMBK(X23,X3,X26),X45,X26,X3) = c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)) ),
c_0_117 ).
fof(c_0_408_409,plain,
! [X49,X51,X45,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X49,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_409_410,plain,
! [X49,X51,X45,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X49,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_410_411,plain,
! [X30,X21,X28,X23,X16] :
( hBOOL(hAPP(X16,X21))
| X30 = X21
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X21,X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_411_412,axiom,
! [X25,X45,X26,X3] :
( c_Set_Oimage(X25,X45,X26,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)) ),
c_0_121 ).
fof(c_0_412_413,axiom,
! [X25,X45,X26,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X25,X45,X26,X3)
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)) ),
c_0_122 ).
fof(c_0_413_414,plain,
! [X49,X51,X45,X3] :
( c_lessequals(X45,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_414_415,plain,
! [X49,X51,X45,X3] :
( c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X49,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_415_416,plain,
! [X23,X51,X45,X3] :
( c_in(X23,X51,X3)
| c_in(X23,X45,X3)
| ~ c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_416_417,plain,
! [X9,X51,X45,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| c_in(X9,X45,X3)
| ~ c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_417_418,plain,
! [X9,X51,X45,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool))
| c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_418_419,plain,
! [X16,X11,X3] :
( X16 = X11
| ~ c_in(X16,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_419_420,plain,
! [X24,X9,X45,X3] :
( hBOOL(hAPP(X45,X9))
| X24 = X9
| ~ hBOOL(hAPP(c_Set_Oinsert(X24,X45,X3),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_420_421,plain,
! [X23] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X23),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X23)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_421_422,plain,
! [X11,X48,X49,X3] :
( c_lessequals(c_Set_Oinsert(X11,X49,X3),c_Set_Oinsert(X11,X48,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X49,X48,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_422_423,axiom,
! [X73,X25,X26,X3] :
( c_Option_Omap(X25,X73,X26,X3) != c_Option_Ooption_ONone(X3)
| X73 = c_Option_Ooption_ONone(X26) ),
c_0_132 ).
fof(c_0_423_424,plain,
! [X9,X51,X45,X3] :
( c_lessequals(c_Set_Oinsert(X9,X45,X3),X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_in(X9,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_424_425,plain,
! [X30,X21,X28] :
( X30 = X21
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X21,X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_425_426,plain,
! [X9,X51,X45,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X9))
| ~ hBOOL(hAPP(X51,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_426_427,plain,
! [X9,X51,X45,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X9))
| ~ hBOOL(hAPP(X45,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_427_428,plain,
! [X9,X51,X45,X3] :
( c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X9,X45,X3),X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_428_429,axiom,
! [X61,X62,X63,X64,X56,X57,X3] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X64),X57),X62) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X63),X56),X61)
| X64 = X63 ),
c_0_138 ).
fof(c_0_429_430,axiom,
! [X61,X62,X63,X64,X56,X57,X3] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X64),X57),X62) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X63),X56),X61)
| X57 = X56 ),
c_0_139 ).
fof(c_0_430_431,axiom,
! [X61,X62,X63,X64,X56,X57,X3] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X64),X57),X62) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X63),X56),X61)
| X62 = X61 ),
c_0_140 ).
fof(c_0_431_432,plain,
! [X9,X51,X45,X3] :
( c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_432_433,plain,
! [X9,X51,X45,X3] :
( c_lessequals(X45,c_Set_Oinsert(X9,X51,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_433_434,plain,
! [X9,X51,X45,X3] :
( c_in(X9,X51,X3)
| ~ c_lessequals(c_Set_Oinsert(X9,X45,X3),X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_434_435,axiom,
! [X21,X23,X16] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X16,X23)),X21),X21))
| hBOOL(hAPP(X16,X21)) ),
c_0_144 ).
fof(c_0_435_436,plain,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X9,X3)
| ~ c_lessequals(X16,X9,X3)
| ~ c_lessequals(X11,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_436_437,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X9,X3)
| ~ c_lessequals(X50,X9,X3)
| ~ c_lessequals(X24,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_437_438,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3)
| ~ c_lessequals(X24,X50,X3)
| ~ c_lessequals(X9,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_438_439,plain,
! [X71,X30,X21,X23] :
( X71 = X30
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X71))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X21),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_439_440,axiom,
! [X16,X11,X3] :
( c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X11 = X16 ),
c_0_149 ).
fof(c_0_440_441,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_441_442,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X50,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_442_443,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X50,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_443_444,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X24,X50,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_444_445,plain,
! [X12,X30,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,c_Set_Oinsert(X30,X12,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_445_446,plain,
! [X49,X51,X45,X3] :
( c_lessequals(X45,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X51,X49,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_446_447,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X24,X50,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_447_448,plain,
! [X50,X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,X50,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_448_449,plain,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X16,X9,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_449_450,plain,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X11,X9,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_450_451,plain,
! [X16,X11,X45,X3] :
( c_in(X11,X45,X3)
| X11 = X16
| ~ c_in(X11,c_Set_Oinsert(X16,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_451_452,plain,
! [X16,X51,X45,X3] :
( c_lessequals(X45,c_Set_Oinsert(X16,X51,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_452_453,axiom,
! [X21,X28,X23,X16] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X16,X23),X21,X28,X21)
| hBOOL(hAPP(X16,X21)) ),
c_0_162 ).
fof(c_0_453_454,plain,
! [X23,X51,X45,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_454_455,plain,
! [X23,X51,X45,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_455_456,plain,
! [X24,X9,X45,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X24,X45,X3),X9))
| ~ hBOOL(hAPP(X45,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_456_457,axiom,
! [X9,X51,X45,X3] :
( c_Set_Oinsert(X9,X45,X3) != c_Set_Oinsert(X9,X51,X3)
| c_in(X9,X51,X3)
| c_in(X9,X45,X3)
| X45 = X51 ),
c_0_166 ).
fof(c_0_457_458,plain,
! [X27,X11,X26,X3] :
( hAPP(X27,X11) != c_Option_Ooption_ONone(X26)
| ~ c_in(X11,c_Map_Odom(X27,X3,X26),X3) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_458_459,plain,
! [X34,X12,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_lessequals(X12,X34,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X34,X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_459_460,plain,
! [X12,X13,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_lessequals(X13,X14,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_460_461,plain,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(X17,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_461_462,plain,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(X14,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_462_463,axiom,
! [X24,X9,X25,X26,X3] :
( hAPP(X25,X9) != hAPP(c_Option_Ooption_OSome(X3),X24)
| c_Set_Oinsert(X9,c_Map_Odom(X25,X26,X3),X26) = c_Map_Odom(X25,X26,X3) ),
c_0_172 ).
fof(c_0_463_464,plain,
! [X9,X51,X45,X3] :
( c_in(X9,X51,X3)
| ~ c_in(X9,X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_464_465,plain,
! [X23,X51,X45,X3] :
( c_in(X23,X51,X3)
| ~ c_in(X23,X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_465_466,plain,
! [X9,X51,X45,X3] :
( c_in(X9,X51,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_in(X9,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_466_467,plain,
! [X30,X51,X45,X3] :
( c_in(X30,X51,X3)
| ~ c_in(X30,X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_467_468,plain,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X3)
| ~ c_lessequals(X9,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_468_469,plain,
! [X9,X16,X11,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X3),X3)
| ~ c_lessequals(X9,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_469_470,plain,
! [X16,X11,X51,X3] :
( c_in(X11,c_Set_Oinsert(X16,X51,X3),X3)
| ~ c_in(X11,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_470_471,plain,
! [X16,X11,X45,X3] :
( c_in(X11,c_Set_Oinsert(X16,X45,X3),X3)
| ~ c_in(X11,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_471_472,plain,
! [X51,X45,X3] :
( X45 = X51
| ~ c_lessequals(X51,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_472_473,plain,
! [X51,X45,X3] :
( X45 = X51
| ~ c_lessequals(X51,X45,tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_473_474,plain,
! [X9,X69,X25,X26,X3] :
( ~ class_HOL_Oord(X26)
| c_lessequals(hAPP(X25,X9),hAPP(X69,X9),X26)
| ~ c_lessequals(X25,X69,tc_fun(X3,X26)) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_474_475,plain,
! [X50,X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X50,X9,X3)
| ~ c_lessequals(X50,X24,X3)
| ~ c_lessequals(X24,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_475_476,plain,
! [X50,X24,X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X50,X3)
| ~ c_lessequals(X24,X50,X3)
| ~ c_lessequals(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_476_477,plain,
! [X45,X3] :
( X45 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X45,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_477_478,plain,
! [X12,X13,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X13,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X13,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_478_479,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_479_480,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_480_481,plain,
! [X9,X18,X3] :
( ~ hBOOL(hAPP(X18,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_481_482,axiom,
! [X27,X16,X11,X26,X3] :
( hAPP(X27,X11) != hAPP(c_Option_Ooption_OSome(X3),X16)
| c_in(X11,c_Map_Odom(X27,X26,X3),X26) ),
c_0_191 ).
fof(c_0_482_483,plain,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X14,X3)
| ~ c_Finite__Set_Ofinite(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_483_484,plain,
! [X14,X17,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X17,X14,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X14,X3)
| ~ c_Finite__Set_Ofinite(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_484_485,plain,
! [X11,X45,X3] :
( c_Finite__Set_Ofinite(X45,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X11,X45,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_485_486,plain,
! [X11,X2,X18] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X18))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X18,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_486_487,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) != X51
| c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
c_0_196 ).
fof(c_0_487_488,plain,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) = X51
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_488_489,plain,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) = X45
| ~ c_lessequals(X51,X45,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_489_490,plain,
! [X9,X29,X18,X3] :
( hBOOL(hAPP(X29,X9))
| ~ hBOOL(hAPP(X18,X9))
| ~ c_lessequals(X18,X29,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_490_491,plain,
! [X9,X29,X18,X3] :
( hBOOL(hAPP(X29,X9))
| ~ c_lessequals(X18,X29,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X18,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_491_492,plain,
! [X9,X18,X3] :
( hBOOL(hAPP(X18,X9))
| ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_492_493,plain,
! [X12,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3)
| ~ c_lessequals(X12,X14,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_493_494,axiom,
! [X25,X26,X3] :
( c_Map_Odom(X25,X3,X26) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X25 = c_COMBK(c_Option_Ooption_ONone(X26),tc_Option_Ooption(X26),X3) ),
c_0_203 ).
fof(c_0_494_495,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X51 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_204 ).
fof(c_0_495_496,axiom,
! [X51,X45,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X45,X51,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X45 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_205 ).
fof(c_0_496_497,axiom,
! [X8,X9,X3] :
( c_Set_Oinsert(X9,X8,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_in(X9,X8,X3) ),
c_0_206 ).
fof(c_0_497_498,plain,
! [X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X24
| ~ c_lessequals(X24,X9,X3)
| ~ c_lessequals(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_498_499,plain,
! [X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X24
| ~ c_lessequals(X24,X9,X3)
| ~ c_lessequals(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_499_500,plain,
! [X24,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X24
| ~ c_lessequals(X9,X24,X3)
| ~ c_lessequals(X24,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_500_501,axiom,
! [X27,X11,X26,X3] :
( c_in(X11,c_Map_Odom(X27,X3,X26),X3)
| hAPP(X27,X11) = c_Option_Ooption_ONone(X26) ),
c_0_210 ).
fof(c_0_501_502,plain,
! [X33,X31,X16] :
( c_Com_OWT(X31)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X16,X31,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_502_503,plain,
! [X33,X31,X16] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X16,X31,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_503_504,plain,
! [X23,X11,X1] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X1,X11,X23)) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_504_505,axiom,
! [X59,X60,X6,X7,X54,X55] :
( c_Com_Ocom_OCall(X60,X7,X55) != c_Com_Ocom_OCall(X59,X6,X54)
| X55 = X54 ),
c_0_214 ).
fof(c_0_505_506,axiom,
! [X59,X60,X6,X7,X54,X55] :
( c_Com_Ocom_OCall(X60,X7,X55) != c_Com_Ocom_OCall(X59,X6,X54)
| X7 = X6 ),
c_0_215 ).
fof(c_0_506_507,axiom,
! [X59,X60,X6,X7,X54,X55] :
( c_Com_Ocom_OCall(X60,X7,X55) != c_Com_Ocom_OCall(X59,X6,X54)
| X60 = X59 ),
c_0_216 ).
fof(c_0_507_508,axiom,
! [X54,X55,X76,X77,X78,X79] :
( c_Com_Ocom_OCond(X55,X79,X77) != c_Com_Ocom_OCond(X54,X78,X76)
| X77 = X76 ),
c_0_217 ).
fof(c_0_508_509,axiom,
! [X54,X55,X76,X77,X78,X79] :
( c_Com_Ocom_OCond(X55,X79,X77) != c_Com_Ocom_OCond(X54,X78,X76)
| X79 = X78 ),
c_0_218 ).
fof(c_0_509_510,axiom,
! [X54,X55,X76,X77,X78,X79] :
( c_Com_Ocom_OCond(X55,X79,X77) != c_Com_Ocom_OCond(X54,X78,X76)
| X55 = X54 ),
c_0_219 ).
fof(c_0_510_511,axiom,
! [X52,X53,X54,X55,X56,X57] :
( c_Com_Ocom_OLocal(X53,X55,X57) != c_Com_Ocom_OLocal(X52,X54,X56)
| X57 = X56 ),
c_0_220 ).
fof(c_0_511_512,axiom,
! [X52,X53,X54,X55,X56,X57] :
( c_Com_Ocom_OLocal(X53,X55,X57) != c_Com_Ocom_OLocal(X52,X54,X56)
| X55 = X54 ),
c_0_221 ).
fof(c_0_512_513,axiom,
! [X52,X53,X54,X55,X56,X57] :
( c_Com_Ocom_OLocal(X53,X55,X57) != c_Com_Ocom_OLocal(X52,X54,X56)
| X53 = X52 ),
c_0_222 ).
fof(c_0_513_514,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_514_515,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_515_516,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_516_517,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X24,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_517_518,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_518_519,plain,
! [X51,X45,X3] :
( c_Finite__Set_Ofinite(X45,X3)
| ~ c_Finite__Set_Ofinite(X51,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_519_520,plain,
! [X51,X45,X3] :
( c_Finite__Set_Ofinite(X45,X3)
| ~ c_lessequals(X45,X51,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_520_521,plain,
! [X15,X11,X2] :
( c_Com_OWT(c_Com_Ocom_OCall(X2,X15,X11))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_521_522,plain,
! [X30,X21] :
( X30 = X21
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X21),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_522_523,plain,
! [X30,X28,X3] :
( c_Hoare__Mirabelle_Otriple__valid(X28,X30,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X28),X30,X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_523_524,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) != X24
| c_lessequals(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_524_525,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = X9
| ~ c_lessequals(X24,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_525_526,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = X24
| ~ c_lessequals(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_526_527,plain,
! [X11,X45,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X11,X45,X3),X3)
| ~ c_Finite__Set_Ofinite(X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_527_528,plain,
! [X11,X45,X3] :
( c_Set_Oinsert(X11,X45,X3) = X45
| ~ c_in(X11,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_528_529,plain,
! [X12,X14,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X14,X12,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X14,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_529_530,plain,
! [X31,X32,X16] :
( c_Com_OWT(c_Com_Ocom_OCond(X16,X32,X31))
| ~ c_Com_OWT(X31)
| ~ c_Com_OWT(X32) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_530_531,plain,
! [X23,X11,X1] :
( c_Com_OWT(c_Com_Ocom_OLocal(X1,X11,X23))
| ~ c_Com_OWT(X23) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_531_532,plain,
! [X24,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X24,X9,X3)
| c_lessequals(X9,X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_532_533,plain,
! [X9,X86,X3] :
( hBOOL(hAPP(X86,X9))
| ~ c_in(X9,X86,X3) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_533_534,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_534_535,plain,
! [X24,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X24,X3) = c_Lattices_Oupper__semilattice__class_Osup(X24,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_535_536,plain,
! [X51,X45,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X45,X51,X3) != c_Orderings_Obot__class_Obot(X3)
| X45 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_536_537,plain,
! [X51,X45,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X45,X51,X3) != c_Orderings_Obot__class_Obot(X3)
| X51 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_537_538,plain,
! [X9,X86,X3] :
( c_in(X9,X86,X3)
| ~ hBOOL(hAPP(X86,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_538_539,plain,
! [X18] :
( hAPP(c_Com_Obody,X18) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X18))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X18)) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_539_540,plain,
! [X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_540_541,plain,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Orderings_Otop__class_Otop(X3),X3) = c_Orderings_Otop__class_Otop(X3) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_541_542,plain,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X3),X9,X3) = c_Orderings_Otop__class_Otop(X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_542_543,plain,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Orderings_Obot__class_Obot(X3),X3) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_543_544,plain,
! [X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X3),X9,X3) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_544_545,plain,
! [X9,X3] :
( ~ class_Orderings_Obot(X3)
| c_lessequals(c_Orderings_Obot__class_Obot(X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_545_546,plain,
! [X9,X3] :
( ~ class_Orderings_Otop(X3)
| c_lessequals(X9,c_Orderings_Otop__class_Otop(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_546_547,axiom,
! [X10,X11,X3] :
( hAPP(c_Option_Ooption_OSome(X3),X11) != hAPP(c_Option_Ooption_OSome(X3),X10)
| X11 = X10 ),
c_0_256 ).
fof(c_0_547_548,plain,
! [X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X9,X3) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_548_549,plain,
! [X9,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X9,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_549_550,plain,
! [X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_550_551,plain,
! [X33,X31] :
( c_Com_OWT(X31)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X31,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_551_552,plain,
! [X33,X31] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X31,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_552_553,plain,
! [X23,X16] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X16,X23)) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_553_554,plain,
! [X15,X16] :
( hAPP(c_Com_Obody,X15) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X16)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X16) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_554_555,axiom,
! [X76,X77,X78,X79] :
( c_Com_Ocom_OSemi(X79,X77) != c_Com_Ocom_OSemi(X78,X76)
| X77 = X76 ),
c_0_264 ).
fof(c_0_555_556,axiom,
! [X76,X77,X78,X79] :
( c_Com_Ocom_OSemi(X79,X77) != c_Com_Ocom_OSemi(X78,X76)
| X79 = X78 ),
c_0_265 ).
fof(c_0_556_557,axiom,
! [X54,X55,X56,X57] :
( c_Com_Ocom_OWhile(X55,X57) != c_Com_Ocom_OWhile(X54,X56)
| X55 = X54 ),
c_0_266 ).
fof(c_0_557_558,axiom,
! [X54,X55,X56,X57] :
( c_Com_Ocom_OWhile(X55,X57) != c_Com_Ocom_OWhile(X54,X56)
| X57 = X56 ),
c_0_267 ).
fof(c_0_558_559,axiom,
! [X59,X60,X54,X55] :
( c_Com_Ocom_OAss(X60,X55) != c_Com_Ocom_OAss(X59,X54)
| X55 = X54 ),
c_0_268 ).
fof(c_0_559_560,axiom,
! [X59,X60,X54,X55] :
( c_Com_Ocom_OAss(X60,X55) != c_Com_Ocom_OAss(X59,X54)
| X60 = X59 ),
c_0_269 ).
fof(c_0_560_561,plain,
! [X31,X32] :
( c_Com_OWT(c_Com_Ocom_OSemi(X32,X31))
| ~ c_Com_OWT(X31)
| ~ c_Com_OWT(X32) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_561_562,plain,
! [X5,X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X5,X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4)
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_562_563,axiom,
! [X15] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X15))
| hAPP(c_Com_Obody,X15) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
c_0_272 ).
fof(c_0_563_564,axiom,
! [X6,X7] :
( hAPP(c_Com_Ocom_OBODY,X7) != hAPP(c_Com_Ocom_OBODY,X6)
| X7 = X6 ),
c_0_273 ).
fof(c_0_564_565,plain,
! [X23,X16] :
( c_Com_OWT(c_Com_Ocom_OWhile(X16,X23))
| ~ c_Com_OWT(X23) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_565_566,plain,
! [X5,X4] :
( class_Lattices_Oupper__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_566_567,plain,
! [X5,X4] :
( class_Lattices_Obounded__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Obounded__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_567_568,plain,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_568_569,plain,
! [X5,X4] :
( class_Lattices_Olattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_569_570,plain,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_570_571,plain,
! [X5,X4] :
( class_Orderings_Otop(tc_fun(X5,X4))
| ~ class_Orderings_Otop(X4) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_571_572,plain,
! [X5,X4] :
( class_Orderings_Obot(tc_fun(X5,X4))
| ~ class_Orderings_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_572_573,plain,
! [X5,X4] :
( class_HOL_Oord(tc_fun(X5,X4))
| ~ class_HOL_Oord(X4) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_573_574,plain,
! [X9,X3] :
( X9 = c_Option_Ooption_ONone(X3)
| ~ c_Option_Ois__none(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_574_575,plain,
! [X45,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_575_576,plain,
! [X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_576_577,axiom,
! [X24,X9] :
( c_Suc(X9) != c_Suc(X24)
| X9 = X24 ),
c_0_286 ).
fof(c_0_577_578,axiom,
! [X74,X75] :
( c_Suc(X75) != c_Suc(X74)
| X75 = X74 ),
c_0_287 ).
fof(c_0_578_579,plain,
! [X30] :
( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X30) != X30
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_579_580,axiom,
! [X8,X9] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| X9 = X8 ),
c_0_289 ).
fof(c_0_580_581,plain,
! [X86,X87,X88,X89,X90,X91,X92] :
( c_Hoare__Mirabelle_Ohoare__derivs(X92,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X91,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X86,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X89,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X87,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X90,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X86,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X88,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X87,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X91,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X92,X91,X90,X89,X88,X86))),hAPP(X86,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X92,X91,X90,X89,X88,X86))),hAPP(X89,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X92,X91,X90,X89,X88,X86))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X87,t_a) ),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_581_582,plain,
! [X86,X87,X88,X89,X90,X91,X92] :
( c_Hoare__Mirabelle_Ohoare__derivs(X92,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X91,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X86,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X89,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X87,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X90,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X86,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X88,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X87,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X92,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X90,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X92,X91,X90,X89,X88,X86))),hAPP(X86,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X92,X91,X90,X89,X88,X86))),hAPP(X88,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X92,X91,X90,X89,X88,X86))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X87,t_a) ),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_582_583,plain,
! [X30,X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__valids(X33,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),X30,tc_Com_Opname,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X31,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X34)),X34)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X33,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),X30,tc_Com_Opname,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X31,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X34)),tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),X30,tc_Com_Opname,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X31,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_583_584,plain,
! [X30,X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),X30,tc_Com_Opname,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X31,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X34)),X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X33,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),X30,tc_Com_Opname,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X31,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X34)),tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34))),X30,tc_Com_Opname,tc_fun(X34,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X31,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_584_585,plain,
! [X30,X31,X32,X33,X34,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X34,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X35),hAPP(X33,X30)),hAPP(c_Com_Ocom_OBODY,X30)),hAPP(X31,X30)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X35),tc_bool)),tc_Hoare__Mirabelle_Otriple(X35)),X35)
| ~ c_in(X30,X32,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X34,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X35),X33,tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X35))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X35))),X31,tc_Com_Opname,tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X35)),X32,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X35)),tc_fun(tc_Hoare__Mirabelle_Otriple(X35),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X35),X33,tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X35))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X35))),X31,tc_Com_Opname,tc_fun(X35,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X35)),X32,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X35)),X35) ),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_585_586,plain,
! [X20,X21] :
( c_Hoare__Mirabelle_Ohoare__derivs(X21,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X20,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X20,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X21,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X20,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X20,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_586_587,plain,
! [X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X18,tc_Com_Ostate)
| ~ c_lessequals(X18,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_587_588,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X47,c_Option_Ooption_Ooption__case(X46,X45,hAPP(c_Option_Ooption_OSome(t_b),X44),t_a,t_b)))
| hBOOL(hAPP(X47,hAPP(X45,X44))) ),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_588_589,plain,
! [X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X47,c_Option_Ooption_Ooption__case(X45,X44,hAPP(c_Option_Ooption_OSome(t_b),X46),t_a,t_b)))
| hBOOL(hAPP(X47,hAPP(X44,X46))) ),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_589_590,plain,
! [X44,X45,X46] :
( ~ hBOOL(hAPP(X46,c_Option_Ooption_Ooption__case(X45,X44,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X46,X45)) ),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_590_591,plain,
! [X68,X69,X70,X71,X72,X73,X74] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X68,X72,X71,X74,X73),X70,X69,X74,X73) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X68,X70,X69,X74,X73),X72,X71,X74,X73)
| X72 = X70 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_300])])]) ).
