%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWV825-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 19:22:16 EDT 2022
% Result : Unsatisfiable 155.72s 156.01s
% Output : CNFRefutation 155.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 544
% Syntax : Number of formulae : 3859 ( 983 unt; 0 def)
% Number of atoms : 8665 (2378 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 9321 (4515 ~;4806 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-9 aty)
% Number of functors : 60 ( 60 usr; 15 con; 0-6 aty)
% Number of variables : 14823 (1476 sgn6123 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X45,X46,X28,X29,X47,X48,X30,X9,X49,X50,X2] :
( hAPP(X49,hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X46,X9),X30)
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OSup__binary_0) ).
fof(c_0_1,axiom,
! [X45,X46,X28,X29,X47,X48,X30,X9,X49,X50,X2] :
( hAPP(X50,hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X47,X9),X30)
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OInf__binary_0) ).
fof(c_0_2,axiom,
! [X6,X45,X46,X28,X29,X47,X48,X49,X50,X7,X2] :
( hBOOL(hAPP(hAPP(X28,hAPP(X50,X7)),X6))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OInf__lower_0) ).
fof(c_0_3,axiom,
! [X6,X45,X46,X28,X29,X47,X48,X49,X50,X7,X2] :
( hBOOL(hAPP(hAPP(X28,X6),hAPP(X49,X7)))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OSup__upper_0) ).
fof(c_0_4,axiom,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X2] :
( hAPP(X49,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X9
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OSup__singleton_0) ).
fof(c_0_5,axiom,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X2] :
( hAPP(X50,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X9
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OInf__singleton_0) ).
fof(c_0_6,axiom,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X7,X2] :
( hAPP(X49,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7)) = hAPP(hAPP(X46,X9),hAPP(X49,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OSup__insert_0) ).
fof(c_0_7,axiom,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X7,X2] :
( hAPP(X50,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7)) = hAPP(hAPP(X47,X9),hAPP(X50,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OInf__insert_0) ).
fof(c_0_8,axiom,
! [X45,X46,X28,X29,X47,X48,X49,X50,X2] :
( hAPP(X49,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X48
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OSup__empty_0) ).
fof(c_0_9,axiom,
! [X45,X46,X28,X29,X47,X48,X49,X50,X2] :
( hAPP(X50,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X45
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
file('<stdin>',cls_complete__lattice_OInf__empty_0) ).
fof(c_0_10,axiom,
! [X41,X16,X30,X24,X21,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OCond(X30,X16,X41),X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X21,c_Fun_Ocomp(c_Not,X30,tc_bool,tc_bool,tc_Com_Ostate),X2),X41,X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X21,X30,X2),X16,X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
file('<stdin>',cls_hoare__derivs_OIf_0) ).
fof(c_0_11,axiom,
! [X16,X30,X21,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OWhile(X30,X16),c_Hoare__Mirabelle_Opeek__and(X21,c_Fun_Ocomp(c_Not,X30,tc_bool,tc_bool,tc_Com_Ostate),X2),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X21,X30,X2),X16,X21,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
file('<stdin>',cls_Loop_0) ).
fof(c_0_12,axiom,
! [X5,X6,X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X24,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X21,X24,X16,X6,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq_2) ).
fof(c_0_13,axiom,
! [X5,X6,X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X24,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X21,X24,X16,X6,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(c_0_14,axiom,
! [X5,X6,X16,X67,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X21,X24,X16,X6,X5)))
| ~ hBOOL(hAPP(hAPP(X6,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X21,X24,X16)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(c_0_15,axiom,
! [X5,X6,X16,X67,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X21,X24,X16,X6,X5)))
| ~ hBOOL(hAPP(hAPP(X6,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X21,X24,X16)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq_1) ).
fof(c_0_16,axiom,
! [X41,X16,X23,X24,X21,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OSemi(X16,X41),X23,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X24,X41,X23,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
file('<stdin>',cls_Comp_0) ).
fof(c_0_17,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X15),X7)),
file('<stdin>',cls_Un__Int__crazy_0) ).
fof(c_0_18,axiom,
! [X44,X17,X12,X53,X18,X11,X2] : c_Fun_Ocomp(X12,c_Fun_Ocomp(X17,X44,X53,X18,X2),X18,X11,X2) = c_Fun_Ocomp(c_Fun_Ocomp(X12,X17,X18,X11,X53),X44,X53,X11,X2),
file('<stdin>',cls_o__assoc_0) ).
fof(c_0_19,axiom,
! [X23,X24,X21,X18,X11,X2] : c_COMBS(X21,X24,X23,X11,X18,X2) = hAPP(hAPP(X21,X23),hAPP(X24,X23)),
file('<stdin>',cls_COMBS__def_0) ).
fof(c_0_20,axiom,
c_COMBS(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
file('<stdin>',cls_COMBS__def__raw_0) ).
fof(c_0_21,axiom,
! [X23,X24,X21,X18,X11,X2] : c_COMBC(X21,X24,X23,X11,X18,X2) = hAPP(hAPP(X21,X23),X24),
file('<stdin>',cls_COMBC__def_0) ).
fof(c_0_22,axiom,
c_COMBC(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),v_Q),
file('<stdin>',cls_COMBC__def__raw_0) ).
fof(c_0_23,axiom,
! [X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X21,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X21,X24,X16))) ),
file('<stdin>',cls_conseq_0) ).
fof(c_0_24,axiom,
! [X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X21,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X21,X24,X16))) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(c_0_25,axiom,
! [X54,X17,X12,X18,X11,X2] : hAPP(c_Set_Oimage(c_Fun_Ocomp(X12,X17,X18,X2,X11),X11,X2),X54) = hAPP(c_Set_Oimage(X12,X18,X2),hAPP(c_Set_Oimage(X17,X11,X18),X54)),
file('<stdin>',cls_image__compose_0) ).
fof(c_0_26,axiom,
! [X17,X12,X7,X18,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),hAPP(c_Set_Oimage(X17,X18,X11),X7)) = hAPP(c_Set_Oimage(c_COMBB(X12,X17,X11,X2,X18),X18,X2),X7),
file('<stdin>',cls_image__image_0) ).
fof(c_0_27,axiom,
! [X6,X17,X12,X18,X11,X2] : hAPP(c_Set_Ovimage(c_Fun_Ocomp(X17,X12,X18,X11,X2),X2,X11),X6) = hAPP(c_Set_Ovimage(X12,X2,X18),hAPP(c_Set_Ovimage(X17,X18,X11),X6)),
file('<stdin>',cls_vimage__compose_0) ).
fof(c_0_28,axiom,
! [X12,X9,X7,X11,X2] :
( ~ hBOOL(c_in(hAPP(X12,X9),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X11))
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2,X11) ),
file('<stdin>',cls_inj__on__insert_1) ).
fof(c_0_29,axiom,
! [X63,X64,X62,X51,X21] :
( ~ hBOOL(hAPP(X21,c_Hoare__Mirabelle_Otriple_Otriple__case(X62,c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,t_b),t_b,t_a)))
| hBOOL(hAPP(X21,hAPP(hAPP(hAPP(X62,X64),X51),X63))) ),
file('<stdin>',cls_triple_Osplit_0) ).
fof(c_0_30,axiom,
! [X60,X61,X5,X62,X21] :
( ~ hBOOL(hAPP(X21,c_Hoare__Mirabelle_Otriple_Otriple__case(X62,c_Hoare__Mirabelle_Otriple_Otriple(X5,X61,X60,t_b),t_b,t_a)))
| hBOOL(hAPP(X21,hAPP(hAPP(hAPP(X62,X5),X61),X60))) ),
file('<stdin>',cls_triple_Osplit__asm_0) ).
fof(c_0_31,axiom,
! [X26,X6,X56,X17,X57,X12,X58,X53,X18,X11,X2] :
( hAPP(X12,hAPP(X17,X6)) != hAPP(X57,hAPP(X56,X26))
| hAPP(c_Fun_Ocomp(X12,X17,X11,X2,X18),X6) = hAPP(c_Fun_Ocomp(X57,X56,X53,X2,X58),X26) ),
file('<stdin>',cls_comp__cong_0) ).
fof(c_0_32,axiom,
! [X17,X12,X7,X18,X11,X2] :
( c_Fun_Oinj__on(X17,hAPP(c_Set_Oimage(X12,X2,X18),X7),X18,X11)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X17,X12,X18,X11,X2),X7,X2,X11) ),
file('<stdin>',cls_inj__on__imageI_0) ).
fof(c_0_33,axiom,
! [X12,X10,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Fun_Oinj__on(X12,X10,X2,X11)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
file('<stdin>',cls_inj__on__Un_3) ).
fof(c_0_34,axiom,
! [X42,X41,X16,X30,X9,X53,X18,X11,X2] :
( c_Fun_Ocomp(X9,X30,X18,X11,X2) != c_Fun_Ocomp(X16,X41,X53,X11,X2)
| hAPP(X9,hAPP(X30,X42)) = hAPP(X16,hAPP(X41,X42)) ),
file('<stdin>',cls_o__eq__dest_0) ).
fof(c_0_35,axiom,
! [X17,X12,X7,X18,X11,X2] :
( c_Fun_Oinj__on(c_Fun_Ocomp(X17,X12,X11,X18,X2),X7,X2,X18)
| ~ c_Fun_Oinj__on(X17,hAPP(c_Set_Oimage(X12,X2,X11),X7),X11,X18)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
file('<stdin>',cls_comp__inj__on_0) ).
fof(c_0_36,axiom,
! [X15,X10,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_UN__extend__simps_I3_J_1) ).
fof(c_0_37,axiom,
! [X15,X10,X7,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool)))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_UN__simps_I3_J_1) ).
fof(c_0_38,axiom,
! [X15,X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)),
file('<stdin>',cls_UN__extend__simps_I5_J_0) ).
fof(c_0_39,axiom,
! [X37,X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X7,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Int__UN__distrib_0) ).
fof(c_0_40,axiom,
! [X15,X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))),
file('<stdin>',cls_UN__simps_I5_J_0) ).
fof(c_0_41,axiom,
! [X12,X9,X7,X11,X2] :
( c_Fun_Oinj__on(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2,X11)
| hBOOL(c_in(hAPP(X12,X9),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X11))
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
file('<stdin>',cls_inj__on__insert_2) ).
fof(c_0_42,axiom,
! [X12,X10,X7,X18,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X18,tc_fun(X11,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(c_Set_Ovimage(X12,X2,X11),X10,tc_fun(X11,tc_bool),tc_fun(X2,tc_bool),X18),X18,tc_fun(X2,tc_bool)),
file('<stdin>',cls_vimage__UN_0) ).
fof(c_0_43,axiom,
! [X12,X10,X7,X18,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X18,tc_fun(X11,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(c_Set_Oimage(X12,X11,X2),X10,tc_fun(X11,tc_bool),tc_fun(X2,tc_bool),X18),X18,tc_fun(X2,tc_bool)),
file('<stdin>',cls_image__UN_0) ).
fof(c_0_44,axiom,
! [X8,X9,X10,X7,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(hAPP(c_Set_Oinsert(X11),X9),X10,tc_fun(X11,tc_bool),tc_fun(X11,tc_bool),X2),X2,tc_fun(X11,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X11),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)))
| ~ hBOOL(c_in(X8,X7,X2)) ),
file('<stdin>',cls_UN__insert__distrib_0) ).
fof(c_0_45,axiom,
! [X9,X15,X10,X11,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Set_Oinsert(X2),X9),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_UN__extend__simps_I1_J_1) ).
fof(c_0_46,axiom,
! [X9,X15,X10,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Set_Oinsert(X2),X9),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool)))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_UN__simps_I1_J_1) ).
fof(c_0_47,axiom,
! [X12,X10,X7,X18,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X12,X18,X11),X7),X10,X11,tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(X10,X12,X11,tc_fun(X2,tc_bool),X18),X18,tc_fun(X2,tc_bool)),
file('<stdin>',cls_UN__simps_I10_J_0) ).
fof(c_0_48,axiom,
! [X12,X10,X7,X18,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(X10,X12,X18,tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X12,X11,X18),X7),X10,X18,tc_fun(X2,tc_bool)),
file('<stdin>',cls_UN__extend__simps_I10_J_0) ).
fof(c_0_49,axiom,
! [X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_UN__simps_I3_J_0) ).
fof(c_0_50,axiom,
! [X9,X10,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X9),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_UN__simps_I1_J_0) ).
fof(c_0_51,axiom,
! [X12,X10,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
file('<stdin>',cls_inj__on__Un_2) ).
fof(c_0_52,axiom,
! [X12,X16,X18,X11] : hAPP(c_Fun_Ocomp(c_COMBK(X16,X11,X18),X12,X18,X11,t_a),v_x) = X16,
file('<stdin>',cls_K__record__comp_0) ).
fof(c_0_53,axiom,
! [X12,X10,X7,X11,X2] : c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X12,X11,X2),X7)),hAPP(c_Set_Oimage(X12,X11,X2),X10)),tc_fun(X2,tc_bool)),
file('<stdin>',cls_image__Int__subset_0) ).
fof(c_0_54,axiom,
! [X17,X12,X18,X11,X2] :
( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X12,X17,X2,tc_fun(X11,X11),X18),X18,X11)
| ~ c_Finite__Set_Ofun__left__comm__idem(X12,X2,X11) ),
file('<stdin>',cls_fun__left__comm__idem_Ofun__left__comm__idem__apply_0) ).
fof(c_0_55,axiom,
! [X42,X30,X9,X18,X11,X2] : hAPP(X9,hAPP(X30,X42)) = hAPP(c_Fun_Ocomp(X9,X30,X18,X11,X2),X42),
file('<stdin>',cls_o__eq__dest__lhs_0) ).
fof(c_0_56,axiom,
! [X6,X17,X12,X18,X11,X2] : hAPP(c_Fun_Ocomp(X12,X17,X11,X2,X18),X6) = hAPP(X12,hAPP(X17,X6)),
file('<stdin>',cls_o__apply_0) ).
fof(c_0_57,axiom,
! [X23,X24,X21,X18,X11,X2] : hAPP(c_COMBB(X21,X24,X11,X2,X18),X23) = hAPP(X21,hAPP(X24,X23)),
file('<stdin>',cls_COMBB__def_0) ).
fof(c_0_58,axiom,
! [X17,X12,X18,X11] : hAPP(c_Fun_Ocomp(X12,X17,X18,X11,t_a),v_x) = hAPP(X12,hAPP(X17,v_x)),
file('<stdin>',cls_o__def_0) ).
fof(c_0_59,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
file('<stdin>',cls_COMBB__def__raw_0) ).
fof(c_0_60,axiom,
! [X21,X39,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OSKIP,X21,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
file('<stdin>',cls_hoare__derivs_OSkip_0) ).
fof(c_0_61,axiom,
! [X14,X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),X7),X10),X14,X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X14,X11,tc_fun(X2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X14,X11,tc_fun(X2,tc_bool))),
file('<stdin>',cls_UN__Un_0) ).
fof(c_0_62,axiom,
! [X12,X30,X9,X11,X2] :
( hAPP(X12,X9) = X30
| ~ hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Set_Oinsert(X11),X30),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)))),X2)) ),
file('<stdin>',cls_vimage__singleton__eq_0) ).
fof(c_0_63,axiom,
! [X12,X9,X10,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Set_Oinsert(X11),X9),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Set_Oinsert(X11),X9),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))))),hAPP(c_Set_Ovimage(X12,X2,X11),X10)),
file('<stdin>',cls_vimage__insert_0) ).
fof(c_0_64,axiom,
! [X12,X15,X10,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X2,X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),hAPP(c_Set_Oimage(X12,X2,X11),X7)),hAPP(c_Set_Oimage(X12,X2,X11),X10))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X12,X15,X2,X11) ),
file('<stdin>',cls_inj__on__image__Int_0) ).
fof(c_0_65,axiom,
! [X15,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),X15) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15))
| c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_0) ).
fof(c_0_66,axiom,
! [X12,X9,X52,X2] : hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X52,X2),hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X12,X9)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X52)),
file('<stdin>',cls_vimage__singleton__eq_1) ).
fof(c_0_67,axiom,
! [X12,X10,X7,X11,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X12,X11,X2),X7),hAPP(c_Set_Oimage(X12,X11,X2),X10),tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X12,X11,X2),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X11,tc_bool))),tc_fun(X2,tc_bool)),
file('<stdin>',cls_image__diff__subset_0) ).