fof(c_0_591_592,plain,
! [X70,X71,X72,X73,X74] :
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X71,X70,X74,X72,X73),c_Orderings_Otop__class_Otop(tc_fun(X73,tc_bool)),X73,X72),X72)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X70,c_Orderings_Otop__class_Otop(tc_fun(X73,tc_bool)),X73,X74),X74) ),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_592_593,plain,
! [X45,X46,X47,X48,X49,X50,X51,X52] :
( hAPP(X48,X45) != hAPP(c_Option_Ooption_OSome(X52),X46)
| hAPP(X47,X49) != hAPP(c_Option_Ooption_OSome(X51),X45)
| c_Map_Omap__comp(X48,X47,X49,X51,X52,X50) = hAPP(c_Option_Ooption_OSome(X52),X46) ),
inference(variable_rename,[status(thm)],[c_0_302]) ).
fof(c_0_593_594,plain,
! [X41,X42,X43,X44,X45,X46,X47] :
( hAPP(X43,X41) != c_Option_Ooption_ONone(X47)
| hAPP(X42,X44) != hAPP(c_Option_Ooption_OSome(X46),X41)
| c_Map_Omap__comp(X43,X42,X44,X46,X47,X45) = c_Option_Ooption_ONone(X47) ),
inference(variable_rename,[status(thm)],[c_0_303]) ).
fof(c_0_594_595,plain,
! [X41,X42,X43,X44,X45,X46,X47] :
( hAPP(X41,X44) != hAPP(c_Option_Ooption_OSome(X47),X43)
| c_Map_Omap__comp(X42,X41,X44,X47,X45,X46) = hAPP(X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_595_596,plain,
! [X41,X42,X43,X44,X45,X46] :
( hAPP(X41,X43) != c_Option_Ooption_ONone(X45)
| c_Map_Omap__comp(X42,X41,X43,X45,X46,X44) = c_Option_Ooption_ONone(X46) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_305])])]) ).
fof(c_0_596_597,plain,
! [X41,X42,X43,X44,X45,X46] :
( hAPP(X41,X43) != c_Option_Ooption_ONone(X46)
| c_Map_Omap__comp(X42,X41,X43,X46,X44,X45) = c_Option_Ooption_ONone(X44) ),
inference(variable_rename,[status(thm)],[c_0_306]) ).
fof(c_0_597_598,plain,
! [X83,X84,X85,X86,X87,X88] :
( c_Map_Omap__add(c_Fun_Ofun__upd(X86,X84,hAPP(c_Option_Ooption_OSome(X87),X83),X88,tc_Option_Ooption(X87)),X85,X88,X87) = c_Fun_Ofun__upd(c_Map_Omap__add(X86,X85,X88,X87),X84,hAPP(c_Option_Ooption_OSome(X87),X83),X88,tc_Option_Ooption(X87))
| c_in(X84,c_Map_Odom(X85,X88,X87),X88) ),
inference(variable_rename,[status(thm)],[c_0_307]) ).
fof(c_0_598_599,plain,
! [X30,X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32),hAPP(c_Com_Ocom_OBODY,X30)),X31),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32),hAPP(c_Com_Ocom_OBODY,X30)),X31),X33,tc_Hoare__Mirabelle_Otriple(X34)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X30))),X31),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_308]) ).
fof(c_0_599_600,plain,
! [X28,X29,X30,X31,X32,X33,X34] :
( hAPP(c_Fun_Ofun__upd(X30,X32,hAPP(c_Option_Ooption_OSome(X34),X31),X33,tc_Option_Ooption(X34)),X29) != hAPP(c_Option_Ooption_OSome(X34),X28)
| hAPP(X30,X29) = hAPP(c_Option_Ooption_OSome(X34),X28)
| X31 = X28 ),
inference(variable_rename,[status(thm)],[c_0_309]) ).
fof(c_0_600_601,plain,
! [X28,X29,X30,X31,X32,X33,X34] :
( hAPP(c_Fun_Ofun__upd(X30,X32,hAPP(c_Option_Ooption_OSome(X34),X31),X33,tc_Option_Ooption(X34)),X29) != hAPP(c_Option_Ooption_OSome(X34),X28)
| hAPP(X30,X29) = hAPP(c_Option_Ooption_OSome(X34),X28)
| X29 = X32 ),
inference(variable_rename,[status(thm)],[c_0_310]) ).
fof(c_0_601_602,plain,
! [X42,X43,X44,X45,X46,X47] :
( X45 = X42
| hAPP(c_Fun_Ofun__upd(X44,X43,hAPP(c_Option_Ooption_OSome(X46),X45),X47,tc_Option_Ooption(X46)),X43) != hAPP(c_Option_Ooption_OSome(X46),X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_311])])]) ).
fof(c_0_602_603,plain,
! [X29,X30,X31,X32,X33,X34,X35] :
( c_Fun_Ofun__upd(X32,X33,hAPP(c_Option_Ooption_OSome(X34),X30),X35,tc_Option_Ooption(X34)) != c_Fun_Ofun__upd(X31,X33,hAPP(c_Option_Ooption_OSome(X34),X29),X35,tc_Option_Ooption(X34))
| X30 = X29 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_312])])]) ).
fof(c_0_603_604,plain,
! [X46,X47,X48,X49,X50,X51] :
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X48,X47,X46,X51,X50),X49,X51,X50)
| c_in(X46,c_Set_Oimage(X48,X49,X51,X50),X50)
| ~ c_Fun_Oinj__on(X48,X49,X51,X50) ),
inference(variable_rename,[status(thm)],[c_0_313]) ).
fof(c_0_604_605,plain,
! [X73,X74,X75,X76,X77,X78,X79] :
( c_Hoare__Mirabelle_Ohoare__derivs(X78,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X79),X77),c_Com_Ocom_OSemi(X74,X73)),X75),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X79),tc_bool)),tc_Hoare__Mirabelle_Otriple(X79)),X79)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X78,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X79),X76),X73),X75),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X79),tc_bool)),tc_Hoare__Mirabelle_Otriple(X79)),X79)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X78,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X79),X77),X74),X76),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X79),tc_bool)),tc_Hoare__Mirabelle_Otriple(X79)),X79) ),
inference(variable_rename,[status(thm)],[c_0_314]) ).
fof(c_0_605_606,plain,
! [X30,X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32),hAPP(c_Com_Ocom_OBODY,X30)),X31),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X32),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X30))),X31),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_315]) ).
fof(c_0_606_607,plain,
! [X46,X47,X48,X49,X50,X51] :
( c_Set_Oimage(c_Fun_Ofun__upd(X48,X47,X46,X50,X51),X49,X50,X51) = c_Set_Oimage(X48,X49,X50,X51)
| c_in(X47,X49,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_316])])]) ).
fof(c_0_607_608,plain,
! [X27,X28,X29,X30,X31] :
( c_Map_Odom(c_Fun_Ofun__upd(X29,X28,X27,X31,tc_Option_Ooption(X30)),X31,X30) = c_Set_Oinsert(X28,c_Map_Odom(X29,X31,X30),X31)
| X27 = c_Option_Ooption_ONone(X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_317])])]) ).
fof(c_0_608_609,plain,
! [X27,X28,X29,X30] :
( c_Map_Odom(X28,X30,X29) != c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool)),X30)
| X28 = c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X29),tc_Option_Ooption(X29),X30),X27,hAPP(c_Option_Ooption_OSome(X29),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X28,X27,X30,X29)),X30,tc_Option_Ooption(X29)) ),
inference(variable_rename,[status(thm)],[c_0_318]) ).
fof(c_0_609_610,plain,
! [X30,X31,X32] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X32),X30),X31),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X32),X30),X31),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X30),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(variable_rename,[status(thm)],[c_0_319]) ).
fof(c_0_610_611,plain,
! [X28,X29,X30,X31,X32,X33,X34] :
( hAPP(X30,X29) != hAPP(c_Option_Ooption_OSome(X34),X28)
| X29 = X32
| hAPP(c_Fun_Ofun__upd(X30,X32,hAPP(c_Option_Ooption_OSome(X34),X31),X33,tc_Option_Ooption(X34)),X29) = hAPP(c_Option_Ooption_OSome(X34),X28) ),
inference(variable_rename,[status(thm)],[c_0_320]) ).
fof(c_0_611_612,plain,
! [X51,X52,X53,X54,X55,X56] :
( hAPP(c_Fun_Ofun__upd(X54,X53,X52,X55,X56),X51) = hAPP(X54,X51)
| X51 = X53 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_321])])]) ).
fof(c_0_612_613,plain,
! [X51,X52,X53,X54,X55,X56] :
( hAPP(c_Fun_Ofun__upd(X54,X53,X52,X56,X55),X51) = hAPP(X54,X51)
| X51 = X53 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_322])])]) ).
fof(c_0_613_614,plain,
! [X52,X53,X54,X55,X56] :
( c_lessequals(X54,X53,tc_fun(X56,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X52,X54,X56,X55),c_Set_Oimage(X52,X53,X56,X55),tc_fun(X55,tc_bool))
| ~ c_Fun_Oinj__on(X52,c_Orderings_Otop__class_Otop(tc_fun(X56,tc_bool)),X56,X55) ),
inference(variable_rename,[status(thm)],[c_0_323]) ).
fof(c_0_614_615,plain,
! [X27,X28,X29,X30,X31] :
( c_Fun_Ofun__upd(X29,X28,X27,X31,X30) != X29
| hAPP(X29,X28) = X27 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_324])])]) ).
fof(c_0_615_616,plain,
! [X16,X17] :
( c_Hoare__Mirabelle_Ohoare__derivs(X17,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X16)),X17,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X16))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(variable_rename,[status(thm)],[c_0_325]) ).
fof(c_0_616_617,plain,
! [X34,X35,X36,X37,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X35),X34))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X35),X34))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X37,X36)),X35),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_326])])]) ).
fof(c_0_617_618,plain,
! [X59,X60,X61,X62] :
( c_Fun_Oinj__on(X59,c_Map_Odom(X59,X62,X61),X62,tc_Option_Ooption(X61))
| ~ c_Fun_Oinj__on(c_Map_Omap__add(X60,X59,X62,X61),c_Map_Odom(X59,X62,X61),X62,tc_Option_Ooption(X61)) ),
inference(variable_rename,[status(thm)],[c_0_327]) ).
fof(c_0_618_619,plain,
! [X34,X35,X36,X37,X38] :
( ~ hBOOL(hAPP(X38,X35))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X37),X35),X34))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X37,X36)),X35),X34)) ),
inference(variable_rename,[status(thm)],[c_0_328]) ).
fof(c_0_619_620,plain,
! [X52,X53,X54,X55,X56] :
( c_lessequals(c_Set_Oimage(X52,X54,X56,X55),c_Set_Oimage(X52,X53,X56,X55),tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X56,tc_bool))
| ~ c_Fun_Oinj__on(X52,c_Orderings_Otop__class_Otop(tc_fun(X56,tc_bool)),X56,X55) ),
inference(variable_rename,[status(thm)],[c_0_329]) ).
fof(c_0_620_621,plain,
! [X34,X35,X36,X37,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X35),X34))
| hBOOL(hAPP(X38,X35))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X37,X36)),X35),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_330])])]) ).
fof(c_0_621_622,plain,
! [X46,X47,X48] :
( c_Set_Oimage(X46,X47,X48,X48) = X47
| ~ c_Fun_Oinj__on(X46,X47,X48,X48)
| ~ c_lessequals(c_Set_Oimage(X46,X47,X48,X48),X47,tc_fun(X48,tc_bool))
| ~ c_Finite__Set_Ofinite(X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_331]) ).
fof(c_0_622_623,plain,
! [X23,X24,X25] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X25)),X24),X23))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X25))),X24),X23)) ),
inference(variable_rename,[status(thm)],[c_0_332]) ).
fof(c_0_623_624,plain,
! [X46,X47,X48,X49,X50] :
( c_in(X47,X48,X50)
| ~ c_in(hAPP(X46,X47),c_Set_Oimage(X46,X48,X50,X49),X49)
| ~ c_Fun_Oinj__on(X46,c_Orderings_Otop__class_Otop(tc_fun(X50,tc_bool)),X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_333]) ).
fof(c_0_624_625,plain,
! [X59,X60,X61,X62] :
( c_Fun_Oinj__on(c_Map_Omap__add(X60,X59,X62,X61),c_Map_Odom(X59,X62,X61),X62,tc_Option_Ooption(X61))
| ~ c_Fun_Oinj__on(X59,c_Map_Odom(X59,X62,X61),X62,tc_Option_Ooption(X61)) ),
inference(variable_rename,[status(thm)],[c_0_334]) ).
fof(c_0_625_626,plain,
! [X52,X53,X54,X55,X56] :
( c_Set_Oimage(X52,X54,X56,X55) != c_Set_Oimage(X52,X53,X56,X55)
| ~ c_Fun_Oinj__on(X52,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X56,tc_bool)),X56,X55)
| X54 = X53 ),
inference(variable_rename,[status(thm)],[c_0_335]) ).
fof(c_0_626_627,plain,
! [X30,X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X31),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X33),hAPP(c_Com_Ocom_OBODY,X30)),X32),X34)
| ~ c_Hoare__Mirabelle_Otriple__valid(X31,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X33),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X30))),X32),X34) ),
inference(variable_rename,[status(thm)],[c_0_336]) ).
fof(c_0_627_628,plain,
! [X36,X37,X38,X39,X40] :
( hAPP(X37,X38) != hAPP(c_Option_Ooption_OSome(X40),X36)
| c_Fun_Ofun__upd(X37,X38,hAPP(c_Option_Ooption_OSome(X40),X36),X39,tc_Option_Ooption(X40)) = X37 ),
inference(variable_rename,[status(thm)],[c_0_337]) ).
fof(c_0_628_629,plain,
! [X52,X53,X54,X55,X56] :
( c_Set_Oimage(X52,X54,X56,X55) != c_Set_Oimage(X52,X53,X56,X55)
| ~ c_Fun_Oinj__on(X52,c_Orderings_Otop__class_Otop(tc_fun(X56,tc_bool)),X56,X55)
| X54 = X53 ),
inference(variable_rename,[status(thm)],[c_0_338]) ).
fof(c_0_629_630,plain,
! [X29,X30,X31,X32] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X32)),X30,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X32,X31,X30,X29),X29)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X32),X30,X31,X29) ),
inference(variable_rename,[status(thm)],[c_0_339]) ).
fof(c_0_630_631,plain,
! [X46,X47,X48,X49] :
( c_Finite__Set_Ofinite(X47,X48)
| ~ c_Fun_Oinj__on(X46,X47,X48,X49)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X46,X47,X48,X49),X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_340])])]) ).
fof(c_0_631_632,plain,
! [X30,X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Otriple__valid(X31,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X33),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X30))),X32),X34)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X31),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X34),X33),hAPP(c_Com_Ocom_OBODY,X30)),X32),X34) ),
inference(variable_rename,[status(thm)],[c_0_341]) ).
fof(c_0_632_633,plain,
! [X46,X47,X48,X49,X50] :
( ~ c_lessequals(X46,X48,tc_fun(X49,tc_bool))
| c_lessequals(c_Set_Oimage(X47,X46,X49,X50),c_Set_Oimage(X47,X48,X49,X50),tc_fun(X50,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_342])])]) ).
fof(c_0_633_634,plain,
! [X52,X53,X54,X55,X56] :
( c_lessequals(c_Set_Oimage(X52,X54,X56,X55),c_Set_Oimage(X52,X53,X56,X55),tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X56,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_343]) ).
fof(c_0_634_635,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X24))),X23),X22))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X24)),X23),X22)) ),
inference(variable_rename,[status(thm)],[c_0_344]) ).
fof(c_0_635_636,plain,
! [X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X37,X36,X35)),X34),X33))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X36),X34),X33))
| ~ hBOOL(hAPP(X37,X34)) ),
inference(variable_rename,[status(thm)],[c_0_345]) ).
fof(c_0_636_637,plain,
! [X46,X47,X48] :
( c_Fun_Oinj__on(X46,X47,X48,X48)
| ~ c_lessequals(X47,c_Set_Oimage(X46,X47,X48,X48),tc_fun(X48,tc_bool))
| ~ c_Finite__Set_Ofinite(X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_346]) ).
fof(c_0_637_638,plain,
! [X33,X34,X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X37,X36,X35)),X34),X33))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X35),X34),X33))
| hBOOL(hAPP(X37,X34)) ),
inference(variable_rename,[status(thm)],[c_0_347]) ).
fof(c_0_638_639,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X76,X75),X73,X74,X71)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X76,X75),X72,X74,X71)
| ~ c_Natural_Oevaln(X75,X73,X74,X72)
| ~ hBOOL(hAPP(X76,X73)) ),
inference(variable_rename,[status(thm)],[c_0_348]) ).
fof(c_0_639_640,plain,
! [X46,X47,X48,X49,X50] :
( c_in(hAPP(X46,X47),c_Set_Oimage(X46,X48,X50,X49),X49)
| ~ c_in(X47,X48,X50)
| ~ c_Fun_Oinj__on(X46,c_Orderings_Otop__class_Otop(tc_fun(X50,tc_bool)),X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_349]) ).
fof(c_0_640_641,plain,
! [X24,X25] :
( c_Hoare__Mirabelle_Ohoare__derivs(X25,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X24),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X24)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X25,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X25))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_350]) ).
fof(c_0_641_642,plain,
! [X52,X53,X54,X55,X56,X57] :
( c_in(hAPP(X53,X52),X54,X57)
| ~ c_in(X52,X55,X56)
| ~ c_lessequals(c_Set_Oimage(X53,X55,X56,X57),X54,tc_fun(X57,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_351]) ).
fof(c_0_642_643,plain,
! [X34,X35,X36,X37,X38,X39] :
( c_Natural_Oevaln(X37,X35,X36,X34)
| c_Natural_Oevaln(X38,X35,X36,X34)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X39,X38,X37),X35,X36,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_352])])]) ).
fof(c_0_643_644,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X76,X75),X73,X74,X71)
| ~ c_Natural_Oevaln(X75,X72,X74,X71)
| ~ c_Natural_Oevaln(X76,X73,X74,X72) ),
inference(variable_rename,[status(thm)],[c_0_353]) ).
fof(c_0_644_645,plain,
! [X71,X72,X73,X74,X75] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X75,X74)),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X75,X74)),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X74),X73),X72))
| ~ hBOOL(hAPP(X75,X73)) ),
inference(variable_rename,[status(thm)],[c_0_354]) ).
fof(c_0_645_646,plain,
! [X67,X68,X69,X70,X71,X72,X73] :
( hBOOL(hAPP(hAPP(X72,X71),X67))
| ~ c_Natural_Oevaln(X70,X68,X69,X67)
| ~ hBOOL(hAPP(hAPP(X73,X71),X68))
| ~ c_Hoare__Mirabelle_Otriple__valid(X69,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X73),X70),X72),t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_355])])]) ).
fof(c_0_646_647,plain,
! [X52,X53,X54,X55,X56] :
( c_Finite__Set_Ofinite(X53,X55)
| ~ c_lessequals(X53,c_Set_Oimage(X52,X54,X56,X55),tc_fun(X55,tc_bool))
| ~ c_Finite__Set_Ofinite(X54,X56) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_356])])]) ).
fof(c_0_647_648,plain,
! [X29,X30,X31,X32] :
( X31 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X32,X31,X30,X29))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X32),X30,X31,X29) ),
inference(variable_rename,[status(thm)],[c_0_357]) ).
fof(c_0_648_649,plain,
! [X46,X47,X48,X49,X50] :
( c_Set_Oinsert(hAPP(X47,X46),c_Set_Oimage(X47,X48,X50,X49),X49) = c_Set_Oimage(X47,X48,X50,X49)
| ~ c_in(X46,X48,X50) ),
inference(variable_rename,[status(thm)],[c_0_358]) ).
fof(c_0_649_650,plain,
! [X36,X37,X38,X39,X40,X41] :
( hAPP(c_Map_Omap__add(X38,X37,X40,X41),X39) != hAPP(c_Option_Ooption_OSome(X41),X36)
| hAPP(X38,X39) = hAPP(c_Option_Ooption_OSome(X41),X36)
| hAPP(X37,X39) = hAPP(c_Option_Ooption_OSome(X41),X36) ),
inference(variable_rename,[status(thm)],[c_0_359]) ).
fof(c_0_650_651,plain,
! [X36,X37,X38,X39,X40,X41] :
( hAPP(c_Map_Omap__add(X38,X37,X40,X41),X39) != hAPP(c_Option_Ooption_OSome(X41),X36)
| hAPP(X37,X39) = c_Option_Ooption_ONone(X41)
| hAPP(X37,X39) = hAPP(c_Option_Ooption_OSome(X41),X36) ),
inference(variable_rename,[status(thm)],[c_0_360]) ).
fof(c_0_651_652,plain,
! [X52,X53,X54,X55,X56] :
( c_Fun_Oinj__on(X52,X53,X56,X55)
| ~ c_Fun_Oinj__on(X52,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X56,tc_bool)),X56,X55) ),
inference(variable_rename,[status(thm)],[c_0_361]) ).
fof(c_0_652_653,plain,
! [X52,X53,X54,X55,X56] :
( c_Fun_Oinj__on(X52,X54,X56,X55)
| ~ c_Fun_Oinj__on(X52,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X56,tc_bool)),X56,X55) ),
inference(variable_rename,[status(thm)],[c_0_362]) ).
fof(c_0_653_654,plain,
! [X34,X35,X36,X37,X38,X39] :
( ~ hBOOL(hAPP(X39,X35))
| c_Natural_Oevaln(X38,X35,X36,X34)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X39,X38,X37),X35,X36,X34) ),
inference(variable_rename,[status(thm)],[c_0_363]) ).
fof(c_0_654_655,plain,
! [X68,X69,X70,X71,X72] :
( c_Set_Oinsert(X71,c_Set_Oinsert(X70,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72) != c_Set_Oinsert(X69,c_Set_Oinsert(X68,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72)
| X71 = X68
| X71 = X69 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_364])])]) ).
fof(c_0_655_656,plain,
! [X68,X69,X70,X71,X72] :
( c_Set_Oinsert(X71,c_Set_Oinsert(X70,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72) != c_Set_Oinsert(X69,c_Set_Oinsert(X68,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72)
| X70 = X69
| X71 = X69 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_365])])]) ).
fof(c_0_656_657,plain,
! [X68,X69,X70,X71,X72] :
( c_Set_Oinsert(X71,c_Set_Oinsert(X70,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72) != c_Set_Oinsert(X69,c_Set_Oinsert(X68,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72)
| X71 = X68
| X70 = X68 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_366])])]) ).