fof(c_0_68,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)),X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X7)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X15),X7)),
file('<stdin>',cls_Un__Int__distrib2_0) ).
fof(c_0_69,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X7)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X7)),
file('<stdin>',cls_Int__Un__distrib2_0) ).
fof(c_0_70,axiom,
! [X12,X30,X9,X2] :
( X9 = X30
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X30)) ),
file('<stdin>',cls_fold1Set__sing_0) ).
fof(c_0_71,axiom,
! [X30,X9,X10,X7,X11,X2] :
( hBOOL(c_in(X30,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X11))
| ~ hBOOL(c_in(X30,hAPP(X10,X9),X11))
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_UN__I_0) ).
fof(c_0_72,axiom,
! [X6,X30,X10,X7,X11,X2] :
( hBOOL(c_in(X30,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(c_in(X30,hAPP(X10,X6),X2))
| ~ hBOOL(c_in(X6,X7,X11)) ),
file('<stdin>',cls_UN__iff_2) ).
fof(c_0_73,axiom,
! [X12,X15,X10,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X12,X2,X11),X7),hAPP(c_Set_Oimage(X12,X2,X11),X10),tc_fun(X11,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X12,X15,X2,X11) ),
file('<stdin>',cls_inj__on__image__set__diff_0) ).
fof(c_0_74,axiom,
! [X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X7,X11,tc_fun(X2,tc_bool))),X10) = X10,
file('<stdin>',cls_UN__extend__simps_I2_J_0) ).
fof(c_0_75,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X15)),
file('<stdin>',cls_Un__Int__distrib_0) ).
fof(c_0_76,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15)),
file('<stdin>',cls_Int__Un__distrib_0) ).
fof(c_0_77,axiom,
! [X30,X9,X10,X7,X11,X2] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X30))
| ~ hBOOL(hAPP(hAPP(X10,X9),X30))
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_SUP1__I_0) ).
fof(c_0_78,axiom,
! [X6,X30,X10,X7,X11,X2] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X30))
| ~ hBOOL(hAPP(hAPP(X10,X6),X30))
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_SUP1__iff_2) ).
fof(c_0_79,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_3) ).
fof(c_0_80,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_diff__single__insert_0) ).
fof(c_0_81,axiom,
! [X6,X12,X11,X2] :
( c_Fun_Ocomp(hAPP(X12,X6),hAPP(X12,X6),X11,X11,X11) = hAPP(X12,X6)
| ~ c_Finite__Set_Ofun__left__comm__idem(X12,X2,X11) ),
file('<stdin>',cls_fun__left__comm__idem_Ofun__comp__idem_0) ).
fof(c_0_82,axiom,
! [X6,X21,X7,X2] :
( hBOOL(c_in(X6,X7,X2))
| ~ hBOOL(c_in(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Collect(X21,X2)),X2)) ),
file('<stdin>',cls_Int__Collect_0) ).
fof(c_0_83,axiom,
! [X6,X2] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2))),
file('<stdin>',cls_Nitpick_OEx1__def_2) ).
fof(c_0_84,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_4) ).
fof(c_0_85,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X10,X2))
| hBOOL(c_in(X16,X7,X2))
| ~ hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2)) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_86,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X12,X11,X2),X7)),hAPP(c_Set_Oimage(X12,X11,X2),X10)),
file('<stdin>',cls_image__Un_0) ).
fof(c_0_87,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X12,X2,X11),X7)),hAPP(c_Set_Ovimage(X12,X2,X11),X10)),
file('<stdin>',cls_vimage__Int_0) ).
fof(c_0_88,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X12,X2,X11),X7)),hAPP(c_Set_Ovimage(X12,X2,X11),X10)),
file('<stdin>',cls_vimage__Un_0) ).
fof(c_0_89,axiom,
! [X15,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15))
| ~ c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_1) ).
fof(c_0_90,axiom,
! [X6,X21,X7,X2] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Collect(X21,X2)),X2)) ),
file('<stdin>',cls_Int__Collect_1) ).
fof(c_0_91,axiom,
! [X6,X37,X10,X7,X11,X2] :
( c_lessequals(hAPP(X7,X6),X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X37,X11))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X11,tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_UN__subset__iff_0) ).
fof(c_0_92,axiom,
! [X12,X10,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X2,X11),X7) != hAPP(c_Set_Oimage(X12,X2,X11),X10)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11)
| X7 = X10 ),
file('<stdin>',cls_inj__on__Un__image__eq__iff_0) ).
fof(c_0_93,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X7,X2))
| ~ hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2)) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_94,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2)) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_95,axiom,
! [X38,X37,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),hAPP(X7,X38)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X2,tc_fun(X11,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X2,tc_fun(X11,tc_bool))
| ~ hBOOL(c_in(X38,X37,X2)) ),
file('<stdin>',cls_UN__absorb_0) ).
fof(c_0_96,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)),
file('<stdin>',cls_Int__assoc_0) ).
fof(c_0_97,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),X15) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)),
file('<stdin>',cls_Un__assoc_0) ).
fof(c_0_98,axiom,
! [X6,X10,X7,X11,X2] :
( c_Finite__Set_Ofinite(hAPP(X10,X6),X11)
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X11)
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_finite__UN_0) ).
fof(c_0_99,axiom,
! [X9,X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X11),X9),X7),X10,X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(X10,X9)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool))),
file('<stdin>',cls_UN__insert_0) ).
fof(c_0_100,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_0) ).
fof(c_0_101,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),X15) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__Int__distrib2_0) ).
fof(c_0_102,axiom,
! [X33,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X2)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2)
| c_Finite__Set_Ofold1(X33,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2) = hAPP(hAPP(X33,c_Finite__Set_Ofold1(X33,X7,X2)),c_Finite__Set_Ofold1(X33,X10,X2)) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__Un_0) ).
fof(c_0_103,axiom,
! [X12,X9,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X9),X7,X11))
| ~ hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),X7),X2)) ),
file('<stdin>',cls_vimageD_0) ).
fof(c_0_104,axiom,
! [X12,X9,X10,X11,X2] :
( hBOOL(c_in(hAPP(X12,X9),X10,X11))
| ~ hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),X10),X2)) ),
file('<stdin>',cls_vimageE_0) ).
fof(c_0_105,axiom,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X11)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
file('<stdin>',cls_inj__on__Un_0) ).
fof(c_0_106,axiom,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X10,X2,X11)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
file('<stdin>',cls_inj__on__Un_1) ).
fof(c_0_107,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)),X2) ),
file('<stdin>',cls_distrib__sup__le_0) ).
fof(c_0_108,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)),X2) ),
file('<stdin>',cls_distrib__inf__le_0) ).
fof(c_0_109,axiom,
! [X6,X12,X2] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X6)),
file('<stdin>',cls_fold1Set__sing_1) ).
fof(c_0_110,axiom,
! [X12,X7,X2] :
( hAPP(c_Set_Oimage(X12,X2,X2),X7) = X7
| ~ c_Fun_Oinj__on(X12,X7,X2,X2)
| ~ c_lessequals(hAPP(c_Set_Oimage(X12,X2,X2),X7),X7,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_endo__inj__surj_0) ).
fof(c_0_111,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_112,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_113,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15),X10,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__Int2_0) ).
fof(c_0_114,axiom,
! [X6,X21,X7,X2] :
( hBOOL(c_in(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Collect(X21,X2)),X2))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_Int__Collect_2) ).
fof(c_0_115,axiom,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(X10,X6))
| hBOOL(hAPP(X7,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X6)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_116,axiom,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(X7,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X6)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_117,axiom,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(X10,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X6)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_118,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X7,X15,tc_fun(X2,tc_bool))),
file('<stdin>',cls_Diff__Int_0) ).
fof(c_0_119,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X7,X15,tc_fun(X2,tc_bool))),
file('<stdin>',cls_Diff__Un_0) ).
fof(c_0_120,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X15,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X10,X15,tc_fun(X2,tc_bool))),
file('<stdin>',cls_Un__Diff_0) ).
fof(c_0_121,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X10),tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__Int__distrib_0) ).
fof(c_0_122,axiom,
! [X20,X6,X2] :
( X20 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X20)) ),
file('<stdin>',cls_Nitpick_OEx1__def_3) ).
fof(c_0_123,axiom,
! [X43,X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X43),tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X43,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_124,axiom,
! [X43,X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X15),X43),tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X43,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_125,axiom,
! [X6,X12,X7,X11,X2] :
( hBOOL(hAPP(X7,hAPP(X12,X6)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X12,X2,X11),X7),X6)) ),
file('<stdin>',cls_vimage__code_0) ).
fof(c_0_126,axiom,
! [X9,X15,X10,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)),X15) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15))
| ~ hBOOL(c_in(X9,X15,X2)) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_127,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15)),
file('<stdin>',cls_Int__left__commute_0) ).
fof(c_0_128,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X15)),
file('<stdin>',cls_Un__left__commute_0) ).
fof(c_0_129,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_130,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X10,X2)) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_131,axiom,
! [X66,X55,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X55),X66),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X55),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
file('<stdin>',cls_hoare__derivs_Oinsert_0) ).
fof(c_0_132,axiom,
! [X12,X9,X10,X11,X2] :
( hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X11,X2),X10),X11))
| ~ hBOOL(c_in(hAPP(X12,X9),X10,X2)) ),
file('<stdin>',cls_vimageI_0) ).
fof(c_0_133,axiom,
! [X12,X9,X7,X11,X2] :
( hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X11,X2),X7),X11))
| ~ hBOOL(c_in(hAPP(X12,X9),X7,X2)) ),
file('<stdin>',cls_vimageI2_0) ).
fof(c_0_134,axiom,
! [X12,X9,X10,X11,X2] :
( hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),X10),X2))
| ~ hBOOL(c_in(hAPP(X12,X9),X10,X11)) ),
file('<stdin>',cls_vimage__eq_1) ).
fof(c_0_135,axiom,
! [X6,X12,X10,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X6),X10,X2))
| ~ hBOOL(c_in(X6,X7,X11))
| ~ c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),X7),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_136,axiom,
! [X63,X64,X62,X51,X11,X2] : c_Hoare__Mirabelle_Otriple_Otriple__case(X62,c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X11),X11,X2) = hAPP(hAPP(hAPP(X62,X64),X51),X63),
file('<stdin>',cls_triple_Ocases_0) ).
fof(c_0_137,axiom,
! [X63,X64,X62,X51,X11,X2] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X62,c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X11),X11,X2) = hAPP(hAPP(hAPP(X62,X64),X51),X63),
file('<stdin>',cls_triple_Orecs_0) ).
fof(c_0_138,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X11,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X12,X2,X11),X7),hAPP(c_Set_Ovimage(X12,X2,X11),X10),tc_fun(X2,tc_bool)),
file('<stdin>',cls_vimage__Diff_0) ).
fof(c_0_139,axiom,
! [X16,X10,X7,X2] :
( ~ hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)) ),
file('<stdin>',cls_DiffE_1) ).
fof(c_0_140,axiom,
! [X30,X9,X2] :
( X30 = X9
| ~ hBOOL(c_in(X30,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_141,axiom,
! [X9,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__insert2_0) ).
fof(c_0_142,axiom,
! [X6,X12,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X2,X11),X7),X11))
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_143,axiom,
! [X6,X12,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X11,X2),X7),X2))
| ~ hBOOL(c_in(X6,X7,X11)) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_144,axiom,
! [X6,X12,X7,X11,X2] :
( ~ hBOOL(c_in(X6,X7,X11))
| hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X11,X2),X7),X2)) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_145,axiom,
! [X6,X12,X7,X52,X2] :
( ~ hBOOL(c_in(X6,X7,X52))
| hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X52,X2),X7),X2)) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_146,axiom,
! [X9,X10,X7,X11,X2] :
( c_lessequals(hAPP(X10,X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),tc_fun(X11,tc_bool))
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_UN__upper_0) ).
fof(c_0_147,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X9 = X41
| X9 = X16 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_148,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X30 = X16
| X9 = X16 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_149,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X9 = X41
| X30 = X41 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_150,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X30 = X16
| X30 = X41 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_151,axiom,
! [X12,X7,X11,X2] :
( c_Finite__Set_Ofinite(X7,X11)
| ~ c_Fun_Oinj__on(X12,X7,X11,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X12,X11,X2),X7),X2) ),
file('<stdin>',cls_finite__imageD_0) ).
fof(c_0_152,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Diff__subset__conv_1) ).
fof(c_0_153,axiom,
! [X9,X10,X11,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,X11,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
file('<stdin>',cls_UN__extend__simps_I1_J_0) ).
fof(c_0_154,axiom,
! [X12,X9,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X11)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2,X11) ),
file('<stdin>',cls_inj__on__insert_0) ).
fof(c_0_155,axiom,
! [X12,X7,X11,X2] : c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),hAPP(c_Set_Ovimage(X12,X11,X2),X7)),X7,tc_fun(X2,tc_bool)),
file('<stdin>',cls_image__vimage__subset_0) ).
fof(c_0_156,axiom,
! [X9,X7,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))) = X7
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_insert__Diff_0) ).
fof(c_0_157,axiom,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2,X11)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
file('<stdin>',cls_inj__on__diff_0) ).
fof(c_0_158,axiom,
! [X9,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X7)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),
file('<stdin>',cls_insert__inter__insert_0) ).
fof(c_0_159,axiom,
! [X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,X11,tc_fun(X2,tc_bool))) = X7,
file('<stdin>',cls_UN__extend__simps_I3_J_0) ).
fof(c_0_160,axiom,
! [X20,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X20)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| X6 = X20
| ~ hBOOL(c_in(X20,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_inj__onD_0) ).
fof(c_0_161,axiom,
! [X5,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X5)
| ~ hBOOL(c_in(X5,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| X6 = X5 ),
file('<stdin>',cls_inj__on__def_0) ).
fof(c_0_162,axiom,
! [X20,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X20)
| ~ hBOOL(c_in(X20,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| X6 = X20 ),
file('<stdin>',cls_inj__on__iff_0) ).
fof(c_0_163,axiom,
! [X20,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X20)
| ~ hBOOL(c_in(X20,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| X6 = X20
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
file('<stdin>',cls_inj__on__contraD_0) ).
fof(c_0_164,axiom,
! [X69,X63,X70,X64,X4,X51,X2] :
( c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X70,X4,X69,X2)
| X64 = X70 ),
file('<stdin>',cls_triple_Oinject_0) ).
fof(c_0_165,axiom,
! [X69,X63,X70,X64,X4,X51,X2] :
( c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X70,X4,X69,X2)
| X51 = X4 ),
file('<stdin>',cls_triple_Oinject_1) ).
fof(c_0_166,axiom,
! [X69,X63,X70,X64,X4,X51,X2] :
( c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X70,X4,X69,X2)
| X63 = X69 ),
file('<stdin>',cls_triple_Oinject_2) ).
fof(c_0_167,axiom,
! [X12,X7,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X2)
| ~ c_lessequals(X7,hAPP(c_Set_Oimage(X12,X2,X2),X7),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_finite__surj__inj_0) ).
fof(c_0_168,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X7,X2))
| ~ hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)) ),
file('<stdin>',cls_DiffE_0) ).
fof(c_0_169,axiom,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X11)
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X12,X10,X2,X11) ),
file('<stdin>',cls_subset__inj__on_0) ).
fof(c_0_170,axiom,
! [X9,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10))
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_171,axiom,
! [X13,X14,X7,X11,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_lessequals(hAPP(X14,X13),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X14,X2,X11),X11)
| ~ hBOOL(c_in(X13,X7,X2)) ),
file('<stdin>',cls_le__SUPI_0) ).
fof(c_0_172,axiom,
! [X9,X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)),X2) ),
file('<stdin>',cls_finite__Diff__insert_0) ).
fof(c_0_173,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)) = X7,
file('<stdin>',cls_Un__Diff__Int_0) ).
fof(c_0_174,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Diff__subset__conv_0) ).
fof(c_0_175,axiom,
! [X10,X7,X11,X2] : c_HOL_Ominus__class_Ominus(X7,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X7,
file('<stdin>',cls_INT__extend__simps_I4_J_0) ).
fof(c_0_176,axiom,
! [X6,X12,X2] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X6)),
file('<stdin>',cls_empty__fold1SetE_0) ).
fof(c_0_177,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2))
| hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
file('<stdin>',cls_DiffI_0) ).
fof(c_0_178,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2))
| hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
file('<stdin>',cls_Diff__iff_2) ).
fof(c_0_179,axiom,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X6))
| ~ hBOOL(hAPP(X10,X6))
| ~ hBOOL(hAPP(X7,X6)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_180,axiom,
! [X9,X15,X10,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)),X15) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)),
file('<stdin>',cls_Un__insert__left_0) ).
fof(c_0_181,axiom,
! [X6,X10,X7,X11,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool))
| hAPP(X10,X6) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X11)) ),
file('<stdin>',cls_UNION__empty__conv_I1_J_0) ).
fof(c_0_182,axiom,
! [X6,X10,X7,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(X10,X6) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X11)) ),
file('<stdin>',cls_UNION__empty__conv_I2_J_0) ).
fof(c_0_183,axiom,
! [X6,X12,X7,X11,X2] :
( ~ c_lessequals(X6,X7,tc_fun(X11,tc_bool))
| c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),X6),hAPP(c_Set_Oimage(X12,X11,X2),X7),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_184,axiom,
! [X12,X10,X7,X11,X2] :
( c_lessequals(hAPP(c_Set_Oimage(X12,X2,X11),X7),hAPP(c_Set_Oimage(X12,X2,X11),X10),tc_fun(X11,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_185,axiom,
! [X12,X10,X7,X11,X2] :
( c_lessequals(hAPP(c_Set_Ovimage(X12,X11,X2),X7),hAPP(c_Set_Ovimage(X12,X11,X2),X10),tc_fun(X11,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_vimage__mono_0) ).
fof(c_0_186,axiom,
! [X9,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),
file('<stdin>',cls_insert__Diff__single_0) ).
fof(c_0_187,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X15,tc_fun(X2,tc_bool))),
file('<stdin>',cls_Int__Diff_0) ).
fof(c_0_188,axiom,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X6))
| ~ hBOOL(hAPP(X7,X6)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_189,axiom,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X6))
| ~ hBOOL(hAPP(X10,X6)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_190,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_191,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_192,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X15,X7,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_193,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X15,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_194,axiom,
! [X6,X12,X7,X11,X2] :
( hAPP(hAPP(c_Set_Oinsert(X11),hAPP(X12,X6)),hAPP(c_Set_Oimage(X12,X2,X11),X7)) = hAPP(c_Set_Oimage(X12,X2,X11),X7)
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_195,axiom,
! [X6,X12,X7,X11,X2] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X12,X2,X11),X7),X6))
| ~ hBOOL(hAPP(X7,hAPP(X12,X6))) ),
file('<stdin>',cls_vimage__code_1) ).
fof(c_0_196,axiom,
! [X9,X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2) ),
file('<stdin>',cls_finite__Diff__insert_1) ).
fof(c_0_197,axiom,
! [X43,X15,X10,X7,X2] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X15,X43,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X43,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Diff__mono_0) ).
fof(c_0_198,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X19),X6)) ),
file('<stdin>',cls_sup__inf__distrib2_0) ).
fof(c_0_199,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X19),X6)) ),
file('<stdin>',cls_inf__sup__distrib2_0) ).
fof(c_0_200,axiom,
! [X6,X10,X7,X2] :
( ~ hBOOL(c_in(X6,X10,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_disjoint__iff__not__equal_0) ).
fof(c_0_201,axiom,
! [X9,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__insert_0) ).
fof(c_0_202,axiom,
! [X6,X16,X7,X11,X2] :
( hAPP(c_Set_Oimage(c_COMBK(X16,X11,X2),X2,X11),X7) = hAPP(hAPP(c_Set_Oinsert(X11),X16),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)))
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_image__constant_0) ).
fof(c_0_203,axiom,
! [X30,X9,X7,X2] :
( hBOOL(c_in(X9,X7,X2))
| X9 = X30
| ~ hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X30),X7),X2)) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_204,axiom,
! [X9,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X7),
file('<stdin>',cls_insert__is__Un_0) ).
fof(c_0_205,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_206,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_207,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_208,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_209,axiom,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X16,X9,X2)
| ~ c_lessequals(X9,X30,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_0) ).
fof(c_0_210,axiom,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X30,X41,X2)
| ~ c_lessequals(X9,X30,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_1) ).
fof(c_0_211,axiom,
! [X9,X15,X10,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)
| hBOOL(c_in(X9,X15,X2)) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_212,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X7),
file('<stdin>',cls_Un__Diff__cancel2_0) ).
fof(c_0_213,axiom,
! [X30,X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30) ),
file('<stdin>',cls_Inf__binary_0) ).
fof(c_0_214,axiom,
! [X30,X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30) ),
file('<stdin>',cls_Sup__binary_0) ).
fof(c_0_215,axiom,
! [X9,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),
file('<stdin>',cls_Un__insert__right_0) ).
fof(c_0_216,axiom,
! [X6,X7,X2] :
( X7 = hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_217,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),
file('<stdin>',cls_Int__left__absorb_0) ).
fof(c_0_218,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),
file('<stdin>',cls_Un__left__absorb_0) ).
fof(c_0_219,axiom,
! [X12,X9,X10,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),hAPP(hAPP(c_Set_Oinsert(X11),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X12,X9)),hAPP(c_Set_Oimage(X12,X11,X2),X10)),
file('<stdin>',cls_image__insert_0) ).
fof(c_0_220,axiom,
! [X5,X6,X7,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X5,X2)
| ~ hBOOL(c_in(X5,X7,X2))
| ~ c_lessequals(X6,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X7,X2),X2)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_below__fold1__iff_0) ).
fof(c_0_221,axiom,
! [X12,X10,X7,X11,X2] :
( c_Finite__Set_Ofinite(X10,X11)
| ~ c_lessequals(X10,hAPP(c_Set_Oimage(X12,X2,X11),X7),tc_fun(X11,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_finite__surj_0) ).
fof(c_0_222,axiom,
! [X6,X2] : hBOOL(c_in(X6,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)),
file('<stdin>',cls_singleton__iff_1) ).
fof(c_0_223,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)) ),
file('<stdin>',cls_sup__inf__distrib1_0) ).
fof(c_0_224,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)) ),
file('<stdin>',cls_inf__sup__distrib1_0) ).
fof(c_0_225,axiom,
! [X5,X6,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X5),hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X2),X6),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
file('<stdin>',cls_doubleton__eq__iff_4) ).
fof(c_0_226,axiom,
! [X9,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)
| hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_227,axiom,
! [X6,X7,X2] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) = X7
| hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_Diff__insert__absorb_0) ).
fof(c_0_228,axiom,
! [X6,X10,X7,X2] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X6),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)))
| hBOOL(c_in(X6,X10,X2)) ),
file('<stdin>',cls_insert__Diff__if_1) ).
fof(c_0_229,axiom,
! [X30,X9,X10,X2] :
( hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X30),X10),X2))
| ~ hBOOL(c_in(X9,X10,X2)) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_230,axiom,
! [X30,X9,X7,X2] :
( hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X30),X7),X2))
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_231,axiom,
! [X6,X33,X7,X2] :
( c_Finite__Set_Ofold1(X33,hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X2) = hAPP(hAPP(X33,X6),c_Finite__Set_Ofold1(X33,X7,X2))
| hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__insert_0) ).
fof(c_0_232,axiom,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(X39,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2) ),
file('<stdin>',cls_finite__Un_1) ).
fof(c_0_233,axiom,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(X40,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2) ),
file('<stdin>',cls_finite__Un_0) ).
fof(c_0_234,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X10,X2)) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_235,axiom,
! [X15,X10,X7,X2] :
( c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X15,X7,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X7
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_double__diff_0) ).
fof(c_0_236,axiom,
! [X16,X7,X11,X2] :
( hAPP(c_Set_Ovimage(c_COMBK(X16,X11,X2),X2,X11),X7) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X16,X7,X11)) ),
file('<stdin>',cls_vimage__const_1) ).
fof(c_0_237,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_238,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_239,axiom,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X30,X41,X2)
| ~ c_lessequals(X16,X9,X2) ),
file('<stdin>',cls_atLeastatMost__subset__iff_3) ).
fof(c_0_240,axiom,
! [X16,X7,X11,X2] :
( hAPP(c_Set_Oimage(c_COMBK(X16,X2,X11),X11,X2),X7) = hAPP(hAPP(c_Set_Oinsert(X2),X16),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_image__constant__conv_1) ).
fof(c_0_241,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),
file('<stdin>',cls_Un__Diff__cancel_0) ).
fof(c_0_242,axiom,
! [X6,X10,X7,X2] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X10,X2)) ),
file('<stdin>',cls_insert__Diff1_0) ).
fof(c_0_243,axiom,
! [X17,X12,X11] :
( ~ class_Lattices_Olattice(X11)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X11)),X12),X17),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11),hAPP(X12,v_x)),hAPP(X17,v_x)) ),
file('<stdin>',cls_inf__fun__eq_0) ).
fof(c_0_244,axiom,
! [X17,X12,X11] :
( ~ class_Lattices_Olattice(X11)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X11)),X12),X17),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11),hAPP(X12,v_x)),hAPP(X17,v_x)) ),
file('<stdin>',cls_sup__fun__eq_0) ).
fof(c_0_245,axiom,
! [X38,X2] :
( ~ class_Orderings_Oorder(X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X38),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_SetInterval_Oord__class_OlessThan(X38,X2),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X38),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
file('<stdin>',cls_single__Diff__lessThan_0) ).
fof(c_0_246,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))) = X10
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Diff__partition_0) ).
fof(c_0_247,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_248,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_249,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_250,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_251,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_252,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_253,axiom,
! [X16,X11,X2] : hAPP(c_Set_Oimage(c_COMBK(X16,X2,X11),X11,X2),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_image__constant__conv_0) ).
fof(c_0_254,axiom,
! [X55,X10,X7,X2] :
( hBOOL(c_in(X55,X10,X2))
| ~ hBOOL(c_in(X55,X7,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_255,axiom,
! [X6,X10,X7,X2] :
( hBOOL(c_in(X6,X10,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_256,axiom,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_257,axiom,
! [X6,X10,X7,X2] :
( hBOOL(c_in(X6,X10,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_258,axiom,
! [X9,X43,X15,X2] :
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X9),X15),hAPP(hAPP(c_Set_Oinsert(X2),X9),X43),tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X43,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_259,axiom,
! [X20,X6,X7,X2] :
( hBOOL(hAPP(X7,X6))
| X20 = X6
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X20),X7),X6)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_260,axiom,
! [X6,X10,X7,X2] :
( hBOOL(c_in(X6,X10,X2))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_261,axiom,
! [X14,X7,X11,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBK(X14,X11,X2),X2,X11) = X14
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_SUP__const_0) ).
fof(c_0_262,axiom,
! [X6,X10,X7,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X6),X7) != hAPP(hAPP(c_Set_Oinsert(X2),X6),X10)
| hBOOL(c_in(X6,X10,X2))
| hBOOL(c_in(X6,X7,X2))
| X7 = X10 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_263,axiom,
! [X6,X21,X2] :
( ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_264,axiom,
! [X9,X7,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X7,X2),X9,X2)
| ~ hBOOL(c_in(X9,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_fold1__belowI_0) ).
fof(c_0_265,axiom,
! [X6,X21,X2] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_266,axiom,
! [X10,X7,X2] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X10,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Int__lower2_0) ).
fof(c_0_267,axiom,
! [X10,X7,X2] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X7,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Int__lower1_0) ).
fof(c_0_268,axiom,
! [X10,X7,X2] : c_lessequals(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)),
file('<stdin>',cls_Un__upper1_0) ).
fof(c_0_269,axiom,
! [X10,X7,X2] : c_lessequals(X10,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)),
file('<stdin>',cls_Un__upper2_0) ).
fof(c_0_270,axiom,
! [X6,X10,X7,X2] :
( c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_271,axiom,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool))
| c_lessequals(X9,X30,X2) ),
file('<stdin>',cls_atLeastatMost__subset__iff_2) ).
fof(c_0_272,axiom,
! [X28,X29,X12,X9,X11,X2] :
( ~ c_Orderings_Olinorder(X28,X29,X2)
| c_Finite__Set_Ofold1(X12,hAPP(hAPP(c_Set_Oinsert(X11),X9),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),X11) = X9 ),
file('<stdin>',cls_linorder_OMax__singleton_0) ).
fof(c_0_273,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)) = X7 ),
file('<stdin>',cls_Diff__triv_0) ).
fof(c_0_274,axiom,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X39,X2)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
file('<stdin>',cls_finite__UnI_0) ).
fof(c_0_275,axiom,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X39,X2)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
file('<stdin>',cls_finite__Un_2) ).
fof(c_0_276,axiom,
! [X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X28,X6),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2)
| ~ hBOOL(hAPP(hAPP(X29,X6),X6)) ),
file('<stdin>',cls_linorder_Oantisym__conv2_1) ).
fof(c_0_277,axiom,
! [X20,X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ hBOOL(hAPP(hAPP(X29,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Onot__le_1) ).
fof(c_0_278,axiom,
! [X20,X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ hBOOL(hAPP(hAPP(X28,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_OleD_0) ).
fof(c_0_279,axiom,
! [X20,X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ hBOOL(hAPP(hAPP(X29,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Onot__less__iff__gr__or__eq_1) ).
fof(c_0_280,axiom,
! [X9,X2] : ~ hBOOL(c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('<stdin>',cls_emptyE_0) ).
fof(c_0_281,axiom,
! [X16,X2] : ~ hBOOL(c_in(X16,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('<stdin>',cls_empty__iff_0) ).
fof(c_0_282,axiom,
! [X6,X2] : ~ hBOOL(c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('<stdin>',cls_ex__in__conv_0) ).
fof(c_0_283,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X2)
| ~ c_lessequals(X6,X30,X2)
| ~ c_lessequals(X6,X9,X2) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_284,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2)
| ~ c_lessequals(X6,X19,X2)
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_285,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2)
| ~ c_lessequals(X6,X19,X2)
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_286,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X19,X2)
| ~ c_lessequals(X20,X19,X2)
| ~ c_lessequals(X6,X19,X2) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_287,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19),X6,X2)
| ~ c_lessequals(X19,X6,X2)
| ~ c_lessequals(X20,X6,X2) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_288,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X6,X2)
| ~ c_lessequals(X30,X6,X2)
| ~ c_lessequals(X9,X6,X2) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_289,axiom,
! [X8,X59,X2] :
( ~ class_Orderings_Oorder(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_SetInterval_Oord__class_OlessThan(X59,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X59,X8,X2)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_ivl__disj__int_I4_J_0) ).
fof(c_0_290,axiom,
! [X33,X16,X30,X9,X2] :
( hAPP(hAPP(X33,hAPP(hAPP(X33,X9),X30)),X16) = hAPP(hAPP(X33,X9),hAPP(hAPP(X33,X30),X16))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).
fof(c_0_291,axiom,
! [X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X9 = X30 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_292,axiom,
! [X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_Un__empty_2) ).
fof(c_0_293,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__disjoint_0) ).
fof(c_0_294,axiom,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
file('<stdin>',cls_finite__Int_0) ).
fof(c_0_295,axiom,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X39,X2) ),
file('<stdin>',cls_finite__Int_1) ).
fof(c_0_296,axiom,
! [X15,X10,X7,X2] :
( c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_297,axiom,
! [X25,X20,X26,X6,X2] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X6,X20,X2) != c_HOL_Ominus__class_Ominus(X26,X25,X2)
| c_lessequals(X20,X6,X2)
| ~ c_lessequals(X25,X26,X2) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_298,axiom,
! [X25,X20,X26,X6,X2] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X6,X20,X2) != c_HOL_Ominus__class_Ominus(X26,X25,X2)
| c_lessequals(X25,X26,X2)
| ~ c_lessequals(X20,X6,X2) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_299,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_300,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_301,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_302,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_303,axiom,
! [X6,X10,X2] : hBOOL(c_in(X6,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),X2)),
file('<stdin>',cls_insertCI_1) ).
fof(c_0_304,axiom,
! [X9,X10,X2] : hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),X2)),
file('<stdin>',cls_insertI1_0) ).