fof(c_0_657_658,plain,
! [X68,X69,X70,X71,X72] :
( c_Set_Oinsert(X71,c_Set_Oinsert(X70,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72) != c_Set_Oinsert(X69,c_Set_Oinsert(X68,c_Orderings_Obot__class_Obot(tc_fun(X72,tc_bool)),X72),X72)
| X70 = X69
| X70 = X68 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_367])])]) ).
fof(c_0_658_659,plain,
! [X34,X35,X36,X37,X38,X39] :
( c_Natural_Oevaln(X37,X35,X36,X34)
| hBOOL(hAPP(X39,X35))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X39,X38,X37),X35,X36,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_368])])]) ).
fof(c_0_659_660,plain,
! [X36,X37,X38,X39,X40] :
( hAPP(c_Map_Omap__add(X37,X36,X39,X40),X38) != c_Option_Ooption_ONone(X40)
| hAPP(X37,X38) = c_Option_Ooption_ONone(X40) ),
inference(variable_rename,[status(thm)],[c_0_369]) ).
fof(c_0_660_661,plain,
! [X36,X37,X38,X39,X40] :
( hAPP(c_Map_Omap__add(X37,X36,X39,X40),X38) != c_Option_Ooption_ONone(X40)
| hAPP(X36,X38) = c_Option_Ooption_ONone(X40) ),
inference(variable_rename,[status(thm)],[c_0_370]) ).
fof(c_0_661_662,plain,
! [X46,X47,X48,X49,X50] :
( c_Fun_Oinj__on(X46,X48,X50,X49)
| ~ c_Fun_Oinj__on(X46,c_Set_Oinsert(X47,X48,X50),X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_371]) ).
fof(c_0_662_663,plain,
! [X33,X34,X35,X36,X37,X38] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X37,X36),X34,X35,X33)
| ~ c_Natural_Oevaln(X37,X34,X35,X33)
| ~ hBOOL(hAPP(X38,X34)) ),
inference(variable_rename,[status(thm)],[c_0_372]) ).
fof(c_0_663_664,plain,
! [X29,X30,X31,X32] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X31),X30,c_Suc(X32),X29)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X31)),X30,X32,X29) ),
inference(variable_rename,[status(thm)],[c_0_373]) ).
fof(c_0_664_665,plain,
! [X28,X29,X30,X31] :
( hAPP(X28,X29) = hAPP(c_Option_Ooption_OSome(X30),c_Map_Osko__Map__XdomD__1__1(X29,X28,X31,X30))
| ~ c_in(X29,c_Map_Odom(X28,X31,X30),X31) ),
inference(variable_rename,[status(thm)],[c_0_374]) ).
fof(c_0_665_666,plain,
! [X48,X49,X50,X51,X52] :
( hAPP(c_Map_Omap__add(X50,X49,X52,X51),X48) = hAPP(X49,X48)
| ~ c_in(X48,c_Map_Odom(X49,X52,X51),X52) ),
inference(variable_rename,[status(thm)],[c_0_375]) ).
fof(c_0_666_667,plain,
! [X33,X34,X35,X36,X37,X38] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X37,X36),X34,X35,X33)
| ~ c_Natural_Oevaln(X36,X34,X35,X33)
| hBOOL(hAPP(X38,X34)) ),
inference(variable_rename,[status(thm)],[c_0_376]) ).
fof(c_0_667_668,plain,
! [X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(X32,X31,tc_Hoare__Mirabelle_Otriple(X34)),X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X33,X31,X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_377]) ).
fof(c_0_668_669,plain,
! [X52,X53,X54,X55,X56] :
( c_Fun_Oinj__on(X52,X54,X56,X55)
| ~ c_lessequals(X54,X53,tc_fun(X56,tc_bool))
| ~ c_Fun_Oinj__on(X52,X53,X56,X55) ),
inference(variable_rename,[status(thm)],[c_0_378]) ).
fof(c_0_669_670,plain,
! [X48,X49,X50,X51,X52] :
( hAPP(c_Map_Omap__add(X50,X49,X52,X51),X48) = hAPP(X49,X48)
| c_in(X48,c_Map_Odom(X50,X52,X51),X52) ),
inference(variable_rename,[status(thm)],[c_0_379]) ).
fof(c_0_670_671,plain,
! [X48,X49,X50,X51,X52] :
( hAPP(c_Map_Omap__add(X50,X49,X52,X51),X48) = hAPP(X50,X48)
| c_in(X48,c_Map_Odom(X49,X52,X51),X52) ),
inference(variable_rename,[status(thm)],[c_0_380]) ).
fof(c_0_671_672,plain,
! [X46,X47,X48,X49,X50] :
( ~ c_in(X46,X48,X49)
| c_in(hAPP(X47,X46),c_Set_Oimage(X47,X48,X49,X50),X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_381])])]) ).
fof(c_0_672_673,plain,
! [X46,X47,X48,X49,X50] :
( ~ c_in(X46,X48,X49)
| c_in(hAPP(X47,X46),c_Set_Oimage(X47,X48,X49,X50),X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_382])])]) ).
fof(c_0_673_674,plain,
! [X46,X47,X48,X49,X50] :
( c_in(hAPP(X47,X46),c_Set_Oimage(X47,X48,X49,X50),X50)
| ~ c_in(X46,X48,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_383])])]) ).
fof(c_0_674_675,plain,
! [X46,X47,X48,X49,X50] :
( c_in(hAPP(X47,X46),c_Set_Oimage(X47,X48,X50,X49),X49)
| ~ c_in(X46,X48,X50) ),
inference(variable_rename,[status(thm)],[c_0_384]) ).
fof(c_0_675_676,plain,
! [X19,X20,X21] :
( ~ hBOOL(hAPP(X20,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X21),X19),X20,X21)))
| hBOOL(hAPP(X20,X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_385])])]) ).
fof(c_0_676_677,plain,
! [X71,X72,X73,X74,X75] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X75,X74)),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_386]) ).
fof(c_0_677_678,plain,
! [X66,X67,X68,X69] :
( c_Natural_Oevaln(X69,X67,c_Suc(X68),X66)
| ~ c_Natural_Oevaln(X69,X67,X68,X66) ),
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_678_679,plain,
! [X52,X53,X54,X55,X56] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X55,X54,tc_fun(X56,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X53,X52,tc_fun(X56,tc_bool)),tc_fun(X56,tc_bool))
| ~ c_lessequals(X54,X52,tc_fun(X56,tc_bool))
| ~ c_lessequals(X55,X53,tc_fun(X56,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_388]) ).
fof(c_0_679_680,plain,
! [X36,X37,X38,X39,X40,X41] :
( hAPP(X38,X39) != hAPP(c_Option_Ooption_OSome(X41),X36)
| hAPP(X37,X39) != c_Option_Ooption_ONone(X41)
| hAPP(c_Map_Omap__add(X38,X37,X40,X41),X39) = hAPP(c_Option_Ooption_OSome(X41),X36) ),
inference(variable_rename,[status(thm)],[c_0_389]) ).
fof(c_0_680_681,plain,
! [X46,X47,X48,X49,X50,X51] :
( hAPP(X48,X47) != hAPP(X48,X46)
| ~ c_in(X46,X49,X51)
| ~ c_in(X47,X49,X51)
| X47 = X46
| ~ c_Fun_Oinj__on(X48,X49,X51,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_390])])]) ).
fof(c_0_681_682,plain,
! [X46,X47,X48,X49,X50,X51] :
( hAPP(X48,X47) != hAPP(X48,X46)
| ~ c_in(X46,X49,X51)
| ~ c_in(X47,X49,X51)
| ~ c_Fun_Oinj__on(X48,X49,X51,X50)
| X47 = X46 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_391])])]) ).
fof(c_0_682_683,plain,
! [X46,X47,X48,X49,X50,X51] :
( hAPP(X48,X47) != hAPP(X48,X46)
| ~ c_in(X46,X49,X51)
| ~ c_in(X47,X49,X51)
| ~ c_Fun_Oinj__on(X48,X49,X51,X50)
| X47 = X46 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_392])])]) ).
fof(c_0_683_684,plain,
! [X46,X47,X48,X49,X50,X51] :
( hAPP(X48,X47) != hAPP(X48,X46)
| ~ c_Fun_Oinj__on(X48,X49,X51,X50)
| X47 = X46
| ~ c_in(X46,X49,X51)
| ~ c_in(X47,X49,X51) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_393])])]) ).
fof(c_0_684_685,plain,
! [X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X34),tc_bool)),tc_Hoare__Mirabelle_Otriple(X34)),X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(X32,X31,tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_394]) ).
fof(c_0_685_686,plain,
! [X46,X47,X48] :
( X47 = c_Set_Oinsert(X46,c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool)),X48)
| X47 = c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool))
| ~ c_lessequals(X47,c_Set_Oinsert(X46,c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool)),X48),tc_fun(X48,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_395]) ).
fof(c_0_686_687,plain,
! [X52,X53,X54,X55] :
( hBOOL(hAPP(X53,X52))
| hBOOL(hAPP(X54,X52))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_396])])]) ).
fof(c_0_687_688,plain,
! [X37,X38,X39,X40,X41,X42] :
( hAPP(X38,X40) != hAPP(c_Option_Ooption_OSome(X42),X37)
| hAPP(c_Map_Omap__add(X39,X38,X41,X42),X40) = hAPP(c_Option_Ooption_OSome(X42),X37) ),
inference(variable_rename,[status(thm)],[c_0_397]) ).
fof(c_0_688_689,plain,
! [X36,X37,X38,X39,X40,X41] :
( hAPP(X37,X39) != hAPP(c_Option_Ooption_OSome(X41),X36)
| hAPP(c_Map_Omap__add(X38,X37,X40,X41),X39) = hAPP(c_Option_Ooption_OSome(X41),X36) ),
inference(variable_rename,[status(thm)],[c_0_398]) ).
fof(c_0_689_690,plain,
! [X36,X37,X38,X39,X40] :
( hAPP(X37,X38) != c_Option_Ooption_ONone(X40)
| hAPP(X36,X38) != c_Option_Ooption_ONone(X40)
| hAPP(c_Map_Omap__add(X37,X36,X39,X40),X38) = c_Option_Ooption_ONone(X40) ),
inference(variable_rename,[status(thm)],[c_0_399]) ).
fof(c_0_690_691,plain,
! [X46,X47,X48,X49,X50] :
( c_Set_Oimage(c_COMBK(X47,X49,X50),X48,X50,X49) = c_Set_Oinsert(X47,c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool)),X49)
| ~ c_in(X46,X48,X50) ),
inference(variable_rename,[status(thm)],[c_0_400]) ).
fof(c_0_691_692,plain,
! [X69,X70,X71,X72] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X69,X70,X72,X71),X71)
| ~ c_Finite__Set_Ofinite(X70,X72) ),
inference(variable_rename,[status(thm)],[c_0_401]) ).
fof(c_0_692_693,plain,
! [X31,X32,X33,X34] :
( hBOOL(hAPP(X34,X32))
| X31 = X32
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X34,X33)),X32),X31)) ),
inference(variable_rename,[status(thm)],[c_0_402]) ).
fof(c_0_693_694,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(X29,X28) != hAPP(X29,X27)
| ~ c_Fun_Oinj__on(X29,c_Orderings_Otop__class_Otop(tc_fun(X31,tc_bool)),X31,X30)
| X28 = X27 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_403])])]) ).
fof(c_0_694_695,plain,
! [X24,X25] :
( c_Hoare__Mirabelle_Ohoare__derivs(X25,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X24),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X24)
| c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X25),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_404]) ).
fof(c_0_695_696,plain,
! [X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X34),X32),X31))
| ~ c_Natural_Oevaln(X34,X32,X33,X31) ),
inference(variable_rename,[status(thm)],[c_0_405]) ).
fof(c_0_696_697,plain,
! [X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X34),X33),X32))
| ~ c_Natural_Oevaln(X34,X33,X31,X32) ),
inference(variable_rename,[status(thm)],[c_0_406]) ).
fof(c_0_697_698,plain,
! [X46,X47,X48,X49] :
( c_Set_Oimage(c_COMBK(X46,X49,X48),X47,X48,X49) = c_Set_Oinsert(X46,c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool)),X49)
| X47 = c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_407])])]) ).
fof(c_0_698_699,plain,
! [X52,X53,X54,X55] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(X53,X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X52,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_408]) ).
fof(c_0_699_700,plain,
! [X52,X53,X54,X55] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(X53,X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X52,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_700_701,plain,
! [X31,X32,X33,X34,X35] :
( hBOOL(hAPP(X35,X32))
| X31 = X32
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X35,X34),X32,X33,X31) ),
inference(variable_rename,[status(thm)],[c_0_410]) ).
fof(c_0_701_702,plain,
! [X46,X47,X48,X49] :
( c_Set_Oimage(X46,X47,X48,X49) != c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool))
| X47 = c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_411])])]) ).
fof(c_0_702_703,plain,
! [X46,X47,X48,X49] :
( c_Orderings_Obot__class_Obot(tc_fun(X49,tc_bool)) != c_Set_Oimage(X46,X47,X48,X49)
| X47 = c_Orderings_Obot__class_Obot(tc_fun(X48,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_412])])]) ).
fof(c_0_703_704,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_413]) ).
fof(c_0_704_705,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X53,X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_414]) ).
fof(c_0_705_706,plain,
! [X52,X53,X54,X55] :
( c_in(X52,X53,X55)
| c_in(X52,X54,X55)
| ~ c_in(X52,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X55) ),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_706_707,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| c_in(X52,X54,X55)
| ~ c_lessequals(X54,c_Set_Oinsert(X52,X53,X55),tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_416]) ).
fof(c_0_707_708,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,c_Set_Oinsert(X52,X53,X55),tc_fun(X55,tc_bool))
| c_in(X52,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_417]) ).
fof(c_0_708_709,plain,
! [X17,X18,X19] :
( X17 = X18
| ~ c_in(X17,c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19),X19) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_418])])]) ).
fof(c_0_709_710,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(X48,X47))
| X46 = X47
| ~ hBOOL(hAPP(c_Set_Oinsert(X46,X48,X49),X47)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_419])])]) ).
fof(c_0_710_711,plain,
! [X24] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X24),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X24)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_711_712,plain,
! [X50,X51,X52,X53] :
( c_lessequals(c_Set_Oinsert(X50,X52,X53),c_Set_Oinsert(X50,X51,X53),tc_fun(X53,tc_bool))
| ~ c_lessequals(X52,X51,tc_fun(X53,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_421]) ).
fof(c_0_712_713,plain,
! [X74,X75,X76,X77] :
( c_Option_Omap(X75,X74,X76,X77) != c_Option_Ooption_ONone(X77)
| X74 = c_Option_Ooption_ONone(X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_422])])]) ).
fof(c_0_713_714,plain,
! [X52,X53,X54,X55] :
( c_lessequals(c_Set_Oinsert(X52,X54,X55),X53,tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| ~ c_in(X52,X53,X55) ),
inference(variable_rename,[status(thm)],[c_0_423]) ).
fof(c_0_714_715,plain,
! [X31,X32,X33] :
( X31 = X32
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X32,X33,X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_424])])]) ).
fof(c_0_715_716,plain,
! [X52,X53,X54,X55] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52))
| ~ hBOOL(hAPP(X53,X52)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_425])])]) ).
fof(c_0_716_717,plain,
! [X52,X53,X54,X55] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X52))
| ~ hBOOL(hAPP(X54,X52)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_426])])]) ).
fof(c_0_717_718,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X52,X54,X55),X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_427]) ).
fof(c_0_718_719,plain,
! [X65,X66,X67,X68,X69,X70,X71] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X71),X68),X70),X66) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X71),X67),X69),X65)
| X68 = X67 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_428])])]) ).
fof(c_0_719_720,plain,
! [X65,X66,X67,X68,X69,X70,X71] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X71),X68),X70),X66) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X71),X67),X69),X65)
| X70 = X69 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_429])])]) ).
fof(c_0_720_721,plain,
! [X65,X66,X67,X68,X69,X70,X71] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X71),X68),X70),X66) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X71),X67),X69),X65)
| X66 = X65 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_430])])]) ).
fof(c_0_721_722,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,c_Set_Oinsert(X52,X53,X55),tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| c_in(X52,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_431]) ).
fof(c_0_722_723,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,c_Set_Oinsert(X52,X53,X55),tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| c_in(X52,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_432]) ).
fof(c_0_723_724,plain,
! [X52,X53,X54,X55] :
( c_in(X52,X53,X55)
| ~ c_lessequals(c_Set_Oinsert(X52,X54,X55),X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_724_725,plain,
! [X24,X25,X26] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X26,X25)),X24),X24))
| hBOOL(hAPP(X26,X24)) ),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_725_726,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X17,X20)
| ~ c_lessequals(X18,X17,X20)
| ~ c_lessequals(X19,X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_726_727,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Oupper__semilattice(X54)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X52,X51,X54),X53,X54)
| ~ c_lessequals(X51,X53,X54)
| ~ c_lessequals(X52,X53,X54) ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_727_728,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Oupper__semilattice(X54)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54),X51,X54)
| ~ c_lessequals(X52,X51,X54)
| ~ c_lessequals(X53,X51,X54) ),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_728_729,plain,
! [X72,X73,X74,X75] :
( X72 = X73
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X74),X72))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X74),X73)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_438])])]) ).
fof(c_0_729_730,plain,
! [X17,X18,X19] :
( c_Set_Oinsert(X18,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19) != c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),X19)
| X18 = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_439])])]) ).
fof(c_0_730_731,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Oupper__semilattice(X54)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54),X51,X54) = c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X52,X51,X54),X54) ),
inference(variable_rename,[status(thm)],[c_0_440]) ).
fof(c_0_731_732,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Oupper__semilattice(X54)
| c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X52,X51,X54),X54) = c_Lattices_Oupper__semilattice__class_Osup(X52,c_Lattices_Oupper__semilattice__class_Osup(X53,X51,X54),X54) ),
inference(variable_rename,[status(thm)],[c_0_441]) ).
fof(c_0_732_733,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Olattice(X54)
| c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X52,X51,X54),X54) = c_Lattices_Oupper__semilattice__class_Osup(X52,c_Lattices_Oupper__semilattice__class_Osup(X53,X51,X54),X54) ),
inference(variable_rename,[status(thm)],[c_0_442]) ).
fof(c_0_733_734,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Olattice(X54)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54),X51,X54) = c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X52,X51,X54),X54) ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_734_735,plain,
! [X31,X32,X33,X34] :
( c_Hoare__Mirabelle_Ohoare__derivs(X33,X31,X34)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X33,c_Set_Oinsert(X32,X31,tc_Hoare__Mirabelle_Otriple(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_444]) ).
fof(c_0_735_736,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(X53,X52,tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_736_737,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Oupper__semilattice(X54)
| c_lessequals(X52,X51,X54)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54),X51,X54) ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_737_738,plain,
! [X51,X52,X53,X54] :
( ~ class_Lattices_Oupper__semilattice(X54)
| c_lessequals(X53,X51,X54)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54),X51,X54) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_738_739,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_lessequals(X18,X17,X20)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_739_740,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_lessequals(X19,X17,X20)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_449]) ).
fof(c_0_740_741,plain,
! [X46,X47,X48,X49] :
( c_in(X47,X48,X49)
| X47 = X46
| ~ c_in(X47,c_Set_Oinsert(X46,X48,X49),X49) ),
inference(variable_rename,[status(thm)],[c_0_450]) ).
fof(c_0_741_742,plain,
! [X52,X53,X54,X55] :
( c_lessequals(X54,c_Set_Oinsert(X52,X53,X55),tc_fun(X55,tc_bool))
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_451]) ).
fof(c_0_742_743,plain,
! [X29,X30,X31,X32] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X32,X31),X29,X30,X29)
| hBOOL(hAPP(X32,X29)) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_743_744,plain,
! [X52,X53,X54,X55] :
( c_in(X52,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X55)
| ~ c_in(X52,X53,X55) ),
inference(variable_rename,[status(thm)],[c_0_453]) ).
fof(c_0_744_745,plain,
! [X52,X53,X54,X55] :
( c_in(X52,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,tc_fun(X55,tc_bool)),X55)
| ~ c_in(X52,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_454]) ).
fof(c_0_745_746,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(c_Set_Oinsert(X46,X48,X49),X47))
| ~ hBOOL(hAPP(X48,X47)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_455])])]) ).
fof(c_0_746_747,plain,
! [X52,X53,X54,X55] :
( c_Set_Oinsert(X52,X54,X55) != c_Set_Oinsert(X52,X53,X55)
| c_in(X52,X53,X55)
| c_in(X52,X54,X55)
| X54 = X53 ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_747_748,plain,
! [X28,X29,X30,X31] :
( hAPP(X28,X29) != c_Option_Ooption_ONone(X30)
| ~ c_in(X29,c_Map_Odom(X28,X31,X30),X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_457])])]) ).
fof(c_0_748_749,plain,
! [X35,X36,X37,X38] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,X36,X38)
| ~ c_lessequals(X36,X35,tc_fun(tc_Hoare__Mirabelle_Otriple(X38),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X37,X35,X38) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_749_750,plain,
! [X15,X16,X17,X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(X17,X15,X18)
| ~ c_lessequals(X16,X17,tc_fun(tc_Hoare__Mirabelle_Otriple(X18),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_750_751,plain,
! [X18,X19,X20] :
( c_Finite__Set_Ofinite(X19,X20)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,tc_fun(X20,tc_bool)),X20) ),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_751_752,plain,
! [X18,X19,X20] :
( c_Finite__Set_Ofinite(X18,X20)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,tc_fun(X20,tc_bool)),X20) ),
inference(variable_rename,[status(thm)],[c_0_461]) ).
fof(c_0_752_753,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(X29,X28) != hAPP(c_Option_Ooption_OSome(X31),X27)
| c_Set_Oinsert(X28,c_Map_Odom(X29,X30,X31),X30) = c_Map_Odom(X29,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_462]) ).
fof(c_0_753_754,plain,
! [X52,X53,X54,X55] :
( c_in(X52,X53,X55)
| ~ c_in(X52,X54,X55)
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_463]) ).
fof(c_0_754_755,plain,
! [X52,X53,X54,X55] :
( c_in(X52,X53,X55)
| ~ c_in(X52,X54,X55)
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_755_756,plain,
! [X52,X53,X54,X55] :
( c_in(X52,X53,X55)
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool))
| ~ c_in(X52,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_756_757,plain,
! [X52,X53,X54,X55] :
( c_in(X52,X53,X55)
| ~ c_in(X52,X54,X55)
| ~ c_lessequals(X54,X53,tc_fun(X55,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_757_758,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_lessequals(X17,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X20)
| ~ c_lessequals(X17,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_758_759,plain,
! [X17,X18,X19,X20] :
( ~ class_Lattices_Oupper__semilattice(X20)
| c_lessequals(X17,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X20),X20)
| ~ c_lessequals(X17,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_759_760,plain,
! [X52,X53,X54,X55] :
( c_in(X53,c_Set_Oinsert(X52,X54,X55),X55)
| ~ c_in(X53,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_469]) ).
fof(c_0_760_761,plain,
! [X46,X47,X48,X49] :
( c_in(X47,c_Set_Oinsert(X46,X48,X49),X49)
| ~ c_in(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_761_762,plain,
! [X52,X53,X54] :
( X53 = X52
| ~ c_lessequals(X52,X53,tc_fun(X54,tc_bool))
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_471])])]) ).
fof(c_0_762_763,plain,
! [X52,X53,X54] :
( X53 = X52
| ~ c_lessequals(X52,X53,tc_fun(X54,tc_bool))
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_472])])]) ).
fof(c_0_763_764,plain,
! [X70,X71,X72,X73,X74] :
( ~ class_HOL_Oord(X73)
| c_lessequals(hAPP(X72,X70),hAPP(X71,X70),X73)
| ~ c_lessequals(X72,X71,tc_fun(X74,X73)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_473])])]) ).
fof(c_0_764_765,plain,
! [X51,X52,X53,X54] :
( ~ class_Orderings_Oorder(X54)
| c_lessequals(X51,X53,X54)
| ~ c_lessequals(X51,X52,X54)
| ~ c_lessequals(X52,X53,X54) ),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_765_766,plain,
! [X51,X52,X53,X54] :
( ~ class_Orderings_Opreorder(X54)
| c_lessequals(X53,X51,X54)
| ~ c_lessequals(X52,X51,X54)
| ~ c_lessequals(X53,X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_766_767,plain,
! [X46,X47] :
( X46 = c_Orderings_Obot__class_Obot(tc_fun(X47,tc_bool))
| ~ c_lessequals(X46,c_Orderings_Obot__class_Obot(tc_fun(X47,tc_bool)),tc_fun(X47,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_476]) ).
fof(c_0_767_768,plain,
! [X15,X16,X17,X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(X17,X15,X18)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X17,X16,X18)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_768_769,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27),X27) = c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_769_770,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Olattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27),X27) = c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_770_771,plain,
! [X19,X20,X21] :
( ~ hBOOL(hAPP(X20,X19))
| ~ c_in(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_480])])]) ).
fof(c_0_771_772,plain,
! [X28,X29,X30,X31,X32] :
( hAPP(X28,X30) != hAPP(c_Option_Ooption_OSome(X32),X29)
| c_in(X30,c_Map_Odom(X28,X31,X32),X31) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_772_773,plain,
! [X18,X19,X20] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,tc_fun(X20,tc_bool)),X20)
| ~ c_Finite__Set_Ofinite(X18,X20)
| ~ c_Finite__Set_Ofinite(X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_773_774,plain,
! [X18,X19,X20] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,tc_fun(X20,tc_bool)),X20)
| ~ c_Finite__Set_Ofinite(X18,X20)
| ~ c_Finite__Set_Ofinite(X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_774_775,plain,
! [X46,X47,X48] :
( c_Finite__Set_Ofinite(X47,X48)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X46,X47,X48),X48) ),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_775_776,plain,
! [X19,X20,X21] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X21))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X20,X21,X19)) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_776_777,plain,
! [X52,X53,X54] :
( c_Lattices_Oupper__semilattice__class_Osup(X53,X52,tc_fun(X54,tc_bool)) != X52
| c_lessequals(X53,X52,tc_fun(X54,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_777_778,plain,
! [X52,X53,X54] :
( c_Lattices_Oupper__semilattice__class_Osup(X53,X52,tc_fun(X54,tc_bool)) = X52
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_778_779,plain,
! [X52,X53,X54] :
( c_Lattices_Oupper__semilattice__class_Osup(X53,X52,tc_fun(X54,tc_bool)) = X53
| ~ c_lessequals(X52,X53,tc_fun(X54,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_779_780,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X31,X30))
| ~ hBOOL(hAPP(X32,X30))
| ~ c_lessequals(X32,X31,tc_fun(X33,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_489])])]) ).
fof(c_0_780_781,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X31,X30))
| ~ c_lessequals(X32,X31,tc_fun(X33,tc_bool))
| ~ hBOOL(hAPP(X32,X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_490])])]) ).
fof(c_0_781_782,plain,
! [X19,X20,X21] :
( hBOOL(hAPP(X20,X19))
| ~ c_in(X19,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_491])])]) ).
fof(c_0_782_783,plain,
! [X15,X16,X17] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X17)
| ~ c_lessequals(X15,X16,tc_fun(tc_Hoare__Mirabelle_Otriple(X17),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_783_784,plain,
! [X27,X28,X29] :
( c_Map_Odom(X27,X29,X28) != c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))
| X27 = c_COMBK(c_Option_Ooption_ONone(X28),tc_Option_Ooption(X28),X29) ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_784_785,plain,
! [X52,X53,X54] :
( c_Lattices_Oupper__semilattice__class_Osup(X53,X52,tc_fun(X54,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X54,tc_bool))
| X52 = c_Orderings_Obot__class_Obot(tc_fun(X54,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_785_786,plain,
! [X52,X53,X54] :
( c_Lattices_Oupper__semilattice__class_Osup(X53,X52,tc_fun(X54,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X54,tc_bool))
| X53 = c_Orderings_Obot__class_Obot(tc_fun(X54,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_786_787,plain,
! [X10,X11,X12] :
( c_Set_Oinsert(X11,X10,X12) != c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))
| c_in(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_787_788,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| X26 = X25
| ~ c_lessequals(X25,X26,X27)
| ~ c_lessequals(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_788_789,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| X26 = X25
| ~ c_lessequals(X25,X26,X27)
| ~ c_lessequals(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_789_790,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Oorder(X27)
| X26 = X25
| ~ c_lessequals(X26,X25,X27)
| ~ c_lessequals(X25,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_790_791,plain,
! [X28,X29,X30,X31] :
( c_in(X29,c_Map_Odom(X28,X31,X30),X31)
| hAPP(X28,X29) = c_Option_Ooption_ONone(X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_500])])]) ).
fof(c_0_791_792,plain,
! [X34,X35,X36] :
( c_Com_OWT(X35)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X36,X35,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_501])])]) ).
fof(c_0_792_793,plain,
! [X34,X35,X36] :
( c_Com_OWT(X34)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X36,X35,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_502])])]) ).
fof(c_0_793_794,plain,
! [X24,X25,X26] :
( c_Com_OWT(X24)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X26,X25,X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_503])])]) ).
fof(c_0_794_795,plain,
! [X61,X62,X63,X64,X65,X66] :
( c_Com_Ocom_OCall(X62,X64,X66) != c_Com_Ocom_OCall(X61,X63,X65)
| X66 = X65 ),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_795_796,plain,
! [X61,X62,X63,X64,X65,X66] :
( c_Com_Ocom_OCall(X62,X64,X66) != c_Com_Ocom_OCall(X61,X63,X65)
| X64 = X63 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_505])])]) ).
fof(c_0_796_797,plain,
! [X61,X62,X63,X64,X65,X66] :
( c_Com_Ocom_OCall(X62,X64,X66) != c_Com_Ocom_OCall(X61,X63,X65)
| X62 = X61 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_506])])]) ).
fof(c_0_797_798,plain,
! [X80,X81,X82,X83,X84,X85] :
( c_Com_Ocom_OCond(X81,X85,X83) != c_Com_Ocom_OCond(X80,X84,X82)
| X83 = X82 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_507])])]) ).
fof(c_0_798_799,plain,
! [X80,X81,X82,X83,X84,X85] :
( c_Com_Ocom_OCond(X81,X85,X83) != c_Com_Ocom_OCond(X80,X84,X82)
| X85 = X84 ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_799_800,plain,
! [X80,X81,X82,X83,X84,X85] :
( c_Com_Ocom_OCond(X81,X85,X83) != c_Com_Ocom_OCond(X80,X84,X82)
| X81 = X80 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_509])])]) ).
fof(c_0_800_801,plain,
! [X58,X59,X60,X61,X62,X63] :
( c_Com_Ocom_OLocal(X59,X61,X63) != c_Com_Ocom_OLocal(X58,X60,X62)
| X63 = X62 ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_801_802,plain,
! [X58,X59,X60,X61,X62,X63] :
( c_Com_Ocom_OLocal(X59,X61,X63) != c_Com_Ocom_OLocal(X58,X60,X62)
| X61 = X60 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_511])])]) ).
fof(c_0_802_803,plain,
! [X58,X59,X60,X61,X62,X63] :
( c_Com_Ocom_OLocal(X59,X61,X63) != c_Com_Ocom_OLocal(X58,X60,X62)
| X59 = X58 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_512])])]) ).
fof(c_0_803_804,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X6),X5),X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_513])])]) ).
fof(c_0_804_805,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_lessequals(X26,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_805_806,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_lessequals(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_806_807,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Olattice(X27)
| c_lessequals(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_807_808,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Olattice(X27)
| c_lessequals(X26,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_808_809,plain,
! [X52,X53,X54] :
( c_Finite__Set_Ofinite(X53,X54)
| ~ c_Finite__Set_Ofinite(X52,X54)
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_809_810,plain,
! [X52,X53,X54] :
( c_Finite__Set_Ofinite(X53,X54)
| ~ c_lessequals(X53,X52,tc_fun(X54,tc_bool))
| ~ c_Finite__Set_Ofinite(X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_810_811,plain,
! [X16,X17,X18] :
( c_Com_OWT(c_Com_Ocom_OCall(X18,X16,X17))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_520])])]) ).
fof(c_0_811_812,plain,
! [X31,X32] :
( X31 = X32
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X32),X31)) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_812_813,plain,
! [X31,X32,X33] :
( c_Hoare__Mirabelle_Otriple__valid(X32,X31,X33)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X32),X31,X33) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_813_814,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) != X25
| c_lessequals(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_814_815,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) = X26
| ~ c_lessequals(X25,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_815_816,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) = X25
| ~ c_lessequals(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_816_817,plain,
! [X46,X47,X48] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X46,X47,X48),X48)
| ~ c_Finite__Set_Ofinite(X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_817_818,plain,
! [X46,X47,X48] :
( c_Set_Oinsert(X46,X47,X48) = X47
| ~ c_in(X46,X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_818_819,plain,
! [X15,X16,X17] :
( c_Hoare__Mirabelle_Ohoare__valids(X16,X15,X17)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_819_820,plain,
! [X33,X34,X35] :
( c_Com_OWT(c_Com_Ocom_OCond(X35,X34,X33))
| ~ c_Com_OWT(X33)
| ~ c_Com_OWT(X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_529])])]) ).
fof(c_0_820_821,plain,
! [X24,X25,X26] :
( c_Com_OWT(c_Com_Ocom_OLocal(X26,X25,X24))
| ~ c_Com_OWT(X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_530])])]) ).
fof(c_0_821_822,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Olinorder(X27)
| c_lessequals(X25,X26,X27)
| c_lessequals(X26,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_822_823,plain,
! [X87,X88,X89] :
( hBOOL(hAPP(X88,X87))
| ~ c_in(X87,X88,X89) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_532])])]) ).
fof(c_0_823_824,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Oupper__semilattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) = c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_824_825,plain,
! [X25,X26,X27] :
( ~ class_Lattices_Olattice(X27)
| c_Lattices_Oupper__semilattice__class_Osup(X26,X25,X27) = c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_825_826,plain,
! [X52,X53,X54] :
( ~ class_Lattices_Obounded__lattice(X54)
| c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54) != c_Orderings_Obot__class_Obot(X54)
| X53 = c_Orderings_Obot__class_Obot(X54) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_826_827,plain,
! [X52,X53,X54] :
( ~ class_Lattices_Obounded__lattice(X54)
| c_Lattices_Oupper__semilattice__class_Osup(X53,X52,X54) != c_Orderings_Obot__class_Obot(X54)
| X52 = c_Orderings_Obot__class_Obot(X54) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_827_828,plain,
! [X87,X88,X89] :
( c_in(X87,X88,X89)
| ~ hBOOL(hAPP(X88,X87)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_537])])]) ).
fof(c_0_828_829,plain,
! [X19] :
( hAPP(c_Com_Obody,X19) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X19))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X19)) ),
inference(variable_rename,[status(thm)],[c_0_538]) ).
fof(c_0_829_830,plain,
! [X4] :
( ~ class_Finite__Set_Ofinite_Ofinite(X4)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_830_831,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Orderings_Otop__class_Otop(X11),X11) = c_Orderings_Otop__class_Otop(X11) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_831_832,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X11),X10,X11) = c_Orderings_Otop__class_Otop(X11) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_832_833,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Orderings_Obot__class_Obot(X11),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_833_834,plain,
! [X10,X11] :
( ~ class_Lattices_Obounded__lattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X11),X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_834_835,plain,
! [X10,X11] :
( ~ class_Orderings_Obot(X11)
| c_lessequals(c_Orderings_Obot__class_Obot(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_835_836,plain,
! [X10,X11] :
( ~ class_Orderings_Otop(X11)
| c_lessequals(X10,c_Orderings_Otop__class_Otop(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_836_837,plain,
! [X12,X13,X14] :
( hAPP(c_Option_Ooption_OSome(X14),X13) != hAPP(c_Option_Ooption_OSome(X14),X12)
| X13 = X12 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_546])])]) ).
fof(c_0_837_838,plain,
! [X10,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X10,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_838_839,plain,
! [X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_lessequals(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_839_840,plain,
! [X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_lessequals(X10,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_840_841,plain,
! [X34,X35] :
( c_Com_OWT(X35)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X35,X34)) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_841_842,plain,
! [X34,X35] :
( c_Com_OWT(X34)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X35,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_551])])]) ).
fof(c_0_842_843,plain,
! [X24,X25] :
( c_Com_OWT(X24)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X25,X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_552])])]) ).
fof(c_0_843_844,plain,
! [X17,X18] :
( hAPP(c_Com_Obody,X17) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X18)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X18) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_844_845,plain,
! [X80,X81,X82,X83] :
( c_Com_Ocom_OSemi(X83,X81) != c_Com_Ocom_OSemi(X82,X80)
| X81 = X80 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_554])])]) ).
fof(c_0_845_846,plain,
! [X80,X81,X82,X83] :
( c_Com_Ocom_OSemi(X83,X81) != c_Com_Ocom_OSemi(X82,X80)
| X83 = X82 ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_846_847,plain,
! [X58,X59,X60,X61] :
( c_Com_Ocom_OWhile(X59,X61) != c_Com_Ocom_OWhile(X58,X60)
| X59 = X58 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_556])])]) ).
fof(c_0_847_848,plain,
! [X58,X59,X60,X61] :
( c_Com_Ocom_OWhile(X59,X61) != c_Com_Ocom_OWhile(X58,X60)
| X61 = X60 ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_848_849,plain,
! [X61,X62,X63,X64] :
( c_Com_Ocom_OAss(X62,X64) != c_Com_Ocom_OAss(X61,X63)
| X64 = X63 ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_849_850,plain,
! [X61,X62,X63,X64] :
( c_Com_Ocom_OAss(X62,X64) != c_Com_Ocom_OAss(X61,X63)
| X62 = X61 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_559])])]) ).
fof(c_0_850_851,plain,
! [X33,X34] :
( c_Com_OWT(c_Com_Ocom_OSemi(X34,X33))
| ~ c_Com_OWT(X33)
| ~ c_Com_OWT(X34) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_851_852,plain,
! [X6,X7] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X6,X7))
| ~ class_Finite__Set_Ofinite_Ofinite(X7)
| ~ class_Finite__Set_Ofinite_Ofinite(X6) ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_852_853,plain,
! [X16] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X16))
| hAPP(c_Com_Obody,X16) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_853_854,plain,
! [X8,X9] :
( hAPP(c_Com_Ocom_OBODY,X9) != hAPP(c_Com_Ocom_OBODY,X8)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_854_855,plain,
! [X24,X25] :
( c_Com_OWT(c_Com_Ocom_OWhile(X25,X24))
| ~ c_Com_OWT(X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_564])])]) ).
fof(c_0_855_856,plain,
! [X6,X7] :
( class_Lattices_Oupper__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_856_857,plain,
! [X6,X7] :
( class_Lattices_Obounded__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Obounded__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_857_858,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_858_859,plain,
! [X6,X7] :
( class_Lattices_Olattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_859_860,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_860_861,plain,
! [X6,X7] :
( class_Orderings_Otop(tc_fun(X6,X7))
| ~ class_Orderings_Otop(X7) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_861_862,plain,
! [X6,X7] :
( class_Orderings_Obot(tc_fun(X6,X7))
| ~ class_Orderings_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_862_863,plain,
! [X6,X7] :
( class_HOL_Oord(tc_fun(X6,X7))
| ~ class_HOL_Oord(X7) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_863_864,plain,
! [X10,X11] :
( X10 = c_Option_Ooption_ONone(X11)
| ~ c_Option_Ois__none(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_864_865,plain,
! [X46,X47] :
( ~ class_Finite__Set_Ofinite_Ofinite(X47)
| c_Finite__Set_Ofinite(X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_865_866,plain,
! [X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_866_867,plain,
! [X25,X26] :
( c_Suc(X26) != c_Suc(X25)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_867_868,plain,
! [X76,X77] :
( c_Suc(X77) != c_Suc(X76)
| X77 = X76 ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_868_869,plain,
! [X31] :
( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X31) != X31
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_578])])]) ).
fof(c_0_869_870,plain,
! [X10,X11] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| X11 = X10 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_579])])]) ).
cnf(c_0_870_871,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X5,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_871_872,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_872_873,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_873_874,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_874_875,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_in(X6,X5,tc_Com_Opname) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_875_876,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname) ),
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_876_877,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X1,tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_586]) ).
cnf(c_0_877_878,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_878_879,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_588]) ).
cnf(c_0_879_880,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_589]) ).
cnf(c_0_880_881,plain,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_881_882,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X4,X1,X3,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5),X5)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_882_883,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_OSome(X5),X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X8)
| hAPP(X1,X8) != hAPP(c_Option_Ooption_OSome(X5),X7) ),
inference(split_conjunct,[status(thm)],[c_0_592]) ).
cnf(c_0_883_884,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7)
| hAPP(X1,X7) != c_Option_Ooption_ONone(X5) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_884_885,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(X1,X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_885_886,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_886_887,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_596]) ).
cnf(c_0_887_888,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| c_Map_Omap__add(c_Fun_Ofun__upd(X5,X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X2,X3,X4) = c_Fun_Ofun__upd(c_Map_Omap__add(X5,X2,X3,X4),X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_888_889,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),X5,tc_Hoare__Mirabelle_Otriple(X1)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_598]) ).
cnf(c_0_889_890,plain,
( X1 = X2
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_599]) ).
cnf(c_0_890_891,plain,
( X1 = X2
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_891_892,plain,
( X4 = X6
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6) ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_892_893,plain,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_893_894,plain,
( c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_603]) ).
cnf(c_0_894_895,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X6)),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X5),X6),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_895_896,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_896_897,plain,
( c_in(X1,X2,X3)
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_897_898,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = c_Set_Oinsert(X4,c_Map_Odom(X3,X5,X2),X5) ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_898_899,plain,
( X1 = c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X4,hAPP(c_Option_Ooption_OSome(X2),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X1,X4,X3,X2)),X3,tc_Option_Ooption(X2))
| c_Map_Odom(X1,X3,X2) != c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_899_900,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_900_901,plain,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_901_902,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_611]) ).
cnf(c_0_902_903,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_903_904,plain,
( c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_613]) ).
cnf(c_0_904_905,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_905_906,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(split_conjunct,[status(thm)],[c_0_615]) ).
cnf(c_0_906_907,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_616]) ).
cnf(c_0_907_908,plain,
( c_Fun_Oinj__on(X2,c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4))
| ~ c_Fun_Oinj__on(c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_908_909,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_618]) ).
cnf(c_0_909_910,plain,
( c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_619]) ).
cnf(c_0_910_911,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_911_912,plain,
( c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_621]) ).
cnf(c_0_912_913,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_913_914,plain,
( c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_623]) ).
cnf(c_0_914_915,plain,
( c_Fun_Oinj__on(c_Map_Omap__add(X4,X1,X2,X3),c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3))
| ~ c_Fun_Oinj__on(X1,c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_915_916,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_625]) ).
cnf(c_0_916_917,plain,
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_626]) ).
cnf(c_0_917_918,plain,
( c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_627]) ).
cnf(c_0_918_919,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_919_920,plain,
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4),X4)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_629]) ).
cnf(c_0_920_921,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_921_922,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_631]) ).
cnf(c_0_922_923,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_923_924,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_633]) ).
cnf(c_0_924_925,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_634]) ).
cnf(c_0_925_926,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_635]) ).
cnf(c_0_926_927,plain,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_927_928,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_928_929,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_929_930,plain,
( c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_639]) ).
cnf(c_0_930,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_931,plain,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_932,plain,
( c_Natural_Oevaln(X2,X4,X5,X6)
| c_Natural_Oevaln(X3,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_642]) ).
cnf(c_0_933,plain,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_643]) ).
cnf(c_0_934,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_644]) ).
cnf(c_0_935,plain,
( hBOOL(hAPP(hAPP(X4,X5),X7))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Natural_Oevaln(X3,X6,X1,X7) ),
inference(split_conjunct,[status(thm)],[c_0_645]) ).
cnf(c_0_936,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_646]) ).
cnf(c_0_937,plain,
( X3 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_647]) ).
cnf(c_0_938,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_648]) ).
cnf(c_0_939,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_649]) ).
cnf(c_0_940,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_650]) ).
cnf(c_0_941,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_651]) ).
cnf(c_0_942,plain,
( c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_652]) ).
cnf(c_0_943,plain,
( c_Natural_Oevaln(X2,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_653]) ).
cnf(c_0_944,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_654]) ).
cnf(c_0_945,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_946,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_947,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_948,plain,
( hBOOL(hAPP(X1,X4))
| c_Natural_Oevaln(X3,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_658]) ).
cnf(c_0_949,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_950,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_660]) ).
cnf(c_0_951,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_952,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_662]) ).
cnf(c_0_953,plain,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,c_Suc(X3),X4)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_663]) ).
cnf(c_0_954,plain,
( hAPP(X2,X1) = hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X1,X2,X3,X4))
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_664]) ).
cnf(c_0_955,plain,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1)
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_665]) ).
cnf(c_0_956,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_957,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_667]) ).
cnf(c_0_958,plain,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_668]) ).
cnf(c_0_959,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_669]) ).
cnf(c_0_960,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_670]) ).
cnf(c_0_961,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_962,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_672]) ).
cnf(c_0_963,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_673]) ).
cnf(c_0_964,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_674]) ).
cnf(c_0_965,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X3),X2),X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_675]) ).
cnf(c_0_966,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_676]) ).
cnf(c_0_967,plain,
( c_Natural_Oevaln(X1,X2,c_Suc(X3),X4)
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_968,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_678]) ).
cnf(c_0_969,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_970,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_680]) ).
cnf(c_0_971,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_681]) ).
cnf(c_0_972,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_682]) ).
cnf(c_0_973,plain,
( X1 = X4
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_683]) ).
cnf(c_0_974,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_684]) ).
cnf(c_0_975,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_685]) ).
cnf(c_0_976,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_686]) ).
cnf(c_0_977,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_687]) ).
cnf(c_0_978,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_979,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_689]) ).
cnf(c_0_980,plain,
( c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_690]) ).
cnf(c_0_981,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_691]) ).
cnf(c_0_982,plain,
( X4 = X3
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_692]) ).
cnf(c_0_983,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_693]) ).
cnf(c_0_984,plain,
( c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
inference(split_conjunct,[status(thm)],[c_0_694]) ).
cnf(c_0_985,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_695]) ).
cnf(c_0_986,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_696]) ).
cnf(c_0_987,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_697]) ).
cnf(c_0_988,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_698]) ).
cnf(c_0_989,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_699]) ).
cnf(c_0_990,plain,
( X5 = X3
| hBOOL(hAPP(X1,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_700]) ).
cnf(c_0_991,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_701]) ).
cnf(c_0_992,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Set_Oimage(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_702]) ).
cnf(c_0_993,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_703]) ).
cnf(c_0_994,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_704]) ).
cnf(c_0_995,plain,
( c_in(X1,X2,X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_705]) ).
cnf(c_0_996,plain,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_706]) ).
cnf(c_0_997,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_707]) ).
cnf(c_0_998,plain,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_708]) ).
cnf(c_0_999,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_1000,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_1001,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_711]) ).