fof(c_0_305,axiom,
! [X6,X7,X2] : hBOOL(c_in(X6,hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X2)),
file('<stdin>',cls_insert__iff_1) ).
fof(c_0_306,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X9,X6,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X6,X2) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_307,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X30,X6,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X6,X2) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_308,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,X19,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X19,X2) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_309,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X20,X19,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X19,X2) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_310,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X19,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_311,axiom,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X20,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_312,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X30,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X2) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_313,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X9,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X2) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_314,axiom,
! [X20,X6,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X6),hAPP(hAPP(c_Set_Oinsert(X2),X20),X7)) = hAPP(hAPP(c_Set_Oinsert(X2),X20),hAPP(hAPP(c_Set_Oinsert(X2),X6),X7)),
file('<stdin>',cls_insert__commute_0) ).
fof(c_0_315,axiom,
! [X10,X7,X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__idemp_0) ).
fof(c_0_316,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) != X10
| c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_317,axiom,
! [X30,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X30),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_318,axiom,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| ~ hBOOL(hAPP(hAPP(X28,X6),X20))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Oantisym__conv1_0) ).
fof(c_0_319,axiom,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Oantisym__conv2_0) ).
fof(c_0_320,axiom,
! [X12,X11,X2] : c_Fun_Oinj__on(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X11),
file('<stdin>',cls_inj__on__empty_0) ).
fof(c_0_321,axiom,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X10,X2) ),
file('<stdin>',cls_finite__Diff2_0) ).
fof(c_0_322,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_323,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_324,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X7),
file('<stdin>',cls_Un__commute_0) ).
fof(c_0_325,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X7),
file('<stdin>',cls_Int__commute_0) ).
fof(c_0_326,axiom,
! [X27,X14,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X27,X2),c_Finite__Set_Olinorder__class_OMin(X14,X2),X2)
| ~ c_Finite__Set_Ofinite(X27,X2)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X14,X27,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Min__antimono_0) ).
fof(c_0_327,axiom,
! [X27,X14,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X14,X2),c_Finite__Set_Olinorder__class_OMax(X27,X2),X2)
| ~ c_Finite__Set_Ofinite(X27,X2)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X14,X27,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Max__mono_0) ).
fof(c_0_328,axiom,
! [X9,X21,X2] :
( hBOOL(hAPP(X21,X9))
| ~ hBOOL(c_in(X9,c_Collect(X21,X2),X2)) ),
file('<stdin>',cls_CollectD_0) ).
fof(c_0_329,axiom,
! [X6,X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X6,c_Finite__Set_Olinorder__class_OMax(X7,X2),X2)
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_Max__ge_0) ).
fof(c_0_330,axiom,
! [X6,X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X7,X2),X6,X2)
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_Min__le_0) ).
fof(c_0_331,axiom,
! [X20,X6,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X20),X7),X6))
| ~ hBOOL(hAPP(X7,X6)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_332,axiom,
! [X65,X66,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_lessequals(X66,X65,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X65,X2) ),
file('<stdin>',cls_weaken_0) ).
fof(c_0_333,axiom,
! [X44,X40,X11,X2] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X44,X2,X11),X40),X11)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
file('<stdin>',cls_finite__imageI_0) ).
fof(c_0_334,axiom,
! [X10,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X10) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_Int__empty__left_0) ).
fof(c_0_335,axiom,
! [X10,X7,X11] :
( ~ class_HOL_Ominus(X11)
| hAPP(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(t_a,X11)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X7,v_x),hAPP(X10,v_x),X11) ),
file('<stdin>',cls_fun__diff__def_0) ).
fof(c_0_336,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) = X7
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_337,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) = X10
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_338,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) = X10
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_339,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) = X7
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_340,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X6,X20,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X6,X2),c_SetInterval_Oord__class_OlessThan(X20,X2),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_lessThan__subset__iff_0) ).
fof(c_0_341,axiom,
! [X6,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(X6,c_Complete__Lattice_OSup__class_OSup(X7,X2),X2)
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_Sup__upper_0) ).
fof(c_0_342,axiom,
! [X6,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X7,X2),X6,X2)
| ~ hBOOL(c_in(X6,X7,X2)) ),
file('<stdin>',cls_Inf__lower_0) ).
fof(c_0_343,axiom,
! [X12,X9,X2] : c_Finite__Set_Ofold1(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9,
file('<stdin>',cls_fold1__singleton_0) ).
fof(c_0_344,axiom,
! [X12,X7,X11,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != hAPP(c_Set_Oimage(X12,X11,X2),X7)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_empty__is__image_0) ).
fof(c_0_345,axiom,
! [X12,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X11,X2),X7) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
file('<stdin>',cls_image__is__empty_0) ).
fof(c_0_346,axiom,
! [X5,X6,X33,X11,X2] :
( hAPP(hAPP(c_Set_Oinsert(X11),X6),X5) != c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| hBOOL(c_in(X6,X5,X11))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
file('<stdin>',cls_ab__semigroup__mult_Ononempty__iff_2) ).
fof(c_0_347,axiom,
! [X33,X16,X30,X9,X2] :
( hAPP(hAPP(X33,X9),hAPP(hAPP(X33,X30),X16)) = hAPP(hAPP(X33,X30),hAPP(hAPP(X33,X9),X16))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__left__commute_0) ).
fof(c_0_348,axiom,
! [X7,X2] : c_Fun_Oinj__on(c_COMBI(X2),X7,X2,X2),
file('<stdin>',cls_inj__on__id2_0) ).
fof(c_0_349,axiom,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| hBOOL(hAPP(hAPP(X29,X6),X20))
| hBOOL(hAPP(hAPP(X29,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Oantisym__conv3_0) ).
fof(c_0_350,axiom,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X20),X6))
| X6 = X20
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Oless__linear_0) ).
fof(c_0_351,axiom,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X20),X6))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| X6 = X20
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_OneqE_0) ).
fof(c_0_352,axiom,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| hBOOL(hAPP(hAPP(X29,X20),X6))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Onot__less__iff__gr__or__eq_0) ).
fof(c_0_353,axiom,
! [X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X6),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2)
| hBOOL(hAPP(hAPP(X28,X6),X6)) ),
file('<stdin>',cls_linorder_Oantisym__conv1_1) ).
fof(c_0_354,axiom,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X6),X20))
| hBOOL(hAPP(hAPP(X28,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Onot__leE_0) ).
fof(c_0_355,axiom,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X20),X6))
| hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Onot__le_0) ).
fof(c_0_356,axiom,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X28,X20),X6))
| hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Olinear_0) ).
fof(c_0_357,axiom,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X28,X20),X6))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_OleI_0) ).
fof(c_0_358,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X2)
| ~ c_lessequals(X6,X9,X2) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_359,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X2)
| ~ c_lessequals(X6,X30,X2) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_360,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X6,X2)
| ~ c_lessequals(X30,X6,X2) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_361,axiom,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X6,X2)
| ~ c_lessequals(X9,X6,X2) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_362,axiom,
! [X10,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X10) = X10,
file('<stdin>',cls_Un__empty__left_0) ).
fof(c_0_363,axiom,
! [X10,X7,X2] :
( X7 = X10
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_364,axiom,
! [X10,X7,X2] :
( X7 = X10
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_365,axiom,
! [X19,X6,X12,X11,X2] :
( hAPP(hAPP(X12,X6),hAPP(hAPP(X12,X6),X19)) = hAPP(hAPP(X12,X6),X19)
| ~ c_Finite__Set_Ofun__left__comm__idem(X12,X2,X11) ),
file('<stdin>',cls_fun__left__comm__idem_Ofun__left__idem_0) ).
fof(c_0_366,axiom,
! [X6,X17,X12,X11,X2] :
( ~ class_HOL_Oord(X11)
| c_lessequals(hAPP(X12,X6),hAPP(X17,X6),X11)
| ~ c_lessequals(X12,X17,tc_fun(X2,X11)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_367,axiom,
! [X5,X6,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X6),X5) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X5,X2)) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_368,axiom,
! [X6,X7,X2] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X6)),
file('<stdin>',cls_insert__code_1) ).
fof(c_0_369,axiom,
! [X19,X20,X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X19,X2)
| ~ c_lessequals(X20,X19,X2)
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_370,axiom,
! [X19,X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X19,X6,X2)
| ~ c_lessequals(X19,X20,X2)
| ~ c_lessequals(X20,X6,X2) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_371,axiom,
! [X7,X2] :
( X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_372,axiom,
! [X10,X7,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X7,tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__subset_0) ).
fof(c_0_373,axiom,
! [X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
file('<stdin>',cls_Inf__singleton_0) ).
fof(c_0_374,axiom,
! [X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
file('<stdin>',cls_Max__singleton_0) ).
fof(c_0_375,axiom,
! [X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
file('<stdin>',cls_Min__singleton_0) ).
fof(c_0_376,axiom,
! [X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
file('<stdin>',cls_Sup__singleton_0) ).
fof(c_0_377,axiom,
! [X9,X7,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),X7) = X7
| ~ hBOOL(c_in(X9,X7,X2)) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_378,axiom,
! [X66,X68,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X68,X66,X2) ),
file('<stdin>',cls_cut_0) ).
fof(c_0_379,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X6,X2),c_SetInterval_Oord__class_OlessThan(X20,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_lessThan__subset__iff_1) ).
fof(c_0_380,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_Int__empty__right_0) ).
fof(c_0_381,axiom,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X30,X2) ),
file('<stdin>',cls_atLeastatMost__empty__iff_0) ).
fof(c_0_382,axiom,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2)
| ~ c_lessequals(X9,X30,X2) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_0) ).
fof(c_0_383,axiom,
! [X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X7,X2),X7,X2))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_Min__in_0) ).
fof(c_0_384,axiom,
! [X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X7,X2),X7,X2))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_Max__in_0) ).
fof(c_0_385,axiom,
! [X6,X2] : c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X6,
file('<stdin>',cls_contents__eq_0) ).
fof(c_0_386,axiom,
! [X6,X2] : c_The(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X6,
file('<stdin>',cls_Nitpick_OThe__psimp_0) ).
fof(c_0_387,axiom,
! [X6,X28,X29,X2] :
( ~ c_Orderings_Olinorder(X28,X29,X2)
| ~ hBOOL(hAPP(hAPP(X29,X6),X6)) ),
file('<stdin>',cls_linorder_Onot__less__iff__gr__or__eq_2) ).
fof(c_0_388,axiom,
! [X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X29,X6),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
file('<stdin>',cls_linorder_Oneq__iff_1) ).
fof(c_0_389,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_390,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_391,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_392,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_393,axiom,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(X10,X2) ),
file('<stdin>',cls_finite__Diff2_1) ).
fof(c_0_394,axiom,
! [X9,X21,X2] :
( hBOOL(c_in(X9,c_Collect(X21,X2),X2))
| ~ hBOOL(hAPP(X21,X9)) ),
file('<stdin>',cls_CollectI_0) ).
fof(c_0_395,axiom,
! [X6,X2] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6)),
file('<stdin>',cls_bot1E_0) ).
fof(c_0_396,axiom,
! [X6,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X6),hAPP(hAPP(c_Set_Oinsert(X2),X6),X7)) = hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),
file('<stdin>',cls_insert__absorb2_0) ).
fof(c_0_397,axiom,
! [X6,X22,X2] :
( hBOOL(hAPP(X22,X6))
| ~ hBOOL(c_in(X6,X22,X2)) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_398,axiom,
! [X9,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),c_Complete__Lattice_OSup__class_OSup(X7,X2)) ),
file('<stdin>',cls_Sup__insert_0) ).
fof(c_0_399,axiom,
! [X9,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),c_Complete__Lattice_OInf__class_OInf(X7,X2)) ),
file('<stdin>',cls_Inf__insert_0) ).
fof(c_0_400,axiom,
! [X6,X24,X21,X2] :
( hBOOL(hAPP(X24,X6))
| ~ c_lessequals(X21,X24,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_401,axiom,
! [X6,X24,X21,X2] :
( hBOOL(hAPP(X24,X6))
| ~ hBOOL(hAPP(X21,X6))
| ~ c_lessequals(X21,X24,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_402,axiom,
! [X12,X11,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = hAPP(c_Set_Oimage(X12,X11,X2),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),
file('<stdin>',cls_empty__is__image_1) ).
fof(c_0_403,axiom,
! [X12,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_image__empty_0) ).
fof(c_0_404,axiom,
! [X12,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_vimage__empty_0) ).
fof(c_0_405,axiom,
! [X9,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_406,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X7,
file('<stdin>',cls_Un__empty__right_0) ).
fof(c_0_407,axiom,
! [X66,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_lessequals(X66,X39,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ),
file('<stdin>',cls_asm_0) ).
fof(c_0_408,axiom,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_finite__Diff_0) ).
fof(c_0_409,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| X6 = X20
| ~ c_lessequals(X6,X20,X2)
| ~ c_lessequals(X20,X6,X2) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_410,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| X6 = X20
| ~ c_lessequals(X20,X6,X2)
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_411,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| X6 = X20
| ~ c_lessequals(X20,X6,X2)
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_412,axiom,
! [X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('<stdin>',cls_subset__empty_1) ).
fof(c_0_413,axiom,
! [X25,X26,X6,X2] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X6,X6,X2) != c_HOL_Ominus__class_Ominus(X26,X25,X2)
| X26 = X25 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_414,axiom,
! [X20,X5,X6,X2] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X5,X20,X2) != c_HOL_Ominus__class_Ominus(X6,X6,X2)
| X5 = X20 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_415,axiom,
! [X9,X10,X2] : c_lessequals(X10,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)),
file('<stdin>',cls_subset__insertI_0) ).
fof(c_0_416,axiom,
! [X12,X7,X2] : c_Finite__Set_Ofold1(X12,X7,X2) = c_The(c_Finite__Set_Ofold1Set(X12,X7,X2),X2),
file('<stdin>',cls_fold1__def_0) ).
fof(c_0_417,axiom,
! [X3,X36,X31,X34,X32,X35] :
( c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OCond(X3,X32,X31)
| X36 = X3 ),
file('<stdin>',cls_com_Osimps_I4_J_0) ).
fof(c_0_418,axiom,
! [X3,X36,X31,X34,X32,X35] :
( c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OCond(X3,X32,X31)
| X35 = X32 ),
file('<stdin>',cls_com_Osimps_I4_J_1) ).
fof(c_0_419,axiom,
! [X3,X36,X31,X34,X32,X35] :
( c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OCond(X3,X32,X31)
| X34 = X31 ),
file('<stdin>',cls_com_Osimps_I4_J_2) ).
fof(c_0_420,axiom,
! [X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X9,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
file('<stdin>',cls_atLeastAtMost__singleton_0) ).
fof(c_0_421,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X6,X2) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_422,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X20,X2) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_423,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X20,X2) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_424,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X6,X2) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_425,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_426,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X20,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_427,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X20,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_428,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_429,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)) = X6 ),
file('<stdin>',cls_inf__sup__absorb_0) ).
fof(c_0_430,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)) = X6 ),
file('<stdin>',cls_sup__inf__absorb_0) ).
fof(c_0_431,axiom,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X2) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_432,axiom,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(X10,X2)
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_433,axiom,
! [X6,X22,X2] :
( hBOOL(c_in(X6,X22,X2))
| ~ hBOOL(hAPP(X22,X6)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_434,axiom,
! [X7,X2] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_empty__Diff_0) ).
fof(c_0_435,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
file('<stdin>',cls_bot__empty__eq_0) ).
fof(c_0_436,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = X20
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_437,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = X6
| ~ c_lessequals(X20,X6,X2) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_438,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = X20
| ~ c_lessequals(X20,X6,X2) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_439,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = X6
| ~ c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_440,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) != X20
| c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_441,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) != X6
| c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_442,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X7) = X7,
file('<stdin>',cls_Int__absorb_0) ).
fof(c_0_443,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X7) = X7,
file('<stdin>',cls_Un__absorb_0) ).
fof(c_0_444,axiom,
! [X9,X2] : c_Collect(c_fequal(X9,X2),X2) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
file('<stdin>',cls_singleton__conv2_0) ).
fof(c_0_445,axiom,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X9,X30,X2) ),
file('<stdin>',cls_atLeastatMost__empty__iff_1) ).
fof(c_0_446,axiom,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2)
| c_lessequals(X9,X30,X2) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_1) ).