cnf(c_0_1002,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Option_Omap(X3,X1,X2,X4) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_712]) ).
cnf(c_0_1003,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_713]) ).
cnf(c_0_1004,plain,
( X3 = X1
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_714]) ).
cnf(c_0_1005,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_715]) ).
cnf(c_0_1006,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_1007,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_717]) ).
cnf(c_0_1008,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7) ),
inference(split_conjunct,[status(thm)],[c_0_718]) ).
cnf(c_0_1009,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7) ),
inference(split_conjunct,[status(thm)],[c_0_719]) ).
cnf(c_0_1010,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2) ),
inference(split_conjunct,[status(thm)],[c_0_720]) ).
cnf(c_0_1011,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_721]) ).
cnf(c_0_1012,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_722]) ).
cnf(c_0_1013,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_723]) ).
cnf(c_0_1014,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_724]) ).
cnf(c_0_1015,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_725]) ).
cnf(c_0_1016,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_726]) ).
cnf(c_0_1017,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_727]) ).
cnf(c_0_1018,plain,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_728]) ).
cnf(c_0_1019,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_729]) ).
cnf(c_0_1020,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_730]) ).
cnf(c_0_1021,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1022,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1023,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_733]) ).
cnf(c_0_1024,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_734]) ).
cnf(c_0_1025,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_735]) ).
cnf(c_0_1026,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_736]) ).
cnf(c_0_1027,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_737]) ).
cnf(c_0_1028,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_738]) ).
cnf(c_0_1029,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1030,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_740]) ).
cnf(c_0_1031,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_741]) ).
cnf(c_0_1032,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_742]) ).
cnf(c_0_1033,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_743]) ).
cnf(c_0_1034,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_744]) ).
cnf(c_0_1035,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_745]) ).
cnf(c_0_1036,plain,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_746]) ).
cnf(c_0_1037,plain,
( ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_747]) ).
cnf(c_0_1038,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_748]) ).
cnf(c_0_1039,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X1,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_749]) ).
cnf(c_0_1040,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1041,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_751]) ).
cnf(c_0_1042,plain,
( c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4)
| hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_752]) ).
cnf(c_0_1043,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_753]) ).
cnf(c_0_1044,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_754]) ).
cnf(c_0_1045,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1046,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_756]) ).
cnf(c_0_1047,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1048,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_758]) ).
cnf(c_0_1049,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_759]) ).
cnf(c_0_1050,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1051,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_761]) ).
cnf(c_0_1052,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_762]) ).
cnf(c_0_1053,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1054,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_764]) ).
cnf(c_0_1055,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_765]) ).
cnf(c_0_1056,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_766]) ).
cnf(c_0_1057,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1058,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_768]) ).
cnf(c_0_1059,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_769]) ).
cnf(c_0_1060,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_770]) ).
cnf(c_0_1061,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_771]) ).
cnf(c_0_1062,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_772]) ).
cnf(c_0_1063,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1064,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1065,plain,
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X2))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_775]) ).
cnf(c_0_1066,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_776]) ).
cnf(c_0_1067,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_777]) ).
cnf(c_0_1068,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_778]) ).
cnf(c_0_1069,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_779]) ).
cnf(c_0_1070,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_780]) ).
cnf(c_0_1071,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_781]) ).
cnf(c_0_1072,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_782]) ).
cnf(c_0_1073,plain,
( X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3)
| c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_783]) ).
cnf(c_0_1074,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_784]) ).
cnf(c_0_1075,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1076,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1077,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_787]) ).
cnf(c_0_1078,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_788]) ).
cnf(c_0_1079,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_789]) ).
cnf(c_0_1080,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| c_in(X2,c_Map_Odom(X1,X4,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1081,plain,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_791]) ).
cnf(c_0_1082,plain,
( c_Com_OWT(X3)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_792]) ).
cnf(c_0_1083,plain,
( c_Com_OWT(X3)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_793]) ).
cnf(c_0_1084,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1085,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[c_0_795]) ).
cnf(c_0_1086,plain,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_796]) ).
cnf(c_0_1087,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1088,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[c_0_798]) ).
cnf(c_0_1089,plain,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1090,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1091,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[c_0_801]) ).
cnf(c_0_1092,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_802]) ).
cnf(c_0_1093,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_803]) ).
cnf(c_0_1094,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_804]) ).
cnf(c_0_1095,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1096,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1097,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_807]) ).
cnf(c_0_1098,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1099,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1100,plain,
( c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1101,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1102,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1103,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1104,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1105,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1106,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1107,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1108,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1109,plain,
( c_Com_OWT(c_Com_Ocom_OCond(X3,X1,X2))
| ~ c_Com_OWT(X1)
| ~ c_Com_OWT(X2) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1110,plain,
( c_Com_OWT(c_Com_Ocom_OLocal(X2,X3,X1))
| ~ c_Com_OWT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1111,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1112,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1113,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1114,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1115,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1116,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1117,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1118,plain,
( hAPP(c_Com_Obody,X1) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X1))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1119,plain,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_829]) ).
cnf(c_0_1120,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X2),X2) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_830]) ).
cnf(c_0_1121,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1122,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1123,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_833]) ).
cnf(c_0_1124,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1125,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1126,plain,
( X1 = X2
| hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1127,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1128,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1129,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1130,plain,
( c_Com_OWT(X1)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1131,plain,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1132,plain,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1133,plain,
( c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1134,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1135,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_845]) ).
cnf(c_0_1136,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1137,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1138,plain,
( X1 = X2
| c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1139,plain,
( X1 = X2
| c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1140,plain,
( c_Com_OWT(c_Com_Ocom_OSemi(X1,X2))
| ~ c_Com_OWT(X1)
| ~ c_Com_OWT(X2) ),
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1141,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1142,plain,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1143,plain,
( X1 = X2
| hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1144,plain,
( c_Com_OWT(c_Com_Ocom_OWhile(X2,X1))
| ~ c_Com_OWT(X1) ),
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1145,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1146,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1147,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1148,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1149,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1150,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1151,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1152,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1153,plain,
( X1 = c_Option_Ooption_ONone(X2)
| ~ c_Option_Ois__none(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1154,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1155,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1156,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1157,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1158,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1159,plain,
( X1 = X2
| c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1160,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X5,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
c_0_870,
[final] ).
cnf(c_0_1161,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
c_0_871,
[final] ).
cnf(c_0_1162,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
c_0_872,
[final] ).
cnf(c_0_1163,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
c_0_873,
[final] ).
cnf(c_0_1164,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_in(X6,X5,tc_Com_Opname) ),
c_0_874,
[final] ).
cnf(c_0_1165,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname) ),
c_0_875,
[final] ).
cnf(c_0_1166,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X1,tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
c_0_876,
[final] ).
cnf(c_0_1167,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
c_0_877,
[final] ).
cnf(c_0_1168,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
c_0_878,
[final] ).
cnf(c_0_1169,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b))) ),
c_0_879,
[final] ).
cnf(c_0_1170,plain,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
c_0_880,
[final] ).
cnf(c_0_1171,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X4,X1,X3,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5),X5)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3) ),
c_0_881,
[final] ).
cnf(c_0_1172,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_OSome(X5),X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X8)
| hAPP(X1,X8) != hAPP(c_Option_Ooption_OSome(X5),X7) ),
c_0_882,
[final] ).
cnf(c_0_1173,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7)
| hAPP(X1,X7) != c_Option_Ooption_ONone(X5) ),
c_0_883,
[final] ).
cnf(c_0_1174,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(X1,X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7) ),
c_0_884,
[final] ).
cnf(c_0_1175,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != c_Option_Ooption_ONone(X4) ),
c_0_885,
[final] ).
cnf(c_0_1176,plain,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != c_Option_Ooption_ONone(X4) ),
c_0_886,
[final] ).
cnf(c_0_1177,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| c_Fun_Ofun__upd(c_Map_Omap__add(X5,X2,X3,X4),X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)) = c_Map_Omap__add(c_Fun_Ofun__upd(X5,X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X2,X3,X4) ),
c_0_887,
[final] ).
cnf(c_0_1178,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),X5,tc_Hoare__Mirabelle_Otriple(X1)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1) ),
c_0_888,
[final] ).
cnf(c_0_1179,plain,
( X1 = X2
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
c_0_889,
[final] ).
cnf(c_0_1180,plain,
( X1 = X2
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
c_0_890,
[final] ).
cnf(c_0_1181,plain,
( X4 = X6
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6) ),
c_0_891,
[final] ).
cnf(c_0_1182,plain,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5)) ),
c_0_892,
[final] ).
cnf(c_0_1183,plain,
( c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_893,
[final] ).
cnf(c_0_1184,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X6)),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X5),X6),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
c_0_894,
[final] ).
cnf(c_0_1185,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
c_0_895,
[final] ).
cnf(c_0_1186,plain,
( c_in(X1,X2,X3)
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6) ),
c_0_896,
[final] ).
cnf(c_0_1187,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = c_Set_Oinsert(X4,c_Map_Odom(X3,X5,X2),X5) ),
c_0_897,
[final] ).
cnf(c_0_1188,plain,
( c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X4,hAPP(c_Option_Ooption_OSome(X2),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X1,X4,X3,X2)),X3,tc_Option_Ooption(X2)) = X1
| c_Map_Odom(X1,X3,X2) != c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
c_0_898,
[final] ).
cnf(c_0_1189,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
c_0_899,
[final] ).
cnf(c_0_1190,plain,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
c_0_900,
[final] ).
cnf(c_0_1191,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_901,
[final] ).
cnf(c_0_1192,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_902,
[final] ).
cnf(c_0_1193,plain,
( c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
c_0_903,
[final] ).
cnf(c_0_1194,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
c_0_904,
[final] ).
cnf(c_0_1195,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
c_0_905,
[final] ).
cnf(c_0_1196,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
c_0_906,
[final] ).
cnf(c_0_1197,plain,
( c_Fun_Oinj__on(X2,c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4))
| ~ c_Fun_Oinj__on(c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4)) ),
c_0_907,
[final] ).
cnf(c_0_1198,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_908,
[final] ).
cnf(c_0_1199,plain,
( c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
c_0_909,
[final] ).
cnf(c_0_1200,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
c_0_910,
[final] ).
cnf(c_0_1201,plain,
( c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
c_0_911,
[final] ).
cnf(c_0_1202,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
c_0_912,
[final] ).
cnf(c_0_1203,plain,
( c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
c_0_913,
[final] ).
cnf(c_0_1204,plain,
( c_Fun_Oinj__on(c_Map_Omap__add(X4,X1,X2,X3),c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3))
| ~ c_Fun_Oinj__on(X1,c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3)) ),
c_0_914,
[final] ).
cnf(c_0_1205,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
c_0_915,
[final] ).
cnf(c_0_1206,plain,
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2) ),
c_0_916,
[final] ).
cnf(c_0_1207,plain,
( c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
c_0_917,
[final] ).
cnf(c_0_1208,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
c_0_918,
[final] ).
cnf(c_0_1209,plain,
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4),X4)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4) ),
c_0_919,
[final] ).
cnf(c_0_1210,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_920,
[final] ).
cnf(c_0_1211,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2) ),
c_0_921,
[final] ).
cnf(c_0_1212,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
c_0_922,
[final] ).
cnf(c_0_1213,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_923,
[final] ).
cnf(c_0_1214,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
c_0_924,
[final] ).
cnf(c_0_1215,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
c_0_925,
[final] ).
cnf(c_0_1216,plain,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
c_0_926,
[final] ).
cnf(c_0_1217,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
c_0_927,
[final] ).
cnf(c_0_1218,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
c_0_928,
[final] ).
cnf(c_0_1219,plain,
( c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(X4,X5,X2) ),
c_0_929,
[final] ).
cnf(c_0_1220,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
c_0_930,
[final] ).
cnf(c_0_1221,plain,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
c_0_931,
[final] ).
cnf(c_0_1222,plain,
( c_Natural_Oevaln(X2,X4,X5,X6)
| c_Natural_Oevaln(X3,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
c_0_932,
[final] ).
cnf(c_0_1223,plain,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
c_0_933,
[final] ).
cnf(c_0_1224,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
c_0_934,
[final] ).
cnf(c_0_1225,plain,
( hBOOL(hAPP(hAPP(X4,X5),X7))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Natural_Oevaln(X3,X6,X1,X7) ),
c_0_935,
[final] ).
cnf(c_0_1226,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
c_0_936,
[final] ).
cnf(c_0_1227,plain,
( c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4)) = X3
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4) ),
c_0_937,
[final] ).
cnf(c_0_1228,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
c_0_938,
[final] ).
cnf(c_0_1229,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
c_0_939,
[final] ).
cnf(c_0_1230,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
c_0_940,
[final] ).
cnf(c_0_1231,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
c_0_941,
[final] ).
cnf(c_0_1232,plain,
( c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
c_0_942,
[final] ).
cnf(c_0_1233,plain,
( c_Natural_Oevaln(X2,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_943,
[final] ).
cnf(c_0_1234,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_944,
[final] ).
cnf(c_0_1235,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_945,
[final] ).
cnf(c_0_1236,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_946,
[final] ).
cnf(c_0_1237,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_947,
[final] ).
cnf(c_0_1238,plain,
( hBOOL(hAPP(X1,X4))
| c_Natural_Oevaln(X3,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
c_0_948,
[final] ).
cnf(c_0_1239,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
c_0_949,
[final] ).
cnf(c_0_1240,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
c_0_950,
[final] ).
cnf(c_0_1241,plain,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
c_0_951,
[final] ).
cnf(c_0_1242,plain,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
c_0_952,
[final] ).
cnf(c_0_1243,plain,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,c_Suc(X3),X4)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
c_0_953,
[final] ).
cnf(c_0_1244,plain,
( hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X1,X2,X3,X4)) = hAPP(X2,X1)
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
c_0_954,
[final] ).
cnf(c_0_1245,plain,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1)
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
c_0_955,
[final] ).
cnf(c_0_1246,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
c_0_956,
[final] ).
cnf(c_0_1247,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
c_0_957,
[final] ).
cnf(c_0_1248,plain,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
c_0_958,
[final] ).
cnf(c_0_1249,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1) ),
c_0_959,
[final] ).
cnf(c_0_1250,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1) ),
c_0_960,
[final] ).
cnf(c_0_1251,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
c_0_961,
[final] ).
cnf(c_0_1252,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
c_0_962,
[final] ).
cnf(c_0_1253,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
c_0_963,
[final] ).
cnf(c_0_1254,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
c_0_964,
[final] ).
cnf(c_0_1255,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X3),X2),X1,X3))) ),
c_0_965,
[final] ).
cnf(c_0_1256,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
c_0_966,
[final] ).
cnf(c_0_1257,plain,
( c_Natural_Oevaln(X1,X2,c_Suc(X3),X4)
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
c_0_967,
[final] ).
cnf(c_0_1258,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_968,
[final] ).
cnf(c_0_1259,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
c_0_969,
[final] ).
cnf(c_0_1260,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
c_0_970,
[final] ).
cnf(c_0_1261,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_971,
[final] ).
cnf(c_0_1262,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_972,
[final] ).
cnf(c_0_1263,plain,
( X1 = X4
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
c_0_973,
[final] ).
cnf(c_0_1264,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
c_0_974,
[final] ).
cnf(c_0_1265,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
c_0_975,
[final] ).
cnf(c_0_1266,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_976,
[final] ).
cnf(c_0_1267,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
c_0_977,
[final] ).
cnf(c_0_1268,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
c_0_978,
[final] ).
cnf(c_0_1269,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
c_0_979,
[final] ).
cnf(c_0_1270,plain,
( c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ c_in(X1,X2,X3) ),
c_0_980,
[final] ).
cnf(c_0_1271,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_981,
[final] ).
cnf(c_0_1272,plain,
( X4 = X3
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X4)) ),
c_0_982,
[final] ).
cnf(c_0_1273,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_983,
[final] ).
cnf(c_0_1274,plain,
( c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
c_0_984,
[final] ).
cnf(c_0_1275,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
c_0_985,
[final] ).
cnf(c_0_1276,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
c_0_986,
[final] ).
cnf(c_0_1277,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
c_0_987,
[final] ).
cnf(c_0_1278,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_988,
[final] ).
cnf(c_0_1279,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_989,
[final] ).
cnf(c_0_1280,plain,
( X5 = X3
| hBOOL(hAPP(X1,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X5) ),
c_0_990,
[final] ).
cnf(c_0_1281,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_991,
[final] ).
cnf(c_0_1282,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_992,
[final] ).
cnf(c_0_1283,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_993,
[final] ).
cnf(c_0_1284,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_994,
[final] ).
cnf(c_0_1285,plain,
( c_in(X1,X2,X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_995,
[final] ).
cnf(c_0_1286,plain,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_996,
[final] ).
cnf(c_0_1287,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
c_0_997,
[final] ).
cnf(c_0_1288,plain,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
c_0_998,
[final] ).
cnf(c_0_1289,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_999,
[final] ).
cnf(c_0_1290,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
c_0_1000,
[final] ).
cnf(c_0_1291,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1001,
[final] ).
cnf(c_0_1292,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Option_Omap(X3,X1,X2,X4) != c_Option_Ooption_ONone(X4) ),
c_0_1002,
[final] ).
cnf(c_0_1293,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1003,
[final] ).
cnf(c_0_1294,plain,
( X3 = X1
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3) ),
c_0_1004,
[final] ).
cnf(c_0_1295,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1005,
[final] ).
cnf(c_0_1296,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1006,
[final] ).
cnf(c_0_1297,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1007,
[final] ).
cnf(c_0_1298,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7) ),
c_0_1008,
[final] ).
cnf(c_0_1299,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7) ),
c_0_1009,
[final] ).
cnf(c_0_1300,plain,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2) ),
c_0_1010,
[final] ).
cnf(c_0_1301,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1011,
[final] ).
cnf(c_0_1302,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1012,
[final] ).
cnf(c_0_1303,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1013,
[final] ).
cnf(c_0_1304,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
c_0_1014,
[final] ).
cnf(c_0_1305,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1015,
[final] ).
cnf(c_0_1306,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1016,
[final] ).
cnf(c_0_1307,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1017,
[final] ).
cnf(c_0_1308,plain,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
c_0_1018,
[final] ).
cnf(c_0_1309,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
c_0_1019,
[final] ).
cnf(c_0_1310,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1020,
[final] ).
cnf(c_0_1311,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
c_0_1021,
[final] ).
cnf(c_0_1312,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1022,
[final] ).
cnf(c_0_1313,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1023,
[final] ).
cnf(c_0_1314,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
c_0_1024,
[final] ).
cnf(c_0_1315,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1025,
[final] ).
cnf(c_0_1316,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1026,
[final] ).
cnf(c_0_1317,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1027,
[final] ).
cnf(c_0_1318,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1028,
[final] ).
cnf(c_0_1319,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1029,
[final] ).
cnf(c_0_1320,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
c_0_1030,
[final] ).
cnf(c_0_1321,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1031,
[final] ).
cnf(c_0_1322,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
c_0_1032,
[final] ).
cnf(c_0_1323,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1033,
[final] ).
cnf(c_0_1324,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1034,
[final] ).
cnf(c_0_1325,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1035,
[final] ).
cnf(c_0_1326,plain,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
c_0_1036,
[final] ).
cnf(c_0_1327,plain,
( ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
c_0_1037,
[final] ).
cnf(c_0_1328,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
c_0_1038,
[final] ).
cnf(c_0_1329,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X1,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
c_0_1039,
[final] ).
cnf(c_0_1330,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1040,
[final] ).
cnf(c_0_1331,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1041,
[final] ).
cnf(c_0_1332,plain,
( c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4)
| hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
c_0_1042,
[final] ).
cnf(c_0_1333,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1043,
[final] ).
cnf(c_0_1334,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1044,
[final] ).
cnf(c_0_1335,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1045,
[final] ).
cnf(c_0_1336,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1046,
[final] ).
cnf(c_0_1337,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1047,
[final] ).
cnf(c_0_1338,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1048,
[final] ).
cnf(c_0_1339,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1049,
[final] ).
cnf(c_0_1340,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1050,
[final] ).
cnf(c_0_1341,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1051,
[final] ).
cnf(c_0_1342,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1052,
[final] ).
cnf(c_0_1343,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_1053,
[final] ).
cnf(c_0_1344,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1054,
[final] ).
cnf(c_0_1345,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1055,
[final] ).
cnf(c_0_1346,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
c_0_1056,
[final] ).
cnf(c_0_1347,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
c_0_1057,
[final] ).
cnf(c_0_1348,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1058,
[final] ).
cnf(c_0_1349,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1059,
[final] ).
cnf(c_0_1350,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
c_0_1060,
[final] ).
cnf(c_0_1351,plain,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
c_0_1061,
[final] ).
cnf(c_0_1352,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1062,
[final] ).
cnf(c_0_1353,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1063,
[final] ).
cnf(c_0_1354,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
c_0_1064,
[final] ).
cnf(c_0_1355,plain,
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X2))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3)) ),
c_0_1065,
[final] ).
cnf(c_0_1356,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
c_0_1066,
[final] ).
cnf(c_0_1357,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1067,
[final] ).
cnf(c_0_1358,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1068,
[final] ).
cnf(c_0_1359,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_1069,
[final] ).
cnf(c_0_1360,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_1070,
[final] ).
cnf(c_0_1361,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
c_0_1071,
[final] ).
cnf(c_0_1362,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
c_0_1072,
[final] ).
cnf(c_0_1363,plain,
( X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3)
| c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1073,
[final] ).
cnf(c_0_1364,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1074,
[final] ).
cnf(c_0_1365,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1075,
[final] ).
cnf(c_0_1366,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1076,
[final] ).
cnf(c_0_1367,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1077,
[final] ).
cnf(c_0_1368,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1078,
[final] ).
cnf(c_0_1369,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1079,
[final] ).
cnf(c_0_1370,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| c_in(X2,c_Map_Odom(X1,X4,X3),X4) ),
c_0_1080,
[final] ).
cnf(c_0_1371,plain,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3)) ),
c_0_1081,
[final] ).
cnf(c_0_1372,plain,
( c_Com_OWT(X3)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3)) ),
c_0_1082,
[final] ).
cnf(c_0_1373,plain,
( c_Com_OWT(X3)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X1,X2,X3)) ),
c_0_1083,
[final] ).
cnf(c_0_1374,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
c_0_1084,
[final] ).
cnf(c_0_1375,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
c_0_1085,
[final] ).
cnf(c_0_1376,plain,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
c_0_1086,
[final] ).
cnf(c_0_1377,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
c_0_1087,
[final] ).
cnf(c_0_1378,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
c_0_1088,
[final] ).
cnf(c_0_1379,plain,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
c_0_1089,
[final] ).
cnf(c_0_1380,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
c_0_1090,
[final] ).
cnf(c_0_1381,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
c_0_1091,
[final] ).
cnf(c_0_1382,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
c_0_1092,
[final] ).
cnf(c_0_1383,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_1093,
[final] ).
cnf(c_0_1384,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1094,
[final] ).
cnf(c_0_1385,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1095,
[final] ).
cnf(c_0_1386,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1096,
[final] ).
cnf(c_0_1387,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1097,
[final] ).
cnf(c_0_1388,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
c_0_1098,
[final] ).
cnf(c_0_1389,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_1099,
[final] ).
cnf(c_0_1390,plain,
( c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
c_0_1100,
[final] ).
cnf(c_0_1391,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
c_0_1101,
[final] ).
cnf(c_0_1392,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),X2,X3) ),
c_0_1102,
[final] ).
cnf(c_0_1393,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1103,
[final] ).
cnf(c_0_1394,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1104,
[final] ).
cnf(c_0_1395,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1105,
[final] ).
cnf(c_0_1396,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1106,
[final] ).
cnf(c_0_1397,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
c_0_1107,
[final] ).
cnf(c_0_1398,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
c_0_1108,
[final] ).
cnf(c_0_1399,plain,
( c_Com_OWT(c_Com_Ocom_OCond(X3,X1,X2))
| ~ c_Com_OWT(X1)
| ~ c_Com_OWT(X2) ),
c_0_1109,
[final] ).
cnf(c_0_1400,plain,
( c_Com_OWT(c_Com_Ocom_OLocal(X2,X3,X1))
| ~ c_Com_OWT(X1) ),
c_0_1110,
[final] ).
cnf(c_0_1401,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1111,
[final] ).
cnf(c_0_1402,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
c_0_1112,
[final] ).
cnf(c_0_1403,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1113,
[final] ).
cnf(c_0_1404,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1114,
[final] ).
cnf(c_0_1405,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1115,
[final] ).
cnf(c_0_1406,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1116,
[final] ).
cnf(c_0_1407,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1117,
[final] ).
cnf(c_0_1408,plain,
( hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X1)) = hAPP(c_Com_Obody,X1)
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
c_0_1118,
[final] ).
cnf(c_0_1409,plain,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
c_0_1119,
[final] ).
cnf(c_0_1410,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X2),X2) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1120,
[final] ).
cnf(c_0_1411,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1121,
[final] ).
cnf(c_0_1412,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_1122,
[final] ).
cnf(c_0_1413,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1123,
[final] ).
cnf(c_0_1414,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_1124,
[final] ).
cnf(c_0_1415,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
c_0_1125,
[final] ).
cnf(c_0_1416,plain,
( X1 = X2
| hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2) ),
c_0_1126,
[final] ).
cnf(c_0_1417,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_1127,
[final] ).
cnf(c_0_1418,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1128,
[final] ).
cnf(c_0_1419,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1129,
[final] ).
cnf(c_0_1420,plain,
( c_Com_OWT(X1)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
c_0_1130,
[final] ).
cnf(c_0_1421,plain,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
c_0_1131,
[final] ).
cnf(c_0_1422,plain,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X1,X2)) ),
c_0_1132,
[final] ).
cnf(c_0_1423,plain,
( c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
c_0_1133,
[final] ).
cnf(c_0_1424,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
c_0_1134,
[final] ).
cnf(c_0_1425,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
c_0_1135,
[final] ).
cnf(c_0_1426,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
c_0_1136,
[final] ).
cnf(c_0_1427,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
c_0_1137,
[final] ).
cnf(c_0_1428,plain,
( X1 = X2
| c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2) ),
c_0_1138,
[final] ).
cnf(c_0_1429,plain,
( X1 = X2
| c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4) ),
c_0_1139,
[final] ).
cnf(c_0_1430,plain,
( c_Com_OWT(c_Com_Ocom_OSemi(X1,X2))
| ~ c_Com_OWT(X1)
| ~ c_Com_OWT(X2) ),
c_0_1140,
[final] ).
cnf(c_0_1431,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1141,
[final] ).
cnf(c_0_1432,plain,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
c_0_1142,
[final] ).
cnf(c_0_1433,plain,
( X1 = X2
| hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
c_0_1143,
[final] ).
cnf(c_0_1434,plain,
( c_Com_OWT(c_Com_Ocom_OWhile(X2,X1))
| ~ c_Com_OWT(X1) ),
c_0_1144,
[final] ).
cnf(c_0_1435,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1145,
[final] ).
cnf(c_0_1436,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_1146,
[final] ).
cnf(c_0_1437,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1147,
[final] ).
cnf(c_0_1438,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1148,
[final] ).
cnf(c_0_1439,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1149,
[final] ).
cnf(c_0_1440,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
c_0_1150,
[final] ).
cnf(c_0_1441,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_1151,
[final] ).
cnf(c_0_1442,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_1152,
[final] ).
cnf(c_0_1443,plain,
( X1 = c_Option_Ooption_ONone(X2)
| ~ c_Option_Ois__none(X1,X2) ),
c_0_1153,
[final] ).
cnf(c_0_1444,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1154,
[final] ).
cnf(c_0_1445,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
c_0_1155,
[final] ).
cnf(c_0_1446,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1156,
[final] ).
cnf(c_0_1447,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1157,
[final] ).
cnf(c_0_1448,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) != X1 ),
c_0_1158,
[final] ).
cnf(c_0_1449,plain,
( X1 = X2
| c_Hoare__Mirabelle_Ostate__not__singleton ),
c_0_1159,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1160_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X5,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1160_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X5,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1160_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X5,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1160_3,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),hAPP(X5,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X3,X4,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1161_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1161_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1161_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1161_3,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X3,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X6,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Finite__Set_Ofinite(X1,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),X4,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),X7,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),X5,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),X1,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(X3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X7,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),hAPP(X6,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(X2,X4,X3,X5,X6,X7))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1162_0,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__valids(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__valids(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1163_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1163_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1164_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_in(X6,X5,tc_Com_Opname) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1164_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_in(X6,X5,tc_Com_Opname) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1164_2,axiom,
( ~ c_in(X6,X5,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2))),X4,tc_Com_Opname,tc_fun(X2,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X5,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1165_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1165_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1165_2,axiom,
( ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1166_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X1,tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_1,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X1,tc_Com_Ostate)
| ~ c_Com_OWT__bodies
| ~ c_lessequals(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_2,axiom,
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X1,tc_Com_Ostate)
| ~ c_lessequals(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_3,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X1,tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1167_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1167_1,axiom,
( ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1168_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1168_1,axiom,
( ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1169_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1169_1,axiom,
( ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1170_0,axiom,
( X1 = X2
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1170_1,axiom,
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X1,X4,X5,X6),X2,X7,X5,X6) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X3,X2,X7,X5,X6),X1,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1171_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X4,X1,X3,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5),X5)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1171]) ).
cnf(c_0_1171_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3)
| c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X4,X1,X3,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1171]) ).
cnf(c_0_1172_0,axiom,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_OSome(X5),X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X8)
| hAPP(X1,X8) != hAPP(c_Option_Ooption_OSome(X5),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_1,axiom,
( hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X8)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_OSome(X5),X7)
| hAPP(X1,X8) != hAPP(c_Option_Ooption_OSome(X5),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_2,axiom,
( hAPP(X1,X8) != hAPP(c_Option_Ooption_OSome(X5),X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X8)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(c_Option_Ooption_OSome(X5),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1173_0,axiom,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7)
| hAPP(X1,X7) != c_Option_Ooption_ONone(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1173_1,axiom,
( hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X1,X7) != c_Option_Ooption_ONone(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1173_2,axiom,
( hAPP(X1,X7) != c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1174_0,axiom,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(X1,X7)
| hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1174_1,axiom,
( hAPP(X2,X3) != hAPP(c_Option_Ooption_OSome(X4),X7)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = hAPP(X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1175_0,axiom,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1175_1,axiom,
( hAPP(X2,X3) != c_Option_Ooption_ONone(X4)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1176_0,axiom,
( c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5)
| hAPP(X2,X3) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1176_1,axiom,
( hAPP(X2,X3) != c_Option_Ooption_ONone(X4)
| c_Map_Omap__comp(X1,X2,X3,X4,X5,X6) = c_Option_Ooption_ONone(X5) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1177_0,axiom,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| c_Fun_Ofun__upd(c_Map_Omap__add(X5,X2,X3,X4),X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)) = c_Map_Omap__add(c_Fun_Ofun__upd(X5,X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1177_1,axiom,
( c_Fun_Ofun__upd(c_Map_Omap__add(X5,X2,X3,X4),X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)) = c_Map_Omap__add(c_Fun_Ofun__upd(X5,X1,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X2,X3,X4)
| c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1178_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),X5,tc_Hoare__Mirabelle_Otriple(X1)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1178_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),X5,tc_Hoare__Mirabelle_Otriple(X1)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool)),tc_Hoare__Mirabelle_Otriple(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1179_0,axiom,
( X1 = X2
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1179_1,axiom,
( hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1179_2,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1180_0,axiom,
( X1 = X2
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1180_1,axiom,
( hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1180_2,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1181_0,axiom,
( X4 = X6
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1181_1,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6)
| X4 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1182_0,axiom,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1182_1,axiom,
( c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1183_0,axiom,
( c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1183_1,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1183_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X6,X5,X3,X4),X2,X3,X4)
| c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1184_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X6)),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X5),X6),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1184_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X6)),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X5),X6),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1184_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X5),X6),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X6)),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1185_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1185_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1186_0,axiom,
( c_in(X1,X2,X3)
| c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1186_1,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X4,X1,X5,X3,X6),X2,X3,X6) = c_Set_Oimage(X4,X2,X3,X6)
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1187_0,axiom,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = c_Set_Oinsert(X4,c_Map_Odom(X3,X5,X2),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1187_1,axiom,
( c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = c_Set_Oinsert(X4,c_Map_Odom(X3,X5,X2),X5)
| X1 = c_Option_Ooption_ONone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1188_0,axiom,
( c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X4,hAPP(c_Option_Ooption_OSome(X2),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X1,X4,X3,X2)),X3,tc_Option_Ooption(X2)) = X1
| c_Map_Odom(X1,X3,X2) != c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1188_1,axiom,
( c_Map_Odom(X1,X3,X2) != c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X4,hAPP(c_Option_Ooption_OSome(X2),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(X1,X4,X3,X2)),X3,tc_Option_Ooption(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1189_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1189_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1189_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1190_0,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1190_1,axiom,
( X6 = X2
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1190_2,axiom,
( hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1191_0,axiom,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1191_1,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1192_0,axiom,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1192_1,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1193_0,axiom,
( c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1193_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1193_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1194_0,axiom,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1194_1,axiom,
( c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1195_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1195_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),X2,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1196_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1196_1,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1196_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1197_0,axiom,
( c_Fun_Oinj__on(X2,c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4))
| ~ c_Fun_Oinj__on(c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1197_1,axiom,
( ~ c_Fun_Oinj__on(c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4))
| c_Fun_Oinj__on(X2,c_Map_Odom(X2,X3,X4),X3,tc_Option_Ooption(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1198_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1198_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1198_2,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1199_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1199_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1199_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_lessequals(c_Set_Oimage(X1,X4,X2,X3),c_Set_Oimage(X1,X5,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1200_0,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1200_1,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1200_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3)),X4),X5))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X4),X5))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1201_0,axiom,
( c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1201_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1201_2,axiom,
( ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,X1,X2,X2) = X1
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1201_3,axiom,
( ~ c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_lessequals(c_Set_Oimage(X3,X1,X2,X2),X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Set_Oimage(X3,X1,X2,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1202_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1202_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1203_0,axiom,
( c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1203_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(X4,X5,X2)
| ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1203_2,axiom,
( ~ c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(X4,X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1204_0,axiom,
( c_Fun_Oinj__on(c_Map_Omap__add(X4,X1,X2,X3),c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3))
| ~ c_Fun_Oinj__on(X1,c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1204_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3))
| c_Fun_Oinj__on(c_Map_Omap__add(X4,X1,X2,X3),c_Map_Odom(X1,X2,X3),X2,tc_Option_Ooption(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1205_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1205_1,axiom,
( ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1205_2,axiom,
( c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5)
| ~ c_Fun_Oinj__on(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1206_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1206]) ).
cnf(c_0_1206_1,axiom,
( ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2)
| c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1206]) ).
cnf(c_0_1207_0,axiom,
( c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1207]) ).
cnf(c_0_1207_1,axiom,
( hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1207]) ).
cnf(c_0_1208_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1208_1,axiom,
( ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2
| c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1208_2,axiom,
( c_Set_Oimage(X3,X1,X4,X5) != c_Set_Oimage(X3,X2,X4,X5)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1209_0,axiom,
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4),X4)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1209]) ).
cnf(c_0_1209_1,axiom,
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1209]) ).
cnf(c_0_1210_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1210_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Finite__Set_Ofinite(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1210_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1211_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1211_1,axiom,
( ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5),X2)
| c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1212_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1212_1,axiom,
( ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1213_0,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1213_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1214_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1214_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1215_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1215_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1215_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1216_0,axiom,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1216_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1216_2,axiom,
( ~ c_lessequals(X1,c_Set_Oimage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1217_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1217_1,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1217_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1218_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_2,axiom,
( ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_3,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6)
| ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1219_0,axiom,
( c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| ~ c_in(X4,X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1219_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3)
| ~ c_in(X4,X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1219_2,axiom,
( ~ c_in(X4,X5,X2)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
| c_in(hAPP(X1,X4),c_Set_Oimage(X1,X5,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1220_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1220_1,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1220_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1220_3,axiom,
( ~ c_Com_OWT(X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1221_0,axiom,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_1,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_in(hAPP(X1,X6),X5,X4)
| ~ c_in(X6,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_2,axiom,
( ~ c_in(X6,X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_in(hAPP(X1,X6),X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1222_0,axiom,
( c_Natural_Oevaln(X2,X4,X5,X6)
| c_Natural_Oevaln(X3,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1222_1,axiom,
( c_Natural_Oevaln(X3,X4,X5,X6)
| c_Natural_Oevaln(X2,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1222_2,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| c_Natural_Oevaln(X3,X4,X5,X6)
| c_Natural_Oevaln(X2,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1223_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_1,axiom,
( ~ c_Natural_Oevaln(X1,X2,X3,X4)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
| ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_2,axiom,
( ~ c_Natural_Oevaln(X5,X4,X3,X6)
| ~ c_Natural_Oevaln(X1,X2,X3,X4)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1224_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1225_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),X7))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Natural_Oevaln(X3,X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_1,axiom,
( ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),t_a)
| hBOOL(hAPP(hAPP(X4,X5),X7))
| ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Natural_Oevaln(X3,X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),t_a)
| hBOOL(hAPP(hAPP(X4,X5),X7))
| ~ c_Natural_Oevaln(X3,X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_3,axiom,
( ~ c_Natural_Oevaln(X3,X6,X1,X7)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),t_a)
| hBOOL(hAPP(hAPP(X4,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1226_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1226_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1226_2,axiom,
( ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1227_0,axiom,
( c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4)) = X3
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1227]) ).
cnf(c_0_1227_1,axiom,
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X3,X4)
| c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1227]) ).
cnf(c_0_1228_0,axiom,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1228_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1229_0,axiom,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1229_1,axiom,
( hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1229_2,axiom,
( hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1230_0,axiom,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1230_1,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1230_2,axiom,
( hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1231_0,axiom,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1231_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| c_Fun_Oinj__on(X1,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1232_0,axiom,
( c_Fun_Oinj__on(X1,X2,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1232_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
| c_Fun_Oinj__on(X1,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1233_0,axiom,
( c_Natural_Oevaln(X2,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1233_1,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| c_Natural_Oevaln(X2,X4,X5,X6)
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1233_2,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| c_Natural_Oevaln(X2,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1234_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1234_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1234_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1235_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1235]) ).
cnf(c_0_1235_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1235]) ).
cnf(c_0_1235_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1235]) ).
cnf(c_0_1236_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1236_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1236_2,axiom,
( c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1237_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1237_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1237_2,axiom,
( c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1238_0,axiom,
( hBOOL(hAPP(X1,X4))
| c_Natural_Oevaln(X3,X4,X5,X6)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1238_1,axiom,
( c_Natural_Oevaln(X3,X4,X5,X6)
| hBOOL(hAPP(X1,X4))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1238_2,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)
| c_Natural_Oevaln(X3,X4,X5,X6)
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1239_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1239_1,axiom,
( hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1240_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1240_1,axiom,
( hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1241_0,axiom,
( c_Fun_Oinj__on(X1,X3,X4,X5)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1241_1,axiom,
( ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| c_Fun_Oinj__on(X1,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1242_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1242_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1242_2,axiom,
( ~ c_Natural_Oevaln(X3,X2,X4,X5)
| ~ hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1243_0,axiom,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,c_Suc(X3),X4)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1243_1,axiom,
( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4)
| c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,c_Suc(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1244_0,axiom,
( hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X1,X2,X3,X4)) = hAPP(X2,X1)
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1244]) ).
cnf(c_0_1244_1,axiom,
( ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X1,X2,X3,X4)) = hAPP(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1244]) ).
cnf(c_0_1245_0,axiom,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1)
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1245_1,axiom,
( ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1246_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1246_1,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| hBOOL(hAPP(X1,X2))
| ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1246_2,axiom,
( ~ c_Natural_Oevaln(X3,X2,X4,X5)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1247_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1247_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1247_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1248_0,axiom,
( c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1248_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,X5,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1248_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1249_0,axiom,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1249_1,axiom,
( hAPP(c_Map_Omap__add(X2,X5,X3,X4),X1) = hAPP(X5,X1)
| c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1250_0,axiom,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1250]) ).
cnf(c_0_1250_1,axiom,
( hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X5,X1)
| c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1250]) ).
cnf(c_0_1251_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1251]) ).
cnf(c_0_1251_1,axiom,
( ~ c_in(X2,X3,X4)
| c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1251]) ).
cnf(c_0_1252_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1252]) ).
cnf(c_0_1252_1,axiom,
( ~ c_in(X2,X3,X4)
| c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1252]) ).
cnf(c_0_1253_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1253]) ).
cnf(c_0_1253_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1253]) ).
cnf(c_0_1254_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1254]) ).
cnf(c_0_1254_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1254]) ).
cnf(c_0_1255_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X3),X2),X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1255]) ).
cnf(c_0_1255_1,axiom,
( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(X3),X2),X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1255]) ).
cnf(c_0_1256_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1256]) ).
cnf(c_0_1256_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1256]) ).
cnf(c_0_1256_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1256]) ).
cnf(c_0_1257_0,axiom,
( c_Natural_Oevaln(X1,X2,c_Suc(X3),X4)
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1257_1,axiom,
( ~ c_Natural_Oevaln(X1,X2,X3,X4)
| c_Natural_Oevaln(X1,X2,c_Suc(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1258_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1258_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1258_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1259_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1259_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1259_2,axiom,
( hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1260_0,axiom,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ c_in(X5,X2,X3)
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_2,axiom,
( ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ c_in(X6,X2,X3)
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_3,axiom,
( ~ c_in(X6,X2,X3)
| ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_4,axiom,
( hAPP(X1,X5) != hAPP(X1,X6)
| ~ c_in(X6,X2,X3)
| ~ c_in(X5,X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1261_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_2,axiom,
( ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_3,axiom,
( ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1262_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X1,X4,X5)
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_2,axiom,
( ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ c_in(X2,X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_3,axiom,
( ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_in(X2,X4,X5)
| ~ c_in(X1,X4,X5)
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1263_0,axiom,
( X1 = X4
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_1,axiom,
( ~ c_in(X1,X2,X3)
| X1 = X4
| ~ c_in(X4,X2,X3)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_2,axiom,
( ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| X1 = X4
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_3,axiom,
( ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| X1 = X4
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_4,axiom,
( hAPP(X5,X1) != hAPP(X5,X4)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1264_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1264_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1265_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1265_1,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1265_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1266_0,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1266_1,axiom,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1266_2,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1267_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1267]) ).
cnf(c_0_1267_1,axiom,
( hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1267]) ).
cnf(c_0_1268_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1268_1,axiom,
( hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1269_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1269_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1269_2,axiom,
( hAPP(X1,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1270_0,axiom,
( c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1270]) ).
cnf(c_0_1270_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oimage(c_COMBK(X4,X5,X3),X2,X3,X5) = c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1270]) ).
cnf(c_0_1271_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1271_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1272_0,axiom,
( X4 = X3
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1272_1,axiom,
( hBOOL(hAPP(X1,X3))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1272_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X4))
| hBOOL(hAPP(X1,X3))
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1273_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1273_1,axiom,
( ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1273_2,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1274_0,axiom,
( c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1274_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1274_2,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1274_3,axiom,
( ~ c_Com_OWT(X2)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1275_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1275]) ).
cnf(c_0_1275_1,axiom,
( ~ c_Natural_Oevaln(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1275]) ).
cnf(c_0_1276_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1276]) ).
cnf(c_0_1276_1,axiom,
( ~ c_Natural_Oevaln(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1276]) ).
cnf(c_0_1277_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1277]) ).
cnf(c_0_1277_1,axiom,
( c_Set_Oimage(c_COMBK(X3,X4,X2),X1,X2,X4) = c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1277]) ).
cnf(c_0_1278_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1278_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1278_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1279_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1279_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1279_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1280_0,axiom,
( X5 = X3
| hBOOL(hAPP(X1,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1280_1,axiom,
( hBOOL(hAPP(X1,X3))
| X5 = X3
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1280_2,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X5)
| hBOOL(hAPP(X1,X3))
| X5 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1281_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1281_1,axiom,
( c_Set_Oimage(X3,X1,X2,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1282_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1282]) ).
cnf(c_0_1282_1,axiom,
( c_Set_Oimage(X4,X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1282]) ).
cnf(c_0_1283_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1283]) ).
cnf(c_0_1283_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1283]) ).
cnf(c_0_1284_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1284]) ).
cnf(c_0_1284_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1284]) ).
cnf(c_0_1285_0,axiom,
( c_in(X1,X2,X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1285_1,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1285_2,axiom,
( ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4)
| c_in(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1286_0,axiom,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1286]) ).
cnf(c_0_1286_1,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1286]) ).
cnf(c_0_1286_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1286]) ).
cnf(c_0_1287_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1287_1,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1287_2,axiom,
( ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1288_0,axiom,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1288]) ).
cnf(c_0_1288_1,axiom,
( ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1288]) ).
cnf(c_0_1289_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1289_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1289_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1290_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1290_1,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1290_2,axiom,
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1290_3,axiom,
( ~ c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1291_0,axiom,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1291]) ).
cnf(c_0_1291_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1291]) ).
cnf(c_0_1292_0,axiom,
( X1 = c_Option_Ooption_ONone(X2)
| c_Option_Omap(X3,X1,X2,X4) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1292]) ).
cnf(c_0_1292_1,axiom,
( c_Option_Omap(X3,X1,X2,X4) != c_Option_Ooption_ONone(X4)
| X1 = c_Option_Ooption_ONone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1292]) ).
cnf(c_0_1293_0,axiom,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1293_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1293_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1294_0,axiom,
( X3 = X1
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1294]) ).
cnf(c_0_1294_1,axiom,
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3)
| X3 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1294]) ).
cnf(c_0_1295_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1295_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1296_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1296]) ).
cnf(c_0_1296_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1296]) ).
cnf(c_0_1297_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1297]) ).
cnf(c_0_1297_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1297]) ).
cnf(c_0_1298_0,axiom,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1298_1,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1299_0,axiom,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1299_1,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1300_0,axiom,
( X1 = X2
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1300]) ).
cnf(c_0_1300_1,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1300]) ).
cnf(c_0_1301_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1301_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1301_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1302_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1302_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1302_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1303_0,axiom,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1303_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1304_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1304_1,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1305_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1305_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1305_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1305_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1306_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1306_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1306_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1306_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1307_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1307_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1307_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1307_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1308_0,axiom,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1308_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1308_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1309_0,axiom,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1309_1,axiom,
( c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1310_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1310]) ).
cnf(c_0_1310_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1310]) ).
cnf(c_0_1311_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1311]) ).
cnf(c_0_1311_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1311]) ).
cnf(c_0_1312_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1312]) ).
cnf(c_0_1312_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1312]) ).
cnf(c_0_1313_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1313]) ).
cnf(c_0_1313_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1313]) ).
cnf(c_0_1314_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1314]) ).
cnf(c_0_1314_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1314]) ).
cnf(c_0_1315_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1315]) ).
cnf(c_0_1315_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1315]) ).
cnf(c_0_1315_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1315]) ).