fof(c_0_447,axiom,
! [X9,X7,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2)
| ~ c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_448,axiom,
! [X1,X2] : hAPP(c_Set_Ovimage(c_COMBI(X2),X2,X2),X1) = X1,
file('<stdin>',cls_vimage__ident_0) ).
fof(c_0_449,axiom,
! [X1,X2] : hAPP(c_Set_Oimage(c_COMBI(X2),X2,X2),X1) = X1,
file('<stdin>',cls_image__ident_0) ).
fof(c_0_450,axiom,
! [X1,X73,X2] :
( X73 = X1
| ~ hBOOL(hAPP(c_fequal(X73,X2),X1)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_451,axiom,
! [X39,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
file('<stdin>',cls_empty_0) ).
fof(c_0_452,axiom,
! [X7,X2] : c_HOL_Ominus__class_Ominus(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X7,
file('<stdin>',cls_Diff__empty_0) ).
fof(c_0_453,axiom,
! [X7,X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7,tc_fun(X2,tc_bool)),
file('<stdin>',cls_empty__subsetI_0) ).
fof(c_0_454,axiom,
! [X9,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),X7) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_insert__not__empty_0) ).
fof(c_0_455,axiom,
! [X9,X7,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),
file('<stdin>',cls_empty__not__insert_0) ).
fof(c_0_456,axiom,
! [X24,X21,X11,X2] : hAPP(c_COMBK(X21,X2,X11),X24) = X21,
file('<stdin>',cls_COMBK__def_0) ).
fof(c_0_457,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X20,X6,X2)
| c_lessequals(X6,X20,X2) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_458,axiom,
! [X6,X21,X2] :
( c_Collect(X21,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_Collect__empty__eq_0) ).
fof(c_0_459,axiom,
! [X6,X21,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Collect(X21,X2)
| ~ hBOOL(hAPP(X21,X6)) ),
file('<stdin>',cls_empty__Collect__eq_0) ).
fof(c_0_460,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X6) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_461,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X6) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_462,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X6) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_463,axiom,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X6) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_464,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
file('<stdin>',cls_COMBK__def__raw_0) ).
fof(c_0_465,axiom,
! [X3,X36,X4,X34,X35] : c_Com_Ocom_OWhile(X3,X4) != c_Com_Ocom_OCond(X36,X35,X34),
file('<stdin>',cls_com_Osimps_I53_J_0) ).
fof(c_0_466,axiom,
! [X3,X31,X34,X32,X35] : c_Com_Ocom_OCond(X3,X32,X31) != c_Com_Ocom_OSemi(X35,X34),
file('<stdin>',cls_com_Osimps_I45_J_0) ).
fof(c_0_467,axiom,
! [X3,X36,X4,X34,X35] : c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OWhile(X3,X4),
file('<stdin>',cls_com_Osimps_I52_J_0) ).
fof(c_0_468,axiom,
! [X3,X31,X34,X32,X35] : c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OCond(X3,X32,X31),
file('<stdin>',cls_com_Osimps_I44_J_0) ).
fof(c_0_469,axiom,
! [X7,X2] : c_HOL_Ominus__class_Ominus(X7,X7,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('<stdin>',cls_Diff__cancel_0) ).
fof(c_0_470,axiom,
! [X33,X30,X9,X2] :
( hAPP(hAPP(X33,X9),X30) = hAPP(hAPP(X33,X30),X9)
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__commute_0) ).
fof(c_0_471,axiom,
! [X10,X7,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X7),X10) != c_Orderings_Obot__class_Obot(X2)
| X10 = c_Orderings_Obot__class_Obot(X2) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_472,axiom,
! [X10,X7,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X7),X10) != c_Orderings_Obot__class_Obot(X2)
| X7 = c_Orderings_Obot__class_Obot(X2) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_473,axiom,
! [X3,X31,X32] : c_Com_Ocom_OCond(X3,X32,X31) != c_Com_Ocom_OSKIP,
file('<stdin>',cls_com_Osimps_I15_J_0) ).
fof(c_0_474,axiom,
! [X3,X31,X32] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X3,X32,X31),
file('<stdin>',cls_com_Osimps_I14_J_0) ).
fof(c_0_475,axiom,
! [X2] : c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X2),X2,tc_fun(X2,tc_bool)),
file('<stdin>',cls_fun__left__comm__idem__insert_0) ).
fof(c_0_476,axiom,
! [X6,X2] : hBOOL(hAPP(c_fequal(X6,X2),X6)),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_477,axiom,
! [X7,X2] : c_lessequals(X7,X7,tc_fun(X2,tc_bool)),
file('<stdin>',cls_subset__refl_0) ).
fof(c_0_478,axiom,
! [X6,X2] : c_lessequals(X6,X6,tc_fun(X2,tc_bool)),
file('<stdin>',cls_equalityE_0) ).
fof(c_0_479,axiom,
! [X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = c_Orderings_Obot__class_Obot(X2) ),
file('<stdin>',cls_Sup__empty_0) ).
fof(c_0_480,axiom,
! [X11] :
( ~ class_Orderings_Obot(X11)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X11)),v_x) = c_Orderings_Obot__class_Obot(X11) ),
file('<stdin>',cls_bot__fun__eq_0) ).
fof(c_0_481,axiom,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Orderings_Obot__class_Obot(X2)),X6) = c_Orderings_Obot__class_Obot(X2) ),
file('<stdin>',cls_inf__bot__left_0) ).
fof(c_0_482,axiom,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2)),X6) = X6 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_483,axiom,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),c_Orderings_Obot__class_Obot(X2)) = c_Orderings_Obot__class_Obot(X2) ),
file('<stdin>',cls_inf__bot__right_0) ).
fof(c_0_484,axiom,
! [X6,X2] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_485,axiom,
! [X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X2),X2,X2) ),
file('<stdin>',cls_fun__left__comm__idem__inf_0) ).
fof(c_0_486,axiom,
! [X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X2),X2,X2) ),
file('<stdin>',cls_fun__left__comm__idem__sup_0) ).
fof(c_0_487,axiom,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),c_Orderings_Obot__class_Obot(X2)) = X6 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_488,axiom,
! [X2] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('<stdin>',cls_finite_OemptyI_0) ).
fof(c_0_489,axiom,
! [X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X6,X2) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_490,axiom,
! [X6,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X6,X6,X2) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_491,axiom,
! [X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X6) = X6 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_492,axiom,
! [X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X6) = X6 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_493,axiom,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_SetInterval_Oord__class_OlessThan(X6,X2) != c_SetInterval_Oord__class_OlessThan(X20,X2)
| X6 = X20 ),
file('<stdin>',cls_lessThan__eq__iff_0) ).
fof(c_0_494,axiom,
! [X3,X36,X4,X51] :
( c_Com_Ocom_OWhile(X36,X51) != c_Com_Ocom_OWhile(X3,X4)
| X51 = X4 ),
file('<stdin>',cls_com_Osimps_I5_J_1) ).
fof(c_0_495,axiom,
! [X3,X36,X4,X51] :
( c_Com_Ocom_OWhile(X36,X51) != c_Com_Ocom_OWhile(X3,X4)
| X36 = X3 ),
file('<stdin>',cls_com_Osimps_I5_J_0) ).
fof(c_0_496,axiom,
! [X31,X34,X32,X35] :
( c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OSemi(X32,X31)
| X35 = X32 ),
file('<stdin>',cls_com_Osimps_I3_J_0) ).
fof(c_0_497,axiom,
! [X31,X34,X32,X35] :
( c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OSemi(X32,X31)
| X34 = X31 ),
file('<stdin>',cls_com_Osimps_I3_J_1) ).
fof(c_0_498,axiom,
! [X71,X72] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X71,X72))
| ~ class_Finite__Set_Ofinite_Ofinite(X72)
| ~ class_Finite__Set_Ofinite_Ofinite(X71) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_499,axiom,
! [X3,X4,X34,X35] : c_Com_Ocom_OWhile(X3,X4) != c_Com_Ocom_OSemi(X35,X34),
file('<stdin>',cls_com_Osimps_I47_J_0) ).
fof(c_0_500,axiom,
! [X3,X4,X34,X35] : c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OWhile(X3,X4),
file('<stdin>',cls_com_Osimps_I46_J_0) ).
fof(c_0_501,axiom,
! [X6,X2] : c_The(c_fequal(X6,X2),X2) = X6,
file('<stdin>',cls_the__sym__eq__trivial_0) ).
fof(c_0_502,axiom,
! [X71,X72] :
( class_HOL_Oord(tc_fun(X71,X72))
| ~ class_HOL_Oord(X72) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_503,axiom,
! [X71,X72] :
( class_HOL_Ominus(tc_fun(X71,X72))
| ~ class_HOL_Ominus(X72) ),
file('<stdin>',clsarity_fun__HOL_Ominus) ).
fof(c_0_504,axiom,
! [X71,X72] :
( class_Orderings_Obot(tc_fun(X71,X72))
| ~ class_Orderings_Obot(X72) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_505,axiom,
! [X71,X72] :
( class_Orderings_Oorder(tc_fun(X71,X72))
| ~ class_Orderings_Oorder(X72) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_506,axiom,
! [X71,X72] :
( class_Lattices_Olattice(tc_fun(X71,X72))
| ~ class_Lattices_Olattice(X72) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_507,axiom,
! [X71,X72] :
( class_Orderings_Opreorder(tc_fun(X71,X72))
| ~ class_Orderings_Opreorder(X72) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_508,axiom,
! [X71,X72] :
( class_Lattices_Obounded__lattice(tc_fun(X71,X72))
| ~ class_Lattices_Obounded__lattice(X72) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_509,axiom,
! [X71,X72] :
( class_Lattices_Odistrib__lattice(tc_fun(X71,X72))
| ~ class_Lattices_Odistrib__lattice(X72) ),
file('<stdin>',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(c_0_510,axiom,
! [X71,X72] :
( class_Lattices_Olower__semilattice(tc_fun(X71,X72))
| ~ class_Lattices_Olattice(X72) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_511,axiom,
! [X71,X72] :
( class_Lattices_Oupper__semilattice(tc_fun(X71,X72))
| ~ class_Lattices_Olattice(X72) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_512,axiom,
! [X71,X72] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X71,X72))
| ~ class_Complete__Lattice_Ocomplete__lattice(X72) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_513,axiom,
! [X31,X32] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X32,X31),
file('<stdin>',cls_com_Osimps_I12_J_0) ).
fof(c_0_514,axiom,
! [X31,X32] : c_Com_Ocom_OSemi(X32,X31) != c_Com_Ocom_OSKIP,
file('<stdin>',cls_com_Osimps_I13_J_0) ).
fof(c_0_515,axiom,
! [X3,X4] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X3,X4),
file('<stdin>',cls_com_Osimps_I16_J_0) ).
fof(c_0_516,axiom,
! [X3,X4] : c_Com_Ocom_OWhile(X3,X4) != c_Com_Ocom_OSKIP,
file('<stdin>',cls_com_Osimps_I17_J_0) ).
fof(c_0_517,axiom,
! [X7,X2] :
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X7,X2) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_518,axiom,
! [X21,X2] : hAPP(c_COMBI(X2),X21) = X21,
file('<stdin>',cls_COMBI__def_0) ).
fof(c_0_519,axiom,
hAPP(c_COMBI(t_a),v_P) = v_P,
file('<stdin>',cls_COMBI__def__raw_0) ).
fof(c_0_520,axiom,
! [X21,X2] : c_Collect(X21,X2) = X21,
file('<stdin>',cls_Collect__def_0) ).
fof(c_0_521,axiom,
class_HOL_Oord(tc_bool),
file('<stdin>',clsarity_bool__HOL_Oord) ).
fof(c_0_522,axiom,
class_HOL_Ominus(tc_bool),
file('<stdin>',clsarity_bool__HOL_Ominus) ).
fof(c_0_523,axiom,
class_Orderings_Obot(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Obot) ).
fof(c_0_524,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_525,axiom,
class_Lattices_Olattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olattice) ).
fof(c_0_526,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_527,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('<stdin>',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_528,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Obounded__lattice) ).
fof(c_0_529,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(c_0_530,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olower__semilattice) ).
fof(c_0_531,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(c_0_532,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('<stdin>',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_533,plain,
! [X45,X46,X28,X29,X47,X48,X30,X9,X49,X50,X2] :
( hAPP(X49,hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X46,X9),X30)
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_534,plain,
! [X45,X46,X28,X29,X47,X48,X30,X9,X49,X50,X2] :
( hAPP(X50,hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X47,X9),X30)
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_535,plain,
! [X6,X45,X46,X28,X29,X47,X48,X49,X50,X7,X2] :
( hBOOL(hAPP(hAPP(X28,hAPP(X50,X7)),X6))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_536,plain,
! [X6,X45,X46,X28,X29,X47,X48,X49,X50,X7,X2] :
( hBOOL(hAPP(hAPP(X28,X6),hAPP(X49,X7)))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_537,plain,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X2] :
( hAPP(X49,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X9
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_538,plain,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X2] :
( hAPP(X50,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X9
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_539,plain,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X7,X2] :
( hAPP(X49,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7)) = hAPP(hAPP(X46,X9),hAPP(X49,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_540,plain,
! [X45,X46,X28,X29,X47,X48,X9,X49,X50,X7,X2] :
( hAPP(X50,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7)) = hAPP(hAPP(X47,X9),hAPP(X50,X7))
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_541,plain,
! [X45,X46,X28,X29,X47,X48,X49,X50,X2] :
( hAPP(X49,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X48
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_542,plain,
! [X45,X46,X28,X29,X47,X48,X49,X50,X2] :
( hAPP(X50,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X45
| ~ c_Complete__Lattice_Ocomplete__lattice(X50,X49,X28,X29,X47,X46,X48,X45,X2) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_543,plain,
! [X41,X16,X30,X24,X21,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OCond(X30,X16,X41),X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X21,c_Fun_Ocomp(c_Not,X30,tc_bool,tc_bool,tc_Com_Ostate),X2),X41,X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X21,X30,X2),X16,X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_544,plain,
! [X16,X30,X21,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OWhile(X30,X16),c_Hoare__Mirabelle_Opeek__and(X21,c_Fun_Ocomp(c_Not,X30,tc_bool,tc_bool,tc_Com_Ostate),X2),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X21,X30,X2),X16,X21,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_545,plain,
! [X5,X6,X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X24,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X21,X24,X16,X6,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_546,plain,
! [X5,X6,X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X24,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X21,X24,X16,X6,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_547,plain,
! [X5,X6,X16,X67,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X21,X24,X16,X6,X5)))
| ~ hBOOL(hAPP(hAPP(X6,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X21,X24,X16)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_548,plain,
! [X5,X6,X16,X67,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X21,X24,X16,X6,X5)))
| ~ hBOOL(hAPP(hAPP(X6,X67),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X21,X24,X16)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X16,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_549,plain,
! [X41,X16,X23,X24,X21,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OSemi(X16,X41),X23,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X24,X41,X23,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_550,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X15),X7)),
c_0_17 ).
fof(c_0_551,axiom,
! [X44,X17,X12,X53,X18,X11,X2] : c_Fun_Ocomp(X12,c_Fun_Ocomp(X17,X44,X53,X18,X2),X18,X11,X2) = c_Fun_Ocomp(c_Fun_Ocomp(X12,X17,X18,X11,X53),X44,X53,X11,X2),
c_0_18 ).
fof(c_0_552,axiom,
! [X23,X24,X21,X18,X11,X2] : c_COMBS(X21,X24,X23,X11,X18,X2) = hAPP(hAPP(X21,X23),hAPP(X24,X23)),
c_0_19 ).
fof(c_0_553,axiom,
c_COMBS(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
c_0_20 ).
fof(c_0_554,axiom,
! [X23,X24,X21,X18,X11,X2] : c_COMBC(X21,X24,X23,X11,X18,X2) = hAPP(hAPP(X21,X23),X24),
c_0_21 ).
fof(c_0_555,axiom,
c_COMBC(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),v_Q),
c_0_22 ).
fof(c_0_556,axiom,
! [X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X21,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X39,X21,X24,X16))) ),
c_0_23 ).
fof(c_0_557,axiom,
! [X16,X24,X21,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X21,X16,X24,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X21,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X21,X24,X16)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X39,X21,X24,X16))) ),
c_0_24 ).