cnf(c_0_1316_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1316_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1316_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1317_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1317_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1317_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1318_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1318_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1318_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1319_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1319_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1319_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1320_0,axiom,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1320_1,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1320_2,axiom,
( ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| c_in(X1,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1321_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1321]) ).
cnf(c_0_1321_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1321]) ).
cnf(c_0_1322_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1322]) ).
cnf(c_0_1322_1,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1322]) ).
cnf(c_0_1323_0,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1323]) ).
cnf(c_0_1323_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1323]) ).
cnf(c_0_1324_0,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1324]) ).
cnf(c_0_1324_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1324]) ).
cnf(c_0_1325_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1325]) ).
cnf(c_0_1325_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1325]) ).
cnf(c_0_1326_0,axiom,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1326_1,axiom,
( c_in(X3,X1,X4)
| X1 = X2
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1326_2,axiom,
( c_in(X3,X2,X4)
| c_in(X3,X1,X4)
| X1 = X2
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1326_3,axiom,
( c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4)
| c_in(X3,X2,X4)
| c_in(X3,X1,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1327_0,axiom,
( ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1327]) ).
cnf(c_0_1327_1,axiom,
( hAPP(X2,X1) != c_Option_Ooption_ONone(X4)
| ~ c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1327]) ).
cnf(c_0_1328_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1328]) ).
cnf(c_0_1328_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1328]) ).
cnf(c_0_1328_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1328]) ).
cnf(c_0_1329_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X1,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1329]) ).
cnf(c_0_1329_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_lessequals(X1,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1329]) ).
cnf(c_0_1329_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1329]) ).
cnf(c_0_1330_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1330]) ).
cnf(c_0_1330_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1330]) ).
cnf(c_0_1331_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1331]) ).
cnf(c_0_1331_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1331]) ).
cnf(c_0_1332_0,axiom,
( c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4)
| hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1332]) ).
cnf(c_0_1332_1,axiom,
( hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5)
| c_Set_Oinsert(X1,c_Map_Odom(X2,X3,X4),X3) = c_Map_Odom(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1332]) ).
cnf(c_0_1333_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1333_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1333_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1334_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1334_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1334_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1335_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1335]) ).
cnf(c_0_1335_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1335]) ).
cnf(c_0_1335_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1335]) ).
cnf(c_0_1336_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1336]) ).
cnf(c_0_1336_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1336]) ).
cnf(c_0_1336_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1336]) ).
cnf(c_0_1337_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1337]) ).
cnf(c_0_1337_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1337]) ).
cnf(c_0_1337_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1337]) ).
cnf(c_0_1338_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1338]) ).
cnf(c_0_1338_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1338]) ).
cnf(c_0_1338_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1338]) ).
cnf(c_0_1339_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1339]) ).
cnf(c_0_1339_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1339]) ).
cnf(c_0_1340_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1340]) ).
cnf(c_0_1340_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1340]) ).
cnf(c_0_1341_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1341]) ).
cnf(c_0_1341_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1341]) ).
cnf(c_0_1341_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1341]) ).
cnf(c_0_1342_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1342]) ).
cnf(c_0_1342_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1342]) ).
cnf(c_0_1342_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1342]) ).
cnf(c_0_1343_0,axiom,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1343]) ).
cnf(c_0_1343_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1343]) ).
cnf(c_0_1343_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1343]) ).
cnf(c_0_1344_0,axiom,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1344_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1344_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1344_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1345_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1345_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1345_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1345_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1346_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1346]) ).
cnf(c_0_1346_1,axiom,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1346]) ).
cnf(c_0_1347_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1347]) ).
cnf(c_0_1347_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1347]) ).
cnf(c_0_1347_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1347]) ).
cnf(c_0_1348_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1348]) ).
cnf(c_0_1348_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1348]) ).
cnf(c_0_1349_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1349]) ).
cnf(c_0_1349_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1349]) ).
cnf(c_0_1350_0,axiom,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1350]) ).
cnf(c_0_1350_1,axiom,
( ~ hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1350]) ).
cnf(c_0_1351_0,axiom,
( c_in(X1,c_Map_Odom(X2,X3,X4),X3)
| hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1351]) ).
cnf(c_0_1351_1,axiom,
( hAPP(X2,X1) != hAPP(c_Option_Ooption_OSome(X4),X5)
| c_in(X1,c_Map_Odom(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1351]) ).
cnf(c_0_1352_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1352]) ).
cnf(c_0_1352_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1352]) ).
cnf(c_0_1352_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1352]) ).
cnf(c_0_1353_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1353_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1353_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1354_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1354]) ).
cnf(c_0_1354_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1354]) ).
cnf(c_0_1355_0,axiom,
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X2))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1355]) ).
cnf(c_0_1355_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3))
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1355]) ).
cnf(c_0_1356_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1356]) ).
cnf(c_0_1356_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1356]) ).
cnf(c_0_1357_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1357]) ).
cnf(c_0_1357_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1357]) ).
cnf(c_0_1358_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1358]) ).
cnf(c_0_1358_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1358]) ).
cnf(c_0_1359_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1359]) ).
cnf(c_0_1359_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1359]) ).
cnf(c_0_1359_2,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1359]) ).
cnf(c_0_1360_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1360]) ).
cnf(c_0_1360_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1360]) ).
cnf(c_0_1360_2,axiom,
( ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1360]) ).
cnf(c_0_1361_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1361]) ).
cnf(c_0_1361_1,axiom,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1361]) ).
cnf(c_0_1362_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1362]) ).
cnf(c_0_1362_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1362]) ).
cnf(c_0_1363_0,axiom,
( X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3)
| c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1363]) ).
cnf(c_0_1363_1,axiom,
( c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1363]) ).
cnf(c_0_1364_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1364]) ).
cnf(c_0_1364_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1364]) ).
cnf(c_0_1365_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1365]) ).
cnf(c_0_1365_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1365]) ).
cnf(c_0_1366_0,axiom,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1366]) ).
cnf(c_0_1366_1,axiom,
( c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1366]) ).
cnf(c_0_1367_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1367_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1367_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1367_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1368_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1368_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1368_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1368_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1369_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1369_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1369_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1369_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1370_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| c_in(X2,c_Map_Odom(X1,X4,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1370]) ).
cnf(c_0_1370_1,axiom,
( c_in(X2,c_Map_Odom(X1,X4,X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1370]) ).
cnf(c_0_1371_0,axiom,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1371]) ).
cnf(c_0_1371_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3))
| c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1371]) ).
cnf(c_0_1372_0,axiom,
( c_Com_OWT(X3)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1372]) ).
cnf(c_0_1372_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OCond(X1,X2,X3))
| c_Com_OWT(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1372]) ).
cnf(c_0_1373_0,axiom,
( c_Com_OWT(X3)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1373]) ).
cnf(c_0_1373_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OLocal(X1,X2,X3))
| c_Com_OWT(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1373]) ).
cnf(c_0_1374_0,axiom,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1374]) ).
cnf(c_0_1374_1,axiom,
( c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1374]) ).
cnf(c_0_1375_0,axiom,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1375]) ).
cnf(c_0_1375_1,axiom,
( c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1375]) ).
cnf(c_0_1376_0,axiom,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1376]) ).
cnf(c_0_1376_1,axiom,
( c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1376]) ).
cnf(c_0_1377_0,axiom,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1377]) ).
cnf(c_0_1377_1,axiom,
( c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1377]) ).
cnf(c_0_1378_0,axiom,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1378]) ).
cnf(c_0_1378_1,axiom,
( c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1378]) ).
cnf(c_0_1379_0,axiom,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1379]) ).
cnf(c_0_1379_1,axiom,
( c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1379]) ).
cnf(c_0_1380_0,axiom,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1380]) ).
cnf(c_0_1380_1,axiom,
( c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1380]) ).
cnf(c_0_1381_0,axiom,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1381]) ).
cnf(c_0_1381_1,axiom,
( c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1381]) ).
cnf(c_0_1382_0,axiom,
( X1 = X2
| c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1382]) ).
cnf(c_0_1382_1,axiom,
( c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1382]) ).
cnf(c_0_1383_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1383]) ).
cnf(c_0_1383_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1383]) ).
cnf(c_0_1384_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1384]) ).
cnf(c_0_1384_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1384]) ).
cnf(c_0_1385_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1385]) ).
cnf(c_0_1385_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1385]) ).
cnf(c_0_1386_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1386]) ).
cnf(c_0_1386_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1386]) ).
cnf(c_0_1387_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1387]) ).
cnf(c_0_1387_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1387]) ).
cnf(c_0_1388_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1388]) ).
cnf(c_0_1388_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1388]) ).
cnf(c_0_1388_2,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1388]) ).
cnf(c_0_1389_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1389]) ).
cnf(c_0_1389_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1389]) ).
cnf(c_0_1389_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1389]) ).
cnf(c_0_1390_0,axiom,
( c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1390]) ).
cnf(c_0_1390_1,axiom,
( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1))
| c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1390]) ).
cnf(c_0_1391_0,axiom,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1391]) ).
cnf(c_0_1391_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1391]) ).
cnf(c_0_1392_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1392]) ).
cnf(c_0_1392_1,axiom,
( ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X1),X2,X3)
| c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1392]) ).
cnf(c_0_1393_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1393]) ).
cnf(c_0_1393_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1393]) ).
cnf(c_0_1393_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1393]) ).
cnf(c_0_1394_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1394]) ).
cnf(c_0_1394_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1394]) ).
cnf(c_0_1394_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1394]) ).
cnf(c_0_1395_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1395]) ).
cnf(c_0_1395_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1395]) ).
cnf(c_0_1395_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1395]) ).
cnf(c_0_1396_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1396]) ).
cnf(c_0_1396_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1396]) ).
cnf(c_0_1397_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1397]) ).
cnf(c_0_1397_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1397]) ).
cnf(c_0_1398_0,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1398_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1398]) ).
cnf(c_0_1399_0,axiom,
( c_Com_OWT(c_Com_Ocom_OCond(X3,X1,X2))
| ~ c_Com_OWT(X1)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1399]) ).
cnf(c_0_1399_1,axiom,
( ~ c_Com_OWT(X1)
| c_Com_OWT(c_Com_Ocom_OCond(X3,X1,X2))
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1399]) ).
cnf(c_0_1399_2,axiom,
( ~ c_Com_OWT(X2)
| ~ c_Com_OWT(X1)
| c_Com_OWT(c_Com_Ocom_OCond(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1399]) ).
cnf(c_0_1400_0,axiom,
( c_Com_OWT(c_Com_Ocom_OLocal(X2,X3,X1))
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1400]) ).
cnf(c_0_1400_1,axiom,
( ~ c_Com_OWT(X1)
| c_Com_OWT(c_Com_Ocom_OLocal(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1400]) ).
cnf(c_0_1401_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1401]) ).
cnf(c_0_1401_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1401]) ).
cnf(c_0_1401_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1401]) ).
cnf(c_0_1402_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1402]) ).
cnf(c_0_1402_1,axiom,
( ~ c_in(X1,X2,X3)
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1402]) ).
cnf(c_0_1403_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1403]) ).
cnf(c_0_1403_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1403]) ).
cnf(c_0_1404_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1404]) ).
cnf(c_0_1404_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1404]) ).
cnf(c_0_1405_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1405]) ).
cnf(c_0_1405_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1405]) ).
cnf(c_0_1405_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1405]) ).
cnf(c_0_1406_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1406]) ).
cnf(c_0_1406_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1406]) ).
cnf(c_0_1406_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1406]) ).
cnf(c_0_1407_0,axiom,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1407]) ).
cnf(c_0_1407_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1407]) ).
cnf(c_0_1408_0,axiom,
( hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X1)) = hAPP(c_Com_Obody,X1)
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1408]) ).
cnf(c_0_1408_1,axiom,
( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1))
| hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),c_Com_Osko__Com__XWTs__elim__cases__7__1(X1)) = hAPP(c_Com_Obody,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1408]) ).
cnf(c_0_1409_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1409]) ).
cnf(c_0_1409_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1409]) ).
cnf(c_0_1410_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X2),X2) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1410]) ).
cnf(c_0_1410_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(X2),X2) = c_Orderings_Otop__class_Otop(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1410]) ).
cnf(c_0_1411_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1411]) ).
cnf(c_0_1411_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1411]) ).
cnf(c_0_1412_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1412]) ).
cnf(c_0_1412_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1412]) ).
cnf(c_0_1413_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1413]) ).
cnf(c_0_1413_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1413]) ).
cnf(c_0_1414_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1414]) ).
cnf(c_0_1414_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1414]) ).
cnf(c_0_1415_0,axiom,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1415]) ).
cnf(c_0_1415_1,axiom,
( ~ class_Orderings_Otop(X2)
| c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1415]) ).
cnf(c_0_1416_0,axiom,
( X1 = X2
| hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1416]) ).
cnf(c_0_1416_1,axiom,
( hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1416]) ).
cnf(c_0_1417_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1417]) ).
cnf(c_0_1417_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1417]) ).
cnf(c_0_1418_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1418]) ).
cnf(c_0_1418_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1418]) ).
cnf(c_0_1419_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1419]) ).
cnf(c_0_1419_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1419]) ).
cnf(c_0_1420_0,axiom,
( c_Com_OWT(X1)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1420]) ).
cnf(c_0_1420_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2))
| c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1420]) ).
cnf(c_0_1421_0,axiom,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1421]) ).
cnf(c_0_1421_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OSemi(X1,X2))
| c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1421]) ).
cnf(c_0_1422_0,axiom,
( c_Com_OWT(X2)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1422]) ).
cnf(c_0_1422_1,axiom,
( ~ c_Com_OWT(c_Com_Ocom_OWhile(X1,X2))
| c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1422]) ).
cnf(c_0_1423_0,axiom,
( c_Com_OWT(X1)
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1423]) ).
cnf(c_0_1423_1,axiom,
( ~ c_Com_OWT__bodies
| c_Com_OWT(X1)
| hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1423]) ).
cnf(c_0_1423_2,axiom,
( hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)
| ~ c_Com_OWT__bodies
| c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1423]) ).
cnf(c_0_1424_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1424]) ).
cnf(c_0_1424_1,axiom,
( c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1424]) ).
cnf(c_0_1425_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1425]) ).
cnf(c_0_1425_1,axiom,
( c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1425]) ).
cnf(c_0_1426_0,axiom,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1426]) ).
cnf(c_0_1426_1,axiom,
( c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1426]) ).
cnf(c_0_1427_0,axiom,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1427]) ).
cnf(c_0_1427_1,axiom,
( c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1427]) ).
cnf(c_0_1428_0,axiom,
( X1 = X2
| c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1428]) ).
cnf(c_0_1428_1,axiom,
( c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1428]) ).
cnf(c_0_1429_0,axiom,
( X1 = X2
| c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1429]) ).
cnf(c_0_1429_1,axiom,
( c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1429]) ).
cnf(c_0_1430_0,axiom,
( c_Com_OWT(c_Com_Ocom_OSemi(X1,X2))
| ~ c_Com_OWT(X1)
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1430]) ).
cnf(c_0_1430_1,axiom,
( ~ c_Com_OWT(X1)
| c_Com_OWT(c_Com_Ocom_OSemi(X1,X2))
| ~ c_Com_OWT(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1430]) ).
cnf(c_0_1430_2,axiom,
( ~ c_Com_OWT(X2)
| ~ c_Com_OWT(X1)
| c_Com_OWT(c_Com_Ocom_OSemi(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1430]) ).
cnf(c_0_1431_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1431]) ).
cnf(c_0_1431_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1431]) ).
cnf(c_0_1431_2,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1431]) ).
cnf(c_0_1432_0,axiom,
( hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1432]) ).
cnf(c_0_1432_1,axiom,
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X1))
| hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(literals_permutation,[status(thm)],[c_0_1432]) ).
cnf(c_0_1433_0,axiom,
( X1 = X2
| hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1433]) ).
cnf(c_0_1433_1,axiom,
( hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1433]) ).
cnf(c_0_1434_0,axiom,
( c_Com_OWT(c_Com_Ocom_OWhile(X2,X1))
| ~ c_Com_OWT(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1434]) ).
cnf(c_0_1434_1,axiom,
( ~ c_Com_OWT(X1)
| c_Com_OWT(c_Com_Ocom_OWhile(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1434]) ).
cnf(c_0_1435_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1435]) ).
cnf(c_0_1435_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1435]) ).
cnf(c_0_1436_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1436]) ).
cnf(c_0_1436_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1436]) ).
cnf(c_0_1437_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1437]) ).
cnf(c_0_1437_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1437]) ).
cnf(c_0_1438_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1438]) ).
cnf(c_0_1438_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1438]) ).
cnf(c_0_1439_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1439]) ).
cnf(c_0_1439_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1439]) ).
cnf(c_0_1440_0,axiom,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1440]) ).
cnf(c_0_1440_1,axiom,
( ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1440]) ).
cnf(c_0_1441_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1441]) ).
cnf(c_0_1441_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1441]) ).
cnf(c_0_1442_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1442]) ).
cnf(c_0_1442_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1442]) ).
cnf(c_0_1443_0,axiom,
( X1 = c_Option_Ooption_ONone(X2)
| ~ c_Option_Ois__none(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1443]) ).
cnf(c_0_1443_1,axiom,
( ~ c_Option_Ois__none(X1,X2)
| X1 = c_Option_Ooption_ONone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1443]) ).
cnf(c_0_1444_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1444]) ).
cnf(c_0_1444_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1444]) ).
cnf(c_0_1445_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1445]) ).
cnf(c_0_1445_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1445]) ).
cnf(c_0_1446_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1446]) ).
cnf(c_0_1446_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1446]) ).
cnf(c_0_1447_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1447]) ).
cnf(c_0_1447_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1447]) ).
cnf(c_0_1448_0,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_1448]) ).
cnf(c_0_1448_1,axiom,
( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) != X1
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(literals_permutation,[status(thm)],[c_0_1448]) ).
cnf(c_0_1449_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(literals_permutation,[status(thm)],[c_0_1449]) ).
cnf(c_0_1449_1,axiom,
( c_Hoare__Mirabelle_Ostate__not__singleton
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1449]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_931,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('<stdin>',cls_conjecture_4) ).
fof(c_0_1_932,negated_conjecture,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_2_933,negated_conjecture,
c_Com_OWT(v_c),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_3_934,negated_conjecture,
c_Com_OWT__bodies,
file('<stdin>',cls_conjecture_1) ).
fof(c_0_4_935,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('<stdin>',cls_conjecture_0) ).
fof(c_0_5_936,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_6_937,negated_conjecture,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
c_0_1 ).
fof(c_0_7_938,negated_conjecture,
c_Com_OWT(v_c),
c_0_2 ).
fof(c_0_8_939,negated_conjecture,
c_Com_OWT__bodies,
c_0_3 ).
fof(c_0_9_940,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
c_0_4 ).
fof(c_0_10_941,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
c_0_5 ).
fof(c_0_11_942,negated_conjecture,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
c_0_6 ).
fof(c_0_12_943,negated_conjecture,
c_Com_OWT(v_c),
c_0_7 ).
fof(c_0_13_944,negated_conjecture,
c_Com_OWT__bodies,
c_0_8 ).
fof(c_0_14_945,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
c_0_9 ).
cnf(c_0_15_946,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16_947,negated_conjecture,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17_948,negated_conjecture,
c_Com_OWT(v_c),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18_949,negated_conjecture,
c_Com_OWT__bodies,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19_950,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20_951,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
c_0_15,
[final] ).
cnf(c_0_21_952,negated_conjecture,
hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) = hAPP(c_Com_Obody,v_pn),
c_0_16,
[final] ).
cnf(c_0_22_953,negated_conjecture,
c_Com_OWT(v_c),
c_0_17,
[final] ).
cnf(c_0_23_954,negated_conjecture,
c_Com_OWT__bodies,
c_0_18,
[final] ).
cnf(c_0_24_955,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
c_0_19,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_911,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox/tmp/iprover_modulo_6191ba.p',c_0_23) ).
cnf(c_1267,negated_conjecture,
c_Com_OWT__bodies,
inference(copy,[status(esa)],[c_911]) ).
cnf(c_1284,negated_conjecture,
c_Com_OWT__bodies,
inference(copy,[status(esa)],[c_1267]) ).
cnf(c_1287,negated_conjecture,
c_Com_OWT__bodies,
inference(copy,[status(esa)],[c_1284]) ).
cnf(c_1294,negated_conjecture,
c_Com_OWT__bodies,
inference(copy,[status(esa)],[c_1287]) ).
cnf(c_3965,negated_conjecture,
c_Com_OWT__bodies,
inference(copy,[status(esa)],[c_1294]) ).
cnf(c_18,plain,
( ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_6191ba.p',c_0_1166_0) ).
cnf(c_2245,plain,
( ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate) ),
inference(copy,[status(esa)],[c_18]) ).
cnf(c_2246,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(rewriting,[status(thm)],[c_2245]) ).
cnf(c_3971,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3965,c_2246]) ).
cnf(c_3976,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(rewriting,[status(thm)],[c_3971]) ).
cnf(c_912,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/tmp/iprover_modulo_6191ba.p',c_0_24) ).
cnf(c_1269,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(copy,[status(esa)],[c_912]) ).
cnf(c_1285,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(copy,[status(esa)],[c_1269]) ).
cnf(c_1286,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(copy,[status(esa)],[c_1285]) ).
cnf(c_1295,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(copy,[status(esa)],[c_1286]) ).
cnf(c_3967,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(copy,[status(esa)],[c_1295]) ).
cnf(c_4467,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate)
| ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3976,c_3967]) ).
cnf(c_4468,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),X0,tc_Com_Ostate)
| ~ c_lessequals(X0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(rewriting,[status(thm)],[c_4467]) ).
cnf(c_773,plain,
c_lessequals(X0,X0,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/tmp/iprover_modulo_6191ba.p',c_0_878_0) ).
cnf(c_3745,plain,
c_lessequals(X0,X0,tc_fun(X1,tc_bool)),
inference(copy,[status(esa)],[c_773]) ).
cnf(c_4511,plain,
c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(resolution,[status(thm)],[c_4468,c_3745]) ).
cnf(c_4512,plain,
c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(rewriting,[status(thm)],[c_4511]) ).
cnf(c_908,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('/export/starexec/sandbox/tmp/iprover_modulo_6191ba.p',c_0_20) ).
cnf(c_1261,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(copy,[status(esa)],[c_908]) ).
cnf(c_1281,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(copy,[status(esa)],[c_1261]) ).
cnf(c_1290,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(copy,[status(esa)],[c_1281]) ).
cnf(c_1291,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(copy,[status(esa)],[c_1290]) ).
cnf(c_3959,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(copy,[status(esa)],[c_1291]) ).
cnf(c_19578,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4512,c_3959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV908-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n026.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 16:10:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.49 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.49 % Orientation found
% 0.20/0.49 % 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/sandbox/tmp/iprover_proof_b40613.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_6191ba.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_726cc5 | grep -v "SZS"
% 0.20/0.51
% 0.20/0.51 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.51
% 0.20/0.51 %
% 0.20/0.51 % ------ iProver source info
% 0.20/0.51
% 0.20/0.51 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.51 % git: non_committed_changes: true
% 0.20/0.51 % git: last_make_outside_of_git: true
% 0.20/0.51
% 0.20/0.51 %
% 0.20/0.51 % ------ Input Options
% 0.20/0.51
% 0.20/0.51 % --out_options all
% 0.20/0.51 % --tptp_safe_out true
% 0.20/0.51 % --problem_path ""
% 0.20/0.51 % --include_path ""
% 0.20/0.51 % --clausifier .//eprover
% 0.20/0.51 % --clausifier_options --tstp-format
% 0.20/0.51 % --stdin false
% 0.20/0.51 % --dbg_backtrace false
% 0.20/0.51 % --dbg_dump_prop_clauses false
% 0.20/0.51 % --dbg_dump_prop_clauses_file -
% 0.20/0.51 % --dbg_out_stat false
% 0.20/0.51
% 0.20/0.51 % ------ General Options
% 0.20/0.51
% 0.20/0.51 % --fof false
% 0.20/0.51 % --time_out_real 150.
% 0.20/0.51 % --time_out_prep_mult 0.2
% 0.20/0.51 % --time_out_virtual -1.
% 0.20/0.51 % --schedule none
% 0.20/0.51 % --ground_splitting input
% 0.20/0.51 % --splitting_nvd 16
% 0.20/0.51 % --non_eq_to_eq false
% 0.20/0.51 % --prep_gs_sim true
% 0.20/0.51 % --prep_unflatten false
% 0.20/0.51 % --prep_res_sim true
% 0.20/0.51 % --prep_upred true
% 0.20/0.51 % --res_sim_input true
% 0.20/0.51 % --clause_weak_htbl true
% 0.20/0.51 % --gc_record_bc_elim false
% 0.20/0.51 % --symbol_type_check false
% 0.20/0.51 % --clausify_out false
% 0.20/0.51 % --large_theory_mode false
% 0.20/0.51 % --prep_sem_filter none
% 0.20/0.51 % --prep_sem_filter_out false
% 0.20/0.51 % --preprocessed_out false
% 0.20/0.51 % --sub_typing false
% 0.20/0.51 % --brand_transform false
% 0.20/0.51 % --pure_diseq_elim true
% 0.20/0.51 % --min_unsat_core false
% 0.20/0.51 % --pred_elim true
% 0.20/0.51 % --add_important_lit false
% 0.20/0.51 % --soft_assumptions false
% 0.20/0.51 % --reset_solvers false
% 0.20/0.51 % --bc_imp_inh []
% 0.20/0.51 % --conj_cone_tolerance 1.5
% 0.20/0.51 % --prolific_symb_bound 500
% 0.20/0.51 % --lt_threshold 2000
% 0.20/0.51
% 0.20/0.51 % ------ SAT Options
% 0.20/0.51
% 0.20/0.51 % --sat_mode false
% 0.20/0.51 % --sat_fm_restart_options ""
% 0.20/0.51 % --sat_gr_def false
% 0.20/0.51 % --sat_epr_types true
% 0.20/0.51 % --sat_non_cyclic_types false
% 0.20/0.51 % --sat_finite_models false
% 0.20/0.51 % --sat_fm_lemmas false
% 0.20/0.51 % --sat_fm_prep false
% 0.20/0.51 % --sat_fm_uc_incr true
% 0.20/0.51 % --sat_out_model small
% 0.20/0.51 % --sat_out_clauses false
% 0.20/0.51
% 0.20/0.51 % ------ QBF Options
% 0.20/0.51
% 0.20/0.51 % --qbf_mode false
% 0.20/0.51 % --qbf_elim_univ true
% 0.20/0.51 % --qbf_sk_in true
% 0.20/0.51 % --qbf_pred_elim true
% 0.20/0.51 % --qbf_split 32
% 0.20/0.51
% 0.20/0.51 % ------ BMC1 Options
% 0.20/0.51
% 0.20/0.51 % --bmc1_incremental false
% 0.20/0.51 % --bmc1_axioms reachable_all
% 0.20/0.51 % --bmc1_min_bound 0
% 0.20/0.51 % --bmc1_max_bound -1
% 0.20/0.51 % --bmc1_max_bound_default -1
% 0.20/0.51 % --bmc1_symbol_reachability true
% 0.20/0.51 % --bmc1_property_lemmas false
% 0.20/0.51 % --bmc1_k_induction false
% 0.20/0.51 % --bmc1_non_equiv_states false
% 0.20/0.51 % --bmc1_deadlock false
% 0.20/0.51 % --bmc1_ucm false
% 0.20/0.51 % --bmc1_add_unsat_core none
% 0.20/0.51 % --bmc1_unsat_core_children false
% 0.20/0.51 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.51 % --bmc1_out_stat full
% 0.20/0.51 % --bmc1_ground_init false
% 0.20/0.51 % --bmc1_pre_inst_next_state false
% 0.20/0.51 % --bmc1_pre_inst_state false
% 0.20/0.51 % --bmc1_pre_inst_reach_state false
% 0.20/0.51 % --bmc1_out_unsat_core false
% 0.20/0.51 % --bmc1_aig_witness_out false
% 0.20/0.51 % --bmc1_verbose false
% 0.20/0.51 % --bmc1_dump_clauses_tptp false
% 4.53/5.10 % --bmc1_dump_unsat_core_tptp false
% 4.53/5.10 % --bmc1_dump_file -
% 4.53/5.10 % --bmc1_ucm_expand_uc_limit 128
% 4.53/5.10 % --bmc1_ucm_n_expand_iterations 6
% 4.53/5.10 % --bmc1_ucm_extend_mode 1
% 4.53/5.10 % --bmc1_ucm_init_mode 2
% 4.53/5.10 % --bmc1_ucm_cone_mode none
% 4.53/5.10 % --bmc1_ucm_reduced_relation_type 0
% 4.53/5.10 % --bmc1_ucm_relax_model 4
% 4.53/5.10 % --bmc1_ucm_full_tr_after_sat true
% 4.53/5.10 % --bmc1_ucm_expand_neg_assumptions false
% 4.53/5.10 % --bmc1_ucm_layered_model none
% 4.53/5.10 % --bmc1_ucm_max_lemma_size 10
% 4.53/5.10
% 4.53/5.10 % ------ AIG Options
% 4.53/5.10
% 4.53/5.10 % --aig_mode false
% 4.53/5.10
% 4.53/5.10 % ------ Instantiation Options
% 4.53/5.10
% 4.53/5.10 % --instantiation_flag true
% 4.53/5.10 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 4.53/5.10 % --inst_solver_per_active 750
% 4.53/5.10 % --inst_solver_calls_frac 0.5
% 4.53/5.10 % --inst_passive_queue_type priority_queues
% 4.53/5.10 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 4.53/5.10 % --inst_passive_queues_freq [25;2]
% 4.53/5.10 % --inst_dismatching true
% 4.53/5.10 % --inst_eager_unprocessed_to_passive true
% 4.53/5.10 % --inst_prop_sim_given true
% 4.53/5.10 % --inst_prop_sim_new false
% 4.53/5.10 % --inst_orphan_elimination true
% 4.53/5.10 % --inst_learning_loop_flag true
% 4.53/5.10 % --inst_learning_start 3000
% 4.53/5.10 % --inst_learning_factor 2
% 4.53/5.10 % --inst_start_prop_sim_after_learn 3
% 4.53/5.10 % --inst_sel_renew solver
% 4.53/5.10 % --inst_lit_activity_flag true
% 4.53/5.10 % --inst_out_proof true
% 4.53/5.10
% 4.53/5.10 % ------ Resolution Options
% 4.53/5.10
% 4.53/5.10 % --resolution_flag true
% 4.53/5.10 % --res_lit_sel kbo_max
% 4.53/5.10 % --res_to_prop_solver none
% 4.53/5.10 % --res_prop_simpl_new false
% 4.53/5.10 % --res_prop_simpl_given false
% 4.53/5.10 % --res_passive_queue_type priority_queues
% 4.53/5.10 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 4.53/5.10 % --res_passive_queues_freq [15;5]
% 4.53/5.10 % --res_forward_subs full
% 4.53/5.10 % --res_backward_subs full
% 4.53/5.10 % --res_forward_subs_resolution true
% 4.53/5.10 % --res_backward_subs_resolution true
% 4.53/5.10 % --res_orphan_elimination false
% 4.53/5.10 % --res_time_limit 1000.
% 4.53/5.10 % --res_out_proof true
% 4.53/5.10 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_b40613.s
% 4.53/5.10 % --modulo true
% 4.53/5.10
% 4.53/5.10 % ------ Combination Options
% 4.53/5.10
% 4.53/5.10 % --comb_res_mult 1000
% 4.53/5.10 % --comb_inst_mult 300
% 4.53/5.10 % ------
% 4.53/5.10
% 4.53/5.10 % ------ Parsing...% successful
% 4.53/5.10
% 4.53/5.10 % ------ 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 %
% 4.53/5.10
% 4.53/5.10 % ------ Proving...
% 4.53/5.10 % ------ Problem Properties
% 4.53/5.10
% 4.53/5.10 %
% 4.53/5.10 % EPR false
% 4.53/5.10 % Horn false
% 4.53/5.10 % Has equality true
% 4.53/5.10
% 4.53/5.10 % % ------ Input Options Time Limit: Unbounded
% 4.53/5.10
% 4.53/5.10
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 Compiling...
% 4.53/5.10 Loading plugin: done.
% 4.53/5.10 % % ------ Current options:
% 4.53/5.10
% 4.53/5.10 % ------ Input Options
% 4.53/5.10
% 4.53/5.10 % --out_options all
% 4.53/5.10 % --tptp_safe_out true
% 4.53/5.10 % --problem_path ""
% 4.53/5.10 % --include_path ""
% 4.53/5.10 % --clausifier .//eprover
% 4.53/5.10 % --clausifier_options --tstp-format
% 4.53/5.10 % --stdin false
% 4.53/5.10 % --dbg_backtrace false
% 4.53/5.10 % --dbg_dump_prop_clauses false
% 4.53/5.10 % --dbg_dump_prop_clauses_file -
% 4.53/5.10 % --dbg_out_stat false
% 4.53/5.10
% 4.53/5.10 % ------ General Options
% 4.53/5.10
% 4.53/5.10 % --fof false
% 4.53/5.10 % --time_out_real 150.
% 4.53/5.10 % --time_out_prep_mult 0.2
% 4.53/5.10 % --time_out_virtual -1.
% 4.53/5.10 % --schedule none
% 4.53/5.10 % --ground_splitting input
% 4.53/5.10 % --splitting_nvd 16
% 4.53/5.10 % --non_eq_to_eq false
% 4.53/5.10 % --prep_gs_sim true
% 4.53/5.10 % --prep_unflatten false
% 4.53/5.10 % --prep_res_sim true
% 4.53/5.10 % --prep_upred true
% 4.53/5.10 % --res_sim_input true
% 4.53/5.10 % --clause_weak_htbl true
% 4.53/5.10 % --gc_record_bc_elim false
% 4.53/5.10 % --symbol_type_check false
% 4.53/5.10 % --clausify_out false
% 4.53/5.10 % --large_theory_mode false
% 4.53/5.10 % --prep_sem_filter none
% 4.53/5.10 % --prep_sem_filter_out false
% 4.53/5.10 % --preprocessed_out false
% 4.53/5.10 % --sub_typing false
% 4.53/5.10 % --brand_transform false
% 4.53/5.10 % --pure_diseq_elim true
% 4.53/5.10 % --min_unsat_core false
% 4.53/5.10 % --pred_elim true
% 4.53/5.10 % --add_important_lit false
% 4.53/5.10 % --soft_assumptions false
% 4.53/5.10 % --reset_solvers false
% 4.53/5.10 % --bc_imp_inh []
% 4.53/5.10 % --conj_cone_tolerance 1.5
% 4.53/5.10 % --prolific_symb_bound 500
% 4.53/5.10 % --lt_threshold 2000
% 4.53/5.10
% 4.53/5.10 % ------ SAT Options
% 4.53/5.10
% 4.53/5.10 % --sat_mode false
% 4.53/5.10 % --sat_fm_restart_options ""
% 4.53/5.10 % --sat_gr_def false
% 4.53/5.10 % --sat_epr_types true
% 4.53/5.10 % --sat_non_cyclic_types false
% 4.53/5.10 % --sat_finite_models false
% 4.53/5.10 % --sat_fm_lemmas false
% 4.53/5.10 % --sat_fm_prep false
% 4.53/5.10 % --sat_fm_uc_incr true
% 4.53/5.10 % --sat_out_model small
% 4.53/5.10 % --sat_out_clauses false
% 4.53/5.10
% 4.53/5.10 % ------ QBF Options
% 4.53/5.10
% 4.53/5.10 % --qbf_mode false
% 4.53/5.10 % --qbf_elim_univ true
% 4.53/5.10 % --qbf_sk_in true
% 4.53/5.10 % --qbf_pred_elim true
% 4.53/5.10 % --qbf_split 32
% 4.53/5.10
% 4.53/5.10 % ------ BMC1 Options
% 4.53/5.10
% 4.53/5.10 % --bmc1_incremental false
% 4.53/5.10 % --bmc1_axioms reachable_all
% 4.53/5.10 % --bmc1_min_bound 0
% 4.53/5.10 % --bmc1_max_bound -1
% 4.53/5.10 % --bmc1_max_bound_default -1
% 4.53/5.10 % --bmc1_symbol_reachability true
% 4.53/5.10 % --bmc1_property_lemmas false
% 4.53/5.10 % --bmc1_k_induction false
% 4.53/5.10 % --bmc1_non_equiv_states false
% 4.53/5.10 % --bmc1_deadlock false
% 4.53/5.10 % --bmc1_ucm false
% 4.53/5.10 % --bmc1_add_unsat_core none
% 4.53/5.10 % --bmc1_unsat_core_children false
% 4.53/5.10 % --bmc1_unsat_core_extrapolate_axioms false
% 4.53/5.10 % --bmc1_out_stat full
% 4.53/5.10 % --bmc1_ground_init false
% 4.53/5.10 % --bmc1_pre_inst_next_state false
% 4.53/5.10 % --bmc1_pre_inst_state false
% 4.53/5.10 % --bmc1_pre_inst_reach_state false
% 4.53/5.10 % --bmc1_out_unsat_core false
% 4.53/5.10 % --bmc1_aig_witness_out false
% 4.53/5.10 % --bmc1_verbose false
% 4.53/5.10 % --bmc1_dump_clauses_tptp false
% 4.53/5.10 % --bmc1_dump_unsat_core_tptp false
% 4.53/5.10 % --bmc1_dump_file -
% 4.53/5.10 % --bmc1_ucm_expand_uc_limit 128
% 4.53/5.10 % --bmc1_ucm_n_expand_iterations 6
% 5.68/5.96 % --bmc1_ucm_extend_mode 1
% 5.68/5.96 % --bmc1_ucm_init_mode 2
% 5.68/5.96 % --bmc1_ucm_cone_mode none
% 5.68/5.96 % --bmc1_ucm_reduced_relation_type 0
% 5.68/5.96 % --bmc1_ucm_relax_model 4
% 5.68/5.96 % --bmc1_ucm_full_tr_after_sat true
% 5.68/5.96 % --bmc1_ucm_expand_neg_assumptions false
% 5.68/5.96 % --bmc1_ucm_layered_model none
% 5.68/5.96 % --bmc1_ucm_max_lemma_size 10
% 5.68/5.96
% 5.68/5.96 % ------ AIG Options
% 5.68/5.96
% 5.68/5.96 % --aig_mode false
% 5.68/5.96
% 5.68/5.96 % ------ Instantiation Options
% 5.68/5.96
% 5.68/5.96 % --instantiation_flag true
% 5.68/5.96 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 5.68/5.96 % --inst_solver_per_active 750
% 5.68/5.96 % --inst_solver_calls_frac 0.5
% 5.68/5.96 % --inst_passive_queue_type priority_queues
% 5.68/5.96 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 5.68/5.96 % --inst_passive_queues_freq [25;2]
% 5.68/5.96 % --inst_dismatching true
% 5.68/5.96 % --inst_eager_unprocessed_to_passive true
% 5.68/5.96 % --inst_prop_sim_given true
% 5.68/5.96 % --inst_prop_sim_new false
% 5.68/5.96 % --inst_orphan_elimination true
% 5.68/5.96 % --inst_learning_loop_flag true
% 5.68/5.96 % --inst_learning_start 3000
% 5.68/5.96 % --inst_learning_factor 2
% 5.68/5.96 % --inst_start_prop_sim_after_learn 3
% 5.68/5.96 % --inst_sel_renew solver
% 5.68/5.96 % --inst_lit_activity_flag true
% 5.68/5.96 % --inst_out_proof true
% 5.68/5.96
% 5.68/5.96 % ------ Resolution Options
% 5.68/5.96
% 5.68/5.96 % --resolution_flag true
% 5.68/5.96 % --res_lit_sel kbo_max
% 5.68/5.96 % --res_to_prop_solver none
% 5.68/5.96 % --res_prop_simpl_new false
% 5.68/5.96 % --res_prop_simpl_given false
% 5.68/5.96 % --res_passive_queue_type priority_queues
% 5.68/5.96 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 5.68/5.96 % --res_passive_queues_freq [15;5]
% 5.68/5.96 % --res_forward_subs full
% 5.68/5.96 % --res_backward_subs full
% 5.68/5.96 % --res_forward_subs_resolution true
% 5.68/5.96 % --res_backward_subs_resolution true
% 5.68/5.96 % --res_orphan_elimination false
% 5.68/5.96 % --res_time_limit 1000.
% 5.68/5.96 % --res_out_proof true
% 5.68/5.96 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_b40613.s
% 5.68/5.96 % --modulo true
% 5.68/5.96
% 5.68/5.96 % ------ Combination Options
% 5.68/5.96
% 5.68/5.96 % --comb_res_mult 1000
% 5.68/5.96 % --comb_inst_mult 300
% 5.68/5.96 % ------
% 5.68/5.96
% 5.68/5.96
% 5.68/5.96
% 5.68/5.96 % ------ Proving...
% 5.68/5.96 %
% 5.68/5.96
% 5.68/5.96
% 5.68/5.96 % Resolution empty clause
% 5.68/5.96
% 5.68/5.96 % ------ Statistics
% 5.68/5.96
% 5.68/5.96 % ------ General
% 5.68/5.96
% 5.68/5.96 % num_of_input_clauses: 913
% 5.68/5.96 % num_of_input_neg_conjectures: 5
% 5.68/5.96 % num_of_splits: 0
% 5.68/5.96 % num_of_split_atoms: 0
% 5.68/5.96 % num_of_sem_filtered_clauses: 0
% 5.68/5.96 % num_of_subtypes: 0
% 5.68/5.96 % monotx_restored_types: 0
% 5.68/5.96 % sat_num_of_epr_types: 0
% 5.68/5.96 % sat_num_of_non_cyclic_types: 0
% 5.68/5.96 % sat_guarded_non_collapsed_types: 0
% 5.68/5.96 % is_epr: 0
% 5.68/5.96 % is_horn: 0
% 5.68/5.96 % has_eq: 1
% 5.68/5.96 % num_pure_diseq_elim: 0
% 5.68/5.96 % simp_replaced_by: 0
% 5.68/5.96 % res_preprocessed: 10
% 5.68/5.96 % prep_upred: 0
% 5.68/5.96 % prep_unflattend: 0
% 5.68/5.96 % pred_elim_cands: 0
% 5.68/5.96 % pred_elim: 0
% 5.68/5.96 % pred_elim_cl: 0
% 5.68/5.96 % pred_elim_cycles: 0
% 5.68/5.96 % forced_gc_time: 0
% 5.68/5.96 % gc_basic_clause_elim: 0
% 5.68/5.96 % parsing_time: 0.057
% 5.68/5.96 % sem_filter_time: 0.
% 5.68/5.96 % pred_elim_time: 0.
% 5.68/5.96 % out_proof_time: 0.
% 5.68/5.96 % monotx_time: 0.
% 5.68/5.96 % subtype_inf_time: 0.
% 5.68/5.96 % unif_index_cands_time: 0.001
% 5.68/5.96 % unif_index_add_time: 0.002
% 5.68/5.96 % total_time: 5.468
% 5.68/5.96 % num_of_symbols: 106
% 5.68/5.96 % num_of_terms: 30872
% 5.68/5.96
% 5.68/5.96 % ------ Propositional Solver
% 5.68/5.96
% 5.68/5.96 % prop_solver_calls: 1
% 5.68/5.96 % prop_fast_solver_calls: 15
% 5.68/5.96 % prop_num_of_clauses: 1021
% 5.68/5.96 % prop_preprocess_simplified: 2623
% 5.68/5.96 % prop_fo_subsumed: 0
% 5.68/5.96 % prop_solver_time: 0.
% 5.68/5.96 % prop_fast_solver_time: 0.
% 5.68/5.96 % prop_unsat_core_time: 0.
% 5.68/5.96
% 5.68/5.96 % ------ QBF
% 5.68/5.96
% 5.68/5.96 % qbf_q_res: 0
% 5.68/5.96 % qbf_num_tautologies: 0
% 5.68/5.96 % qbf_prep_cycles: 0
% 5.68/5.96
% 5.68/5.96 % ------ BMC1
% 5.68/5.96
% 5.68/5.96 % bmc1_current_bound: -1
% 5.68/5.96 % bmc1_last_solved_bound: -1
% 5.68/5.96 % bmc1_unsat_core_size: -1
% 5.68/5.96 % bmc1_unsat_core_parents_size: -1
% 5.68/5.96 % bmc1_merge_next_fun: 0
% 5.68/5.96 % bmc1_unsat_core_clauses_time: 0.
% 5.68/5.96
% 5.68/5.96 % ------ Instantiation
% 5.68/5.96
% 5.68/5.96 % inst_num_of_clauses: 827
% 5.68/5.96 % inst_num_in_passive: 0
% 5.68/5.96 % inst_num_in_active: 0
% 5.68/5.96 % inst_num_in_unprocessed: 913
% 5.68/5.96 % inst_num_of_loops: 0
% 5.68/5.96 % inst_num_of_learning_restarts: 0
% 5.68/5.96 % inst_num_moves_active_passive: 0
% 5.68/5.96 % inst_lit_activity: 0
% 5.68/5.96 % inst_lit_activity_moves: 0
% 5.68/5.96 % inst_num_tautologies: 0
% 5.68/5.96 % inst_num_prop_implied: 0
% 5.68/5.96 % inst_num_existing_simplified: 0
% 5.68/5.96 % inst_num_eq_res_simplified: 0
% 5.68/5.96 % inst_num_child_elim: 0
% 5.68/5.96 % inst_num_of_dismatching_blockings: 0
% 5.68/5.96 % inst_num_of_non_proper_insts: 0
% 5.68/5.96 % inst_num_of_duplicates: 0
% 5.68/5.96 % inst_inst_num_from_inst_to_res: 0
% 5.68/5.96 % inst_dismatching_checking_time: 0.
% 5.68/5.96
% 5.68/5.96 % ------ Resolution
% 5.68/5.96
% 5.68/5.96 % res_num_of_clauses: 7124
% 5.68/5.96 % res_num_in_passive: 5911
% 5.68/5.96 % res_num_in_active: 742
% 5.68/5.96 % res_num_of_loops: 538
% 5.68/5.96 % res_forward_subset_subsumed: 580
% 5.68/5.96 % res_backward_subset_subsumed: 8
% 5.68/5.96 % res_forward_subsumed: 193
% 5.68/5.96 % res_backward_subsumed: 7
% 5.68/5.96 % res_forward_subsumption_resolution: 12
% 5.68/5.96 % res_backward_subsumption_resolution: 6
% 5.68/5.96 % res_clause_to_clause_subsumption: 6906
% 5.68/5.96 % res_orphan_elimination: 0
% 5.68/5.96 % res_tautology_del: 2
% 5.68/5.96 % res_num_eq_res_simplified: 0
% 5.68/5.96 % res_num_sel_changes: 0
% 5.68/5.96 % res_moves_from_active_to_pass: 0
% 5.68/5.96
% 5.68/5.96 % Status Unsatisfiable
% 5.68/5.96 % SZS status Unsatisfiable
% 5.68/5.96 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------