fof(c_0_558,axiom,
! [X54,X17,X12,X18,X11,X2] : hAPP(c_Set_Oimage(c_Fun_Ocomp(X12,X17,X18,X2,X11),X11,X2),X54) = hAPP(c_Set_Oimage(X12,X18,X2),hAPP(c_Set_Oimage(X17,X11,X18),X54)),
c_0_25 ).
fof(c_0_559,axiom,
! [X17,X12,X7,X18,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),hAPP(c_Set_Oimage(X17,X18,X11),X7)) = hAPP(c_Set_Oimage(c_COMBB(X12,X17,X11,X2,X18),X18,X2),X7),
c_0_26 ).
fof(c_0_560,axiom,
! [X6,X17,X12,X18,X11,X2] : hAPP(c_Set_Ovimage(c_Fun_Ocomp(X17,X12,X18,X11,X2),X2,X11),X6) = hAPP(c_Set_Ovimage(X12,X2,X18),hAPP(c_Set_Ovimage(X17,X18,X11),X6)),
c_0_27 ).
fof(c_0_561,plain,
! [X12,X9,X7,X11,X2] :
( ~ hBOOL(c_in(hAPP(X12,X9),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X11))
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_562,plain,
! [X63,X64,X62,X51,X21] :
( ~ hBOOL(hAPP(X21,c_Hoare__Mirabelle_Otriple_Otriple__case(X62,c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,t_b),t_b,t_a)))
| hBOOL(hAPP(X21,hAPP(hAPP(hAPP(X62,X64),X51),X63))) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_563,plain,
! [X60,X61,X5,X62,X21] :
( ~ hBOOL(hAPP(X21,c_Hoare__Mirabelle_Otriple_Otriple__case(X62,c_Hoare__Mirabelle_Otriple_Otriple(X5,X61,X60,t_b),t_b,t_a)))
| hBOOL(hAPP(X21,hAPP(hAPP(hAPP(X62,X5),X61),X60))) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_564,axiom,
! [X26,X6,X56,X17,X57,X12,X58,X53,X18,X11,X2] :
( hAPP(X12,hAPP(X17,X6)) != hAPP(X57,hAPP(X56,X26))
| hAPP(c_Fun_Ocomp(X12,X17,X11,X2,X18),X6) = hAPP(c_Fun_Ocomp(X57,X56,X53,X2,X58),X26) ),
c_0_31 ).
fof(c_0_565,plain,
! [X17,X12,X7,X18,X11,X2] :
( c_Fun_Oinj__on(X17,hAPP(c_Set_Oimage(X12,X2,X18),X7),X18,X11)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X17,X12,X18,X11,X2),X7,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_566,plain,
! [X12,X10,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Fun_Oinj__on(X12,X10,X2,X11)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_567,axiom,
! [X42,X41,X16,X30,X9,X53,X18,X11,X2] :
( c_Fun_Ocomp(X9,X30,X18,X11,X2) != c_Fun_Ocomp(X16,X41,X53,X11,X2)
| hAPP(X9,hAPP(X30,X42)) = hAPP(X16,hAPP(X41,X42)) ),
c_0_34 ).
fof(c_0_568,plain,
! [X17,X12,X7,X18,X11,X2] :
( c_Fun_Oinj__on(c_Fun_Ocomp(X17,X12,X11,X18,X2),X7,X2,X18)
| ~ c_Fun_Oinj__on(X17,hAPP(c_Set_Oimage(X12,X2,X11),X7),X11,X18)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_569,axiom,
! [X15,X10,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_36 ).
fof(c_0_570,axiom,
! [X15,X10,X7,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool)))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_37 ).
fof(c_0_571,axiom,
! [X15,X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)),
c_0_38 ).
fof(c_0_572,axiom,
! [X37,X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X7,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)),
c_0_39 ).
fof(c_0_573,axiom,
! [X15,X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))),
c_0_40 ).
fof(c_0_574,plain,
! [X12,X9,X7,X11,X2] :
( c_Fun_Oinj__on(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2,X11)
| hBOOL(c_in(hAPP(X12,X9),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X11))
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_575,axiom,
! [X12,X10,X7,X18,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X18,tc_fun(X11,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(c_Set_Ovimage(X12,X2,X11),X10,tc_fun(X11,tc_bool),tc_fun(X2,tc_bool),X18),X18,tc_fun(X2,tc_bool)),
c_0_42 ).
fof(c_0_576,axiom,
! [X12,X10,X7,X18,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X18,tc_fun(X11,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(c_Set_Oimage(X12,X11,X2),X10,tc_fun(X11,tc_bool),tc_fun(X2,tc_bool),X18),X18,tc_fun(X2,tc_bool)),
c_0_43 ).
fof(c_0_577,plain,
! [X8,X9,X10,X7,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(hAPP(c_Set_Oinsert(X11),X9),X10,tc_fun(X11,tc_bool),tc_fun(X11,tc_bool),X2),X2,tc_fun(X11,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X11),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)))
| ~ hBOOL(c_in(X8,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_578,axiom,
! [X9,X15,X10,X11,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Set_Oinsert(X2),X9),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_45 ).
fof(c_0_579,axiom,
! [X9,X15,X10,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Set_Oinsert(X2),X9),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X10,X11,tc_fun(X2,tc_bool)))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_46 ).
fof(c_0_580,axiom,
! [X12,X10,X7,X18,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X12,X18,X11),X7),X10,X11,tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(X10,X12,X11,tc_fun(X2,tc_bool),X18),X18,tc_fun(X2,tc_bool)),
c_0_47 ).
fof(c_0_581,axiom,
! [X12,X10,X7,X18,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBB(X10,X12,X18,tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X12,X11,X18),X7),X10,X18,tc_fun(X2,tc_bool)),
c_0_48 ).
fof(c_0_582,axiom,
! [X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_49 ).
fof(c_0_583,axiom,
! [X9,X10,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X9),X10,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X11),X11,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_50 ).
fof(c_0_584,plain,
! [X12,X10,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_585,axiom,
! [X12,X16,X18,X11] : hAPP(c_Fun_Ocomp(c_COMBK(X16,X11,X18),X12,X18,X11,t_a),v_x) = X16,
c_0_52 ).
fof(c_0_586,axiom,
! [X12,X10,X7,X11,X2] : c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X12,X11,X2),X7)),hAPP(c_Set_Oimage(X12,X11,X2),X10)),tc_fun(X2,tc_bool)),
c_0_53 ).
fof(c_0_587,plain,
! [X17,X12,X18,X11,X2] :
( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X12,X17,X2,tc_fun(X11,X11),X18),X18,X11)
| ~ c_Finite__Set_Ofun__left__comm__idem(X12,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_588,axiom,
! [X42,X30,X9,X18,X11,X2] : hAPP(X9,hAPP(X30,X42)) = hAPP(c_Fun_Ocomp(X9,X30,X18,X11,X2),X42),
c_0_55 ).
fof(c_0_589,axiom,
! [X6,X17,X12,X18,X11,X2] : hAPP(c_Fun_Ocomp(X12,X17,X11,X2,X18),X6) = hAPP(X12,hAPP(X17,X6)),
c_0_56 ).
fof(c_0_590,axiom,
! [X23,X24,X21,X18,X11,X2] : hAPP(c_COMBB(X21,X24,X11,X2,X18),X23) = hAPP(X21,hAPP(X24,X23)),
c_0_57 ).
fof(c_0_591,axiom,
! [X17,X12,X18,X11] : hAPP(c_Fun_Ocomp(X12,X17,X18,X11,t_a),v_x) = hAPP(X12,hAPP(X17,v_x)),
c_0_58 ).
fof(c_0_592,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
c_0_59 ).
fof(c_0_593,axiom,
! [X21,X39,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X21,c_Com_Ocom_OSKIP,X21,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
c_0_60 ).
fof(c_0_594,axiom,
! [X14,X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),X7),X10),X14,X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X14,X11,tc_fun(X2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X14,X11,tc_fun(X2,tc_bool))),
c_0_61 ).
fof(c_0_595,plain,
! [X12,X30,X9,X11,X2] :
( hAPP(X12,X9) = X30
| ~ hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Set_Oinsert(X11),X30),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)))),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_596,axiom,
! [X12,X9,X10,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Set_Oinsert(X11),X9),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Set_Oinsert(X11),X9),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))))),hAPP(c_Set_Ovimage(X12,X2,X11),X10)),
c_0_63 ).
fof(c_0_597,plain,
! [X12,X15,X10,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X2,X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),hAPP(c_Set_Oimage(X12,X2,X11),X7)),hAPP(c_Set_Oimage(X12,X2,X11),X10))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X12,X15,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_598,axiom,
! [X15,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),X15) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15))
| c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
c_0_65 ).
fof(c_0_599,axiom,
! [X12,X9,X52,X2] : hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X52,X2),hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X12,X9)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X52)),
c_0_66 ).
fof(c_0_600,axiom,
! [X12,X10,X7,X11,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X12,X11,X2),X7),hAPP(c_Set_Oimage(X12,X11,X2),X10),tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X12,X11,X2),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X11,tc_bool))),tc_fun(X2,tc_bool)),
c_0_67 ).
fof(c_0_601,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)),X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X7)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X15),X7)),
c_0_68 ).
fof(c_0_602,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X7)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X7)),
c_0_69 ).
fof(c_0_603,plain,
! [X12,X30,X9,X2] :
( X9 = X30
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_604,plain,
! [X30,X9,X10,X7,X11,X2] :
( hBOOL(c_in(X30,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X11))
| ~ hBOOL(c_in(X30,hAPP(X10,X9),X11))
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_605,plain,
! [X6,X30,X10,X7,X11,X2] :
( hBOOL(c_in(X30,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(c_in(X30,hAPP(X10,X6),X2))
| ~ hBOOL(c_in(X6,X7,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_606,plain,
! [X12,X15,X10,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X12,X2,X11),X7),hAPP(c_Set_Oimage(X12,X2,X11),X10),tc_fun(X11,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X12,X15,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_607,axiom,
! [X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X7,X11,tc_fun(X2,tc_bool))),X10) = X10,
c_0_74 ).
fof(c_0_608,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X15)),
c_0_75 ).
fof(c_0_609,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15)),
c_0_76 ).
fof(c_0_610,plain,
! [X30,X9,X10,X7,X11,X2] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X30))
| ~ hBOOL(hAPP(hAPP(X10,X9),X30))
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_611,plain,
! [X6,X30,X10,X7,X11,X2] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X30))
| ~ hBOOL(hAPP(hAPP(X10,X6),X30))
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_612,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_613,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_614,plain,
! [X6,X12,X11,X2] :
( c_Fun_Ocomp(hAPP(X12,X6),hAPP(X12,X6),X11,X11,X11) = hAPP(X12,X6)
| ~ c_Finite__Set_Ofun__left__comm__idem(X12,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_615,plain,
! [X6,X21,X7,X2] :
( hBOOL(c_in(X6,X7,X2))
| ~ hBOOL(c_in(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Collect(X21,X2)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_616,axiom,
! [X6,X2] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2))),
c_0_83 ).
fof(c_0_617,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_618,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X10,X2))
| hBOOL(c_in(X16,X7,X2))
| ~ hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_619,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Oimage(X12,X11,X2),X7)),hAPP(c_Set_Oimage(X12,X11,X2),X10)),
c_0_86 ).
fof(c_0_620,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X11,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X12,X2,X11),X7)),hAPP(c_Set_Ovimage(X12,X2,X11),X10)),
c_0_87 ).
fof(c_0_621,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X12,X2,X11),X7)),hAPP(c_Set_Ovimage(X12,X2,X11),X10)),
c_0_88 ).
fof(c_0_622,plain,
! [X15,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15))
| ~ c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_623,plain,
! [X6,X21,X7,X2] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Collect(X21,X2)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_624,plain,
! [X6,X37,X10,X7,X11,X2] :
( c_lessequals(hAPP(X7,X6),X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X37,X11))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X11,tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_625,plain,
! [X12,X10,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X2,X11),X7) != hAPP(c_Set_Oimage(X12,X2,X11),X10)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11)
| X7 = X10 ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_626,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X7,X2))
| ~ hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_627,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_628,plain,
! [X38,X37,X7,X11,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X11,tc_bool)),hAPP(X7,X38)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X2,tc_fun(X11,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X37,X7,X2,tc_fun(X11,tc_bool))
| ~ hBOOL(c_in(X38,X37,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_629,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)),
c_0_96 ).
fof(c_0_630,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),X15) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)),
c_0_97 ).
fof(c_0_631,plain,
! [X6,X10,X7,X11,X2] :
( c_Finite__Set_Ofinite(hAPP(X10,X6),X11)
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),X11)
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_632,axiom,
! [X9,X10,X7,X11,X2] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X11),X9),X7),X10,X11,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(X10,X9)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool))),
c_0_99 ).
fof(c_0_633,plain,
! [X6,X10,X7,X2] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_634,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),X15) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)),
c_0_101 ).
fof(c_0_635,plain,
! [X33,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X2)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2)
| c_Finite__Set_Ofold1(X33,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2) = hAPP(hAPP(X33,c_Finite__Set_Ofold1(X33,X7,X2)),c_Finite__Set_Ofold1(X33,X10,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_636,plain,
! [X12,X9,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X9),X7,X11))
| ~ hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),X7),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_637,plain,
! [X12,X9,X10,X11,X2] :
( hBOOL(c_in(hAPP(X12,X9),X10,X11))
| ~ hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),X10),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_638,plain,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X11)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_639,plain,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X10,X2,X11)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_640,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_641,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_642,axiom,
! [X6,X12,X2] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X6)),
c_0_109 ).
fof(c_0_643,plain,
! [X12,X7,X2] :
( hAPP(c_Set_Oimage(X12,X2,X2),X7) = X7
| ~ c_Fun_Oinj__on(X12,X7,X2,X2)
| ~ c_lessequals(hAPP(c_Set_Oimage(X12,X2,X2),X7),X7,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_644,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_645,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_646,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15),X10,tc_fun(X2,tc_bool)),
c_0_113 ).
fof(c_0_647,plain,
! [X6,X21,X7,X2] :
( hBOOL(c_in(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Collect(X21,X2)),X2))
| ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_648,plain,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(X10,X6))
| hBOOL(hAPP(X7,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_649,plain,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(X7,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_650,plain,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(X10,X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_651,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X7,X15,tc_fun(X2,tc_bool))),
c_0_118 ).
fof(c_0_652,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X7,X15,tc_fun(X2,tc_bool))),
c_0_119 ).
fof(c_0_653,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X15,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X10,X15,tc_fun(X2,tc_bool))),
c_0_120 ).
fof(c_0_654,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X10),tc_fun(X2,tc_bool)),
c_0_121 ).
fof(c_0_655,plain,
! [X20,X6,X2] :
( X20 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X20)) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_656,plain,
! [X43,X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X15),X43),tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X43,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_657,plain,
! [X43,X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X15),X43),tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X43,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_658,plain,
! [X6,X12,X7,X11,X2] :
( hBOOL(hAPP(X7,hAPP(X12,X6)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X12,X2,X11),X7),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_659,plain,
! [X9,X15,X10,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)),X15) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15))
| ~ hBOOL(c_in(X9,X15,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_660,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X15)),
c_0_127 ).
fof(c_0_661,axiom,
! [X15,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X15)),
c_0_128 ).
fof(c_0_662,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_663,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X2))
| ~ hBOOL(c_in(X16,X10,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_664,plain,
! [X66,X55,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X55),X66),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X55),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_665,plain,
! [X12,X9,X10,X11,X2] :
( hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X11,X2),X10),X11))
| ~ hBOOL(c_in(hAPP(X12,X9),X10,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_666,plain,
! [X12,X9,X7,X11,X2] :
( hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X11,X2),X7),X11))
| ~ hBOOL(c_in(hAPP(X12,X9),X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_667,plain,
! [X12,X9,X10,X11,X2] :
( hBOOL(c_in(X9,hAPP(c_Set_Ovimage(X12,X2,X11),X10),X2))
| ~ hBOOL(c_in(hAPP(X12,X9),X10,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_668,plain,
! [X6,X12,X10,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X6),X10,X2))
| ~ hBOOL(c_in(X6,X7,X11))
| ~ c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),X7),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_669,axiom,
! [X63,X64,X62,X51,X11,X2] : c_Hoare__Mirabelle_Otriple_Otriple__case(X62,c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X11),X11,X2) = hAPP(hAPP(hAPP(X62,X64),X51),X63),
c_0_136 ).
fof(c_0_670,axiom,
! [X63,X64,X62,X51,X11,X2] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X62,c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X11),X11,X2) = hAPP(hAPP(hAPP(X62,X64),X51),X63),
c_0_137 ).
fof(c_0_671,axiom,
! [X12,X10,X7,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X11,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X12,X2,X11),X7),hAPP(c_Set_Ovimage(X12,X2,X11),X10),tc_fun(X2,tc_bool)),
c_0_138 ).
fof(c_0_672,plain,
! [X16,X10,X7,X2] :
( ~ hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_673,plain,
! [X30,X9,X2] :
( X30 = X9
| ~ hBOOL(c_in(X30,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_674,axiom,
! [X9,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)),
c_0_141 ).
fof(c_0_675,plain,
! [X6,X12,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X2,X11),X7),X11))
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_676,plain,
! [X6,X12,X7,X11,X2] :
( hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X11,X2),X7),X2))
| ~ hBOOL(c_in(X6,X7,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_677,plain,
! [X6,X12,X7,X11,X2] :
( ~ hBOOL(c_in(X6,X7,X11))
| hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X11,X2),X7),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_678,plain,
! [X6,X12,X7,X52,X2] :
( ~ hBOOL(c_in(X6,X7,X52))
| hBOOL(c_in(hAPP(X12,X6),hAPP(c_Set_Oimage(X12,X52,X2),X7),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_679,plain,
! [X9,X10,X7,X11,X2] :
( c_lessequals(hAPP(X10,X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X2,tc_fun(X11,tc_bool)),tc_fun(X11,tc_bool))
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_680,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X9 = X41
| X9 = X16 ),
c_0_147 ).
fof(c_0_681,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X30 = X16
| X9 = X16 ),
c_0_148 ).
fof(c_0_682,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X9 = X41
| X30 = X41 ),
c_0_149 ).
fof(c_0_683,axiom,
! [X41,X16,X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X2),X16),hAPP(hAPP(c_Set_Oinsert(X2),X41),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))
| X30 = X16
| X30 = X41 ),
c_0_150 ).
fof(c_0_684,plain,
! [X12,X7,X11,X2] :
( c_Finite__Set_Ofinite(X7,X11)
| ~ c_Fun_Oinj__on(X12,X7,X11,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X12,X11,X2),X7),X2) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_685,plain,
! [X15,X10,X7,X2] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_686,axiom,
! [X9,X10,X11,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,X11,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
c_0_153 ).
fof(c_0_687,plain,
! [X12,X9,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X11)
| ~ c_Fun_Oinj__on(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_688,axiom,
! [X12,X7,X11,X2] : c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),hAPP(c_Set_Ovimage(X12,X11,X2),X7)),X7,tc_fun(X2,tc_bool)),
c_0_155 ).
fof(c_0_689,plain,
! [X9,X7,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))) = X7
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_690,plain,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2,X11)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_691,axiom,
! [X9,X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X7)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)),
c_0_158 ).
fof(c_0_692,axiom,
! [X10,X7,X11,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,X11,tc_fun(X2,tc_bool))) = X7,
c_0_159 ).
fof(c_0_693,plain,
! [X20,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X20)
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| X6 = X20
| ~ hBOOL(c_in(X20,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_694,plain,
! [X5,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X5)
| ~ hBOOL(c_in(X5,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| X6 = X5 ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_695,plain,
! [X20,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X20)
| ~ hBOOL(c_in(X20,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Fun_Oinj__on(X12,X7,X2,X11)
| X6 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_696,plain,
! [X20,X6,X12,X7,X11,X2] :
( hAPP(X12,X6) != hAPP(X12,X20)
| ~ hBOOL(c_in(X20,X7,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| X6 = X20
| ~ c_Fun_Oinj__on(X12,X7,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_697,axiom,
! [X69,X63,X70,X64,X4,X51,X2] :
( c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X70,X4,X69,X2)
| X64 = X70 ),
c_0_164 ).
fof(c_0_698,axiom,
! [X69,X63,X70,X64,X4,X51,X2] :
( c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X70,X4,X69,X2)
| X51 = X4 ),
c_0_165 ).
fof(c_0_699,axiom,
! [X69,X63,X70,X64,X4,X51,X2] :
( c_Hoare__Mirabelle_Otriple_Otriple(X64,X51,X63,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X70,X4,X69,X2)
| X63 = X69 ),
c_0_166 ).
fof(c_0_700,plain,
! [X12,X7,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X2)
| ~ c_lessequals(X7,hAPP(c_Set_Oimage(X12,X2,X2),X7),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_701,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X7,X2))
| ~ hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_702,plain,
! [X12,X10,X7,X11,X2] :
( c_Fun_Oinj__on(X12,X7,X2,X11)
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X12,X10,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_703,plain,
! [X9,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10))
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_704,plain,
! [X13,X14,X7,X11,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_lessequals(hAPP(X14,X13),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X14,X2,X11),X11)
| ~ hBOOL(c_in(X13,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_705,plain,
! [X9,X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_706,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)) = X7,
c_0_173 ).
fof(c_0_707,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_708,axiom,
! [X10,X7,X11,X2] : c_HOL_Ominus__class_Ominus(X7,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X10,X11,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X7,
c_0_175 ).
fof(c_0_709,plain,
! [X6,X12,X2] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X6)),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_710,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2))
| hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_711,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2))
| hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_712,plain,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X6))
| ~ hBOOL(hAPP(X10,X6))
| ~ hBOOL(hAPP(X7,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_713,axiom,
! [X9,X15,X10,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)),X15) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X15)),
c_0_180 ).
fof(c_0_714,plain,
! [X6,X10,X7,X11,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool))
| hAPP(X10,X6) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_715,plain,
! [X6,X10,X7,X11,X2] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X10,X11,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(X10,X6) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_716,plain,
! [X6,X12,X7,X11,X2] :
( ~ c_lessequals(X6,X7,tc_fun(X11,tc_bool))
| c_lessequals(hAPP(c_Set_Oimage(X12,X11,X2),X6),hAPP(c_Set_Oimage(X12,X11,X2),X7),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_717,plain,
! [X12,X10,X7,X11,X2] :
( c_lessequals(hAPP(c_Set_Oimage(X12,X2,X11),X7),hAPP(c_Set_Oimage(X12,X2,X11),X10),tc_fun(X11,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_718,plain,
! [X12,X10,X7,X11,X2] :
( c_lessequals(hAPP(c_Set_Ovimage(X12,X11,X2),X7),hAPP(c_Set_Ovimage(X12,X11,X2),X10),tc_fun(X11,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_719,axiom,
! [X9,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),
c_0_186 ).
fof(c_0_720,axiom,
! [X15,X10,X7,X2] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X15,tc_fun(X2,tc_bool))),
c_0_187 ).
fof(c_0_721,plain,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X6))
| ~ hBOOL(hAPP(X7,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_722,plain,
! [X6,X10,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X6))
| ~ hBOOL(hAPP(X10,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_723,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_724,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_725,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X15,X7,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_726,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X15,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_727,plain,
! [X6,X12,X7,X11,X2] :
( hAPP(hAPP(c_Set_Oinsert(X11),hAPP(X12,X6)),hAPP(c_Set_Oimage(X12,X2,X11),X7)) = hAPP(c_Set_Oimage(X12,X2,X11),X7)
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_728,plain,
! [X6,X12,X7,X11,X2] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X12,X2,X11),X7),X6))
| ~ hBOOL(hAPP(X7,hAPP(X12,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_729,plain,
! [X9,X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_730,plain,
! [X43,X15,X10,X7,X2] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X15,X43,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ c_lessequals(X43,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_731,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X19),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_732,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X19),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_733,plain,
! [X6,X10,X7,X2] :
( ~ hBOOL(c_in(X6,X10,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_734,axiom,
! [X9,X10,X7,X2] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),
c_0_201 ).
fof(c_0_735,plain,
! [X6,X16,X7,X11,X2] :
( hAPP(c_Set_Oimage(c_COMBK(X16,X11,X2),X2,X11),X7) = hAPP(hAPP(c_Set_Oinsert(X11),X16),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)))
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_736,plain,
! [X30,X9,X7,X2] :
( hBOOL(c_in(X9,X7,X2))
| X9 = X30
| ~ hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X30),X7),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_737,axiom,
! [X9,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X7),
c_0_204 ).
fof(c_0_738,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_739,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X7,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_740,plain,
! [X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_741,plain,
! [X15,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X15,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_742,plain,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X16,X9,X2)
| ~ c_lessequals(X9,X30,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_743,plain,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X30,X41,X2)
| ~ c_lessequals(X9,X30,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_744,axiom,
! [X9,X15,X10,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X15)
| hBOOL(c_in(X9,X15,X2)) ),
c_0_211 ).
fof(c_0_745,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X7),
c_0_212 ).
fof(c_0_746,plain,
! [X30,X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_747,plain,
! [X30,X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_748,axiom,
! [X9,X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)),
c_0_215 ).
fof(c_0_749,plain,
! [X6,X7,X2] :
( X7 = hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_750,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),
c_0_217 ).
fof(c_0_751,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),
c_0_218 ).
fof(c_0_752,axiom,
! [X12,X9,X10,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),hAPP(hAPP(c_Set_Oinsert(X11),X9),X10)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X12,X9)),hAPP(c_Set_Oimage(X12,X11,X2),X10)),
c_0_219 ).
fof(c_0_753,plain,
! [X5,X6,X7,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X5,X2)
| ~ hBOOL(c_in(X5,X7,X2))
| ~ c_lessequals(X6,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X7,X2),X2)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_754,plain,
! [X12,X10,X7,X11,X2] :
( c_Finite__Set_Ofinite(X10,X11)
| ~ c_lessequals(X10,hAPP(c_Set_Oimage(X12,X2,X11),X7),tc_fun(X11,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_755,axiom,
! [X6,X2] : hBOOL(c_in(X6,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)),
c_0_222 ).
fof(c_0_756,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_757,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Odistrib__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_758,axiom,
! [X5,X6,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X5),hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X2),X6),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
c_0_225 ).
fof(c_0_759,axiom,
! [X9,X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X9),X10)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10)
| hBOOL(c_in(X9,X7,X2)) ),
c_0_226 ).
fof(c_0_760,axiom,
! [X6,X7,X2] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) = X7
| hBOOL(c_in(X6,X7,X2)) ),
c_0_227 ).
fof(c_0_761,axiom,
! [X6,X10,X7,X2] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X6),c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)))
| hBOOL(c_in(X6,X10,X2)) ),
c_0_228 ).
fof(c_0_762,plain,
! [X30,X9,X10,X2] :
( hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X30),X10),X2))
| ~ hBOOL(c_in(X9,X10,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_763,plain,
! [X30,X9,X7,X2] :
( hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X30),X7),X2))
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_764,plain,
! [X6,X33,X7,X2] :
( c_Finite__Set_Ofold1(X33,hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X2) = hAPP(hAPP(X33,X6),c_Finite__Set_Ofold1(X33,X7,X2))
| hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_765,plain,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(X39,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_766,plain,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(X40,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_767,plain,
! [X6,X10,X7,X2] :
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X10,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_768,plain,
! [X15,X10,X7,X2] :
( c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X15,X7,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X7
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_769,axiom,
! [X16,X7,X11,X2] :
( hAPP(c_Set_Ovimage(c_COMBK(X16,X11,X2),X2,X11),X7) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X16,X7,X11)) ),
c_0_236 ).
fof(c_0_770,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_771,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_772,plain,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X30,X41,X2)
| ~ c_lessequals(X16,X9,X2) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_773,axiom,
! [X16,X7,X11,X2] :
( hAPP(c_Set_Oimage(c_COMBK(X16,X2,X11),X11,X2),X7) = hAPP(hAPP(c_Set_Oinsert(X2),X16),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_240 ).
fof(c_0_774,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),
c_0_241 ).
fof(c_0_775,plain,
! [X6,X10,X7,X2] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X10,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_776,plain,
! [X17,X12,X11] :
( ~ class_Lattices_Olattice(X11)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X11)),X12),X17),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11),hAPP(X12,v_x)),hAPP(X17,v_x)) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_777,plain,
! [X17,X12,X11] :
( ~ class_Lattices_Olattice(X11)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X11)),X12),X17),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11),hAPP(X12,v_x)),hAPP(X17,v_x)) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_778,plain,
! [X38,X2] :
( ~ class_Orderings_Oorder(X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X2),X38),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_SetInterval_Oord__class_OlessThan(X38,X2),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X38),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_779,plain,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))) = X10
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_780,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_781,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_782,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_783,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_784,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_785,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_786,axiom,
! [X16,X11,X2] : hAPP(c_Set_Oimage(c_COMBK(X16,X2,X11),X11,X2),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_253 ).
fof(c_0_787,plain,
! [X55,X10,X7,X2] :
( hBOOL(c_in(X55,X10,X2))
| ~ hBOOL(c_in(X55,X7,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_788,plain,
! [X6,X10,X7,X2] :
( hBOOL(c_in(X6,X10,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_789,plain,
! [X16,X10,X7,X2] :
( hBOOL(c_in(X16,X10,X2))
| ~ hBOOL(c_in(X16,X7,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_790,plain,
! [X6,X10,X7,X2] :
( hBOOL(c_in(X6,X10,X2))
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_791,plain,
! [X9,X43,X15,X2] :
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X9),X15),hAPP(hAPP(c_Set_Oinsert(X2),X9),X43),tc_fun(X2,tc_bool))
| ~ c_lessequals(X15,X43,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_792,plain,
! [X20,X6,X7,X2] :
( hBOOL(hAPP(X7,X6))
| X20 = X6
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X20),X7),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_793,plain,
! [X6,X10,X7,X2] :
( hBOOL(c_in(X6,X10,X2))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_794,plain,
! [X14,X7,X11,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,c_COMBK(X14,X11,X2),X2,X11) = X14
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_795,axiom,
! [X6,X10,X7,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X6),X7) != hAPP(hAPP(c_Set_Oinsert(X2),X6),X10)
| hBOOL(c_in(X6,X10,X2))
| hBOOL(c_in(X6,X7,X2))
| X7 = X10 ),
c_0_262 ).
fof(c_0_796,plain,
! [X6,X21,X2] :
( ~ hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_797,plain,
! [X9,X7,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X7,X2),X9,X2)
| ~ hBOOL(c_in(X9,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_798,plain,
! [X6,X21,X2] :
( hBOOL(hAPP(X21,X6))
| ~ hBOOL(c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_799,axiom,
! [X10,X7,X2] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X10,tc_fun(X2,tc_bool)),
c_0_266 ).
fof(c_0_800,axiom,
! [X10,X7,X2] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10),X7,tc_fun(X2,tc_bool)),
c_0_267 ).
fof(c_0_801,axiom,
! [X10,X7,X2] : c_lessequals(X7,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)),
c_0_268 ).
fof(c_0_802,axiom,
! [X10,X7,X2] : c_lessequals(X10,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10),tc_fun(X2,tc_bool)),
c_0_269 ).
fof(c_0_803,plain,
! [X6,X10,X7,X2] :
( c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_804,plain,
! [X41,X16,X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2),c_SetInterval_Oord__class_OatLeastAtMost(X16,X41,X2),tc_fun(X2,tc_bool))
| c_lessequals(X9,X30,X2) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_805,plain,
! [X28,X29,X12,X9,X11,X2] :
( ~ c_Orderings_Olinorder(X28,X29,X2)
| c_Finite__Set_Ofold1(X12,hAPP(hAPP(c_Set_Oinsert(X11),X9),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),X11) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_806,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)) = X7 ),
c_0_273 ).
fof(c_0_807,plain,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X39,X2)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_808,plain,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X39,X2)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_809,plain,
! [X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X28,X6),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2)
| ~ hBOOL(hAPP(hAPP(X29,X6),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_810,plain,
! [X20,X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ hBOOL(hAPP(hAPP(X29,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_811,plain,
! [X20,X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ hBOOL(hAPP(hAPP(X28,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_812,plain,
! [X20,X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ hBOOL(hAPP(hAPP(X29,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_813,plain,
! [X9,X2] : ~ hBOOL(c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_814,plain,
! [X16,X2] : ~ hBOOL(c_in(X16,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_815,plain,
! [X6,X2] : ~ hBOOL(c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_816,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X2)
| ~ c_lessequals(X6,X30,X2)
| ~ c_lessequals(X6,X9,X2) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_817,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2)
| ~ c_lessequals(X6,X19,X2)
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_818,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2)
| ~ c_lessequals(X6,X19,X2)
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_819,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X19,X2)
| ~ c_lessequals(X20,X19,X2)
| ~ c_lessequals(X6,X19,X2) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_820,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19),X6,X2)
| ~ c_lessequals(X19,X6,X2)
| ~ c_lessequals(X20,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_821,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X6,X2)
| ~ c_lessequals(X30,X6,X2)
| ~ c_lessequals(X9,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_822,plain,
! [X8,X59,X2] :
( ~ class_Orderings_Oorder(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_SetInterval_Oord__class_OlessThan(X59,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X59,X8,X2)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_823,plain,
! [X33,X16,X30,X9,X2] :
( hAPP(hAPP(X33,hAPP(hAPP(X33,X9),X30)),X16) = hAPP(hAPP(X33,X9),hAPP(hAPP(X33,X30),X16))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_824,axiom,
! [X30,X9,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X2),X30),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X9 = X30 ),
c_0_291 ).
fof(c_0_825,axiom,
! [X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_292 ).
fof(c_0_826,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X10,X7,tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_293 ).
fof(c_0_827,plain,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_828,plain,
! [X39,X40,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X40),X39),X2)
| ~ c_Finite__Set_Ofinite(X39,X2) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_829,plain,
! [X15,X10,X7,X2] :
( c_lessequals(X7,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X10,X15,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_830,plain,
! [X25,X20,X26,X6,X2] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X6,X20,X2) != c_HOL_Ominus__class_Ominus(X26,X25,X2)
| c_lessequals(X20,X6,X2)
| ~ c_lessequals(X25,X26,X2) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_831,plain,
! [X25,X20,X26,X6,X2] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X6,X20,X2) != c_HOL_Ominus__class_Ominus(X26,X25,X2)
| c_lessequals(X25,X26,X2)
| ~ c_lessequals(X20,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_832,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_833,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_834,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_835,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_836,axiom,
! [X6,X10,X2] : hBOOL(c_in(X6,hAPP(hAPP(c_Set_Oinsert(X2),X6),X10),X2)),
c_0_303 ).
fof(c_0_837,axiom,
! [X9,X10,X2] : hBOOL(c_in(X9,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),X2)),
c_0_304 ).
fof(c_0_838,axiom,
! [X6,X7,X2] : hBOOL(c_in(X6,hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X2)),
c_0_305 ).
fof(c_0_839,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X9,X6,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_840,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X30,X6,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_841,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,X19,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X19,X2) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_842,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X20,X19,X2)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X19,X2) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_843,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X19,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_844,plain,
! [X19,X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X20,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X19),X2) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_845,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X30,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X2) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_846,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X9,X2)
| ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X2) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_847,axiom,
! [X20,X6,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X6),hAPP(hAPP(c_Set_Oinsert(X2),X20),X7)) = hAPP(hAPP(c_Set_Oinsert(X2),X20),hAPP(hAPP(c_Set_Oinsert(X2),X6),X7)),
c_0_314 ).
fof(c_0_848,axiom,
! [X10,X7,X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X10,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),
c_0_315 ).
fof(c_0_849,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) != X10
| c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
c_0_316 ).
fof(c_0_850,plain,
! [X30,X10,X7,X2] :
( c_lessequals(X7,hAPP(hAPP(c_Set_Oinsert(X2),X30),X10),tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_851,plain,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| ~ hBOOL(hAPP(hAPP(X28,X6),X20))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_852,plain,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_853,axiom,
! [X12,X11,X2] : c_Fun_Oinj__on(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X11),
c_0_320 ).
fof(c_0_854,plain,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X10,X2) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_855,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_322 ).
fof(c_0_856,axiom,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_323 ).
fof(c_0_857,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X10),X7),
c_0_324 ).
fof(c_0_858,axiom,
! [X10,X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X10),X7),
c_0_325 ).
fof(c_0_859,plain,
! [X27,X14,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X27,X2),c_Finite__Set_Olinorder__class_OMin(X14,X2),X2)
| ~ c_Finite__Set_Ofinite(X27,X2)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X14,X27,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_860,plain,
! [X27,X14,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X14,X2),c_Finite__Set_Olinorder__class_OMax(X27,X2),X2)
| ~ c_Finite__Set_Ofinite(X27,X2)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X14,X27,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_861,plain,
! [X9,X21,X2] :
( hBOOL(hAPP(X21,X9))
| ~ hBOOL(c_in(X9,c_Collect(X21,X2),X2)) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_862,plain,
! [X6,X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X6,c_Finite__Set_Olinorder__class_OMax(X7,X2),X2)
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_863,plain,
! [X6,X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X7,X2),X6,X2)
| ~ hBOOL(c_in(X6,X7,X2))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_864,plain,
! [X20,X6,X7,X2] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X20),X7),X6))
| ~ hBOOL(hAPP(X7,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_865,plain,
! [X65,X66,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_lessequals(X66,X65,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X65,X2) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_866,plain,
! [X44,X40,X11,X2] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X44,X2,X11),X40),X11)
| ~ c_Finite__Set_Ofinite(X40,X2) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_867,axiom,
! [X10,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X10) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_334 ).
fof(c_0_868,plain,
! [X10,X7,X11] :
( ~ class_HOL_Ominus(X11)
| hAPP(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(t_a,X11)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X7,v_x),hAPP(X10,v_x),X11) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_869,plain,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) = X7
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_870,plain,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X10) = X10
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_871,plain,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) = X10
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_872,plain,
! [X10,X7,X2] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X10) = X7
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_873,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X6,X20,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X6,X2),c_SetInterval_Oord__class_OlessThan(X20,X2),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_874,plain,
! [X6,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(X6,c_Complete__Lattice_OSup__class_OSup(X7,X2),X2)
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_875,plain,
! [X6,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X7,X2),X6,X2)
| ~ hBOOL(c_in(X6,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_876,axiom,
! [X12,X9,X2] : c_Finite__Set_Ofold1(X12,hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9,
c_0_343 ).
fof(c_0_877,axiom,
! [X12,X7,X11,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != hAPP(c_Set_Oimage(X12,X11,X2),X7)
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_344 ).
fof(c_0_878,axiom,
! [X12,X7,X11,X2] :
( hAPP(c_Set_Oimage(X12,X11,X2),X7) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)) ),
c_0_345 ).
fof(c_0_879,plain,
! [X5,X6,X33,X11,X2] :
( hAPP(hAPP(c_Set_Oinsert(X11),X6),X5) != c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| hBOOL(c_in(X6,X5,X11))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_880,plain,
! [X33,X16,X30,X9,X2] :
( hAPP(hAPP(X33,X9),hAPP(hAPP(X33,X30),X16)) = hAPP(hAPP(X33,X30),hAPP(hAPP(X33,X9),X16))
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_881,axiom,
! [X7,X2] : c_Fun_Oinj__on(c_COMBI(X2),X7,X2,X2),
c_0_348 ).
fof(c_0_882,plain,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| hBOOL(hAPP(hAPP(X29,X6),X20))
| hBOOL(hAPP(hAPP(X29,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_883,plain,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X20),X6))
| X6 = X20
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_884,plain,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X20),X6))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| X6 = X20
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_885,plain,
! [X20,X6,X28,X29,X2] :
( X6 = X20
| hBOOL(hAPP(hAPP(X29,X20),X6))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_886,plain,
! [X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X6),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2)
| hBOOL(hAPP(hAPP(X28,X6),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_887,plain,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X6),X20))
| hBOOL(hAPP(hAPP(X28,X20),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_888,plain,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X29,X20),X6))
| hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_889,plain,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X28,X20),X6))
| hBOOL(hAPP(hAPP(X28,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_890,plain,
! [X20,X6,X28,X29,X2] :
( hBOOL(hAPP(hAPP(X28,X20),X6))
| hBOOL(hAPP(hAPP(X29,X6),X20))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_891,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X2)
| ~ c_lessequals(X6,X9,X2) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_892,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),X30),X2)
| ~ c_lessequals(X6,X30,X2) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_893,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X6,X2)
| ~ c_lessequals(X30,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_894,plain,
! [X6,X30,X9,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),X30),X6,X2)
| ~ c_lessequals(X9,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_895,axiom,
! [X10,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X10) = X10,
c_0_362 ).
fof(c_0_896,plain,
! [X10,X7,X2] :
( X7 = X10
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_897,plain,
! [X10,X7,X2] :
( X7 = X10
| ~ c_lessequals(X10,X7,tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_898,plain,
! [X19,X6,X12,X11,X2] :
( hAPP(hAPP(X12,X6),hAPP(hAPP(X12,X6),X19)) = hAPP(hAPP(X12,X6),X19)
| ~ c_Finite__Set_Ofun__left__comm__idem(X12,X2,X11) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_899,plain,
! [X6,X17,X12,X11,X2] :
( ~ class_HOL_Oord(X11)
| c_lessequals(hAPP(X12,X6),hAPP(X17,X6),X11)
| ~ c_lessequals(X12,X17,tc_fun(X2,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_900,axiom,
! [X5,X6,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X6),X5) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X6,X5,X2)) ),
c_0_367 ).
fof(c_0_901,axiom,
! [X6,X7,X2] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),X6)),
c_0_368 ).
fof(c_0_902,plain,
! [X19,X20,X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X19,X2)
| ~ c_lessequals(X20,X19,X2)
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_903,plain,
! [X19,X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X19,X6,X2)
| ~ c_lessequals(X19,X20,X2)
| ~ c_lessequals(X20,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_904,plain,
! [X7,X2] :
( X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_905,axiom,
! [X10,X7,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X7,tc_fun(X2,tc_bool)),
c_0_372 ).
fof(c_0_906,plain,
! [X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_907,plain,
! [X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_908,plain,
! [X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_909,plain,
! [X9,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_910,plain,
! [X9,X7,X2] :
( hAPP(hAPP(c_Set_Oinsert(X2),X9),X7) = X7
| ~ hBOOL(c_in(X9,X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_911,plain,
! [X66,X68,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,X68,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X68,X66,X2) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_912,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X6,X2),c_SetInterval_Oord__class_OlessThan(X20,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_913,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_380 ).
fof(c_0_914,plain,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X9,X30,X2) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_915,plain,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2)
| ~ c_lessequals(X9,X30,X2) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_916,plain,
! [X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X7,X2),X7,X2))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_917,plain,
! [X7,X2] :
( ~ class_Orderings_Olinorder(X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X7,X2),X7,X2))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_918,axiom,
! [X6,X2] : c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X6,
c_0_385 ).
fof(c_0_919,axiom,
! [X6,X2] : c_The(hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X6,
c_0_386 ).
fof(c_0_920,plain,
! [X6,X28,X29,X2] :
( ~ c_Orderings_Olinorder(X28,X29,X2)
| ~ hBOOL(hAPP(hAPP(X29,X6),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_921,plain,
! [X6,X28,X29,X2] :
( ~ hBOOL(hAPP(hAPP(X29,X6),X6))
| ~ c_Orderings_Olinorder(X28,X29,X2) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_922,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_923,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_924,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_925,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_926,plain,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(X10,X2) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_927,plain,
! [X9,X21,X2] :
( hBOOL(c_in(X9,c_Collect(X21,X2),X2))
| ~ hBOOL(hAPP(X21,X9)) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_928,plain,
! [X6,X2] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6)),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_929,axiom,
! [X6,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X6),hAPP(hAPP(c_Set_Oinsert(X2),X6),X7)) = hAPP(hAPP(c_Set_Oinsert(X2),X6),X7),
c_0_396 ).
fof(c_0_930,plain,
! [X6,X22,X2] :
( hBOOL(hAPP(X22,X6))
| ~ hBOOL(c_in(X6,X22,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_931,plain,
! [X9,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X9),c_Complete__Lattice_OSup__class_OSup(X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_932,plain,
! [X9,X7,X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X9),c_Complete__Lattice_OInf__class_OInf(X7,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_933,plain,
! [X6,X24,X21,X2] :
( hBOOL(hAPP(X24,X6))
| ~ c_lessequals(X21,X24,tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_934,plain,
! [X6,X24,X21,X2] :
( hBOOL(hAPP(X24,X6))
| ~ hBOOL(hAPP(X21,X6))
| ~ c_lessequals(X21,X24,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_935,axiom,
! [X12,X11,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = hAPP(c_Set_Oimage(X12,X11,X2),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),
c_0_402 ).
fof(c_0_936,axiom,
! [X12,X11,X2] : hAPP(c_Set_Oimage(X12,X11,X2),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_403 ).
fof(c_0_937,axiom,
! [X12,X11,X2] : hAPP(c_Set_Ovimage(X12,X2,X11),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_404 ).
fof(c_0_938,plain,
! [X9,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_939,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X7,
c_0_406 ).
fof(c_0_940,plain,
! [X66,X39,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,X66,X2)
| ~ c_lessequals(X66,X39,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_941,plain,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X7,X10,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_942,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| X6 = X20
| ~ c_lessequals(X6,X20,X2)
| ~ c_lessequals(X20,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_943,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| X6 = X20
| ~ c_lessequals(X20,X6,X2)
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_944,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Oorder(X2)
| X6 = X20
| ~ c_lessequals(X20,X6,X2)
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_945,axiom,
! [X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
c_0_412 ).
fof(c_0_946,plain,
! [X25,X26,X6,X2] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X6,X6,X2) != c_HOL_Ominus__class_Ominus(X26,X25,X2)
| X26 = X25 ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_947,plain,
! [X20,X5,X6,X2] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X5,X20,X2) != c_HOL_Ominus__class_Ominus(X6,X6,X2)
| X5 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_948,axiom,
! [X9,X10,X2] : c_lessequals(X10,hAPP(hAPP(c_Set_Oinsert(X2),X9),X10),tc_fun(X2,tc_bool)),
c_0_415 ).
fof(c_0_949,axiom,
! [X12,X7,X2] : c_Finite__Set_Ofold1(X12,X7,X2) = c_The(c_Finite__Set_Ofold1Set(X12,X7,X2),X2),
c_0_416 ).
fof(c_0_950,axiom,
! [X3,X36,X31,X34,X32,X35] :
( c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OCond(X3,X32,X31)
| X36 = X3 ),
c_0_417 ).
fof(c_0_951,axiom,
! [X3,X36,X31,X34,X32,X35] :
( c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OCond(X3,X32,X31)
| X35 = X32 ),
c_0_418 ).
fof(c_0_952,axiom,
! [X3,X36,X31,X34,X32,X35] :
( c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OCond(X3,X32,X31)
| X34 = X31 ),
c_0_419 ).
fof(c_0_953,plain,
! [X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X9,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_954,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_955,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_956,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_957,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20),X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_958,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_959,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X20,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_960,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X20,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_961,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20),X2) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_962,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20)) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_963,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20)) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_964,plain,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X2) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_965,plain,
! [X10,X7,X2] :
( c_Finite__Set_Ofinite(X7,X2)
| ~ c_Finite__Set_Ofinite(X10,X2)
| ~ c_lessequals(X7,X10,tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_966,plain,
! [X6,X22,X2] :
( hBOOL(c_in(X6,X22,X2))
| ~ hBOOL(hAPP(X22,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_967,axiom,
! [X7,X2] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_434 ).
fof(c_0_968,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
c_0_435 ).
fof(c_0_969,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = X20
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_970,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = X6
| ~ c_lessequals(X20,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_971,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = X20
| ~ c_lessequals(X20,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_972,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = X6
| ~ c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_973,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) != X20
| c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_974,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) != X6
| c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_975,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X7),X7) = X7,
c_0_442 ).
fof(c_0_976,axiom,
! [X7,X2] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X7),X7) = X7,
c_0_443 ).
fof(c_0_977,axiom,
! [X9,X2] : c_Collect(c_fequal(X9,X2),X2) = hAPP(hAPP(c_Set_Oinsert(X2),X9),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
c_0_444 ).
fof(c_0_978,plain,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X9,X30,X2) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_979,plain,
! [X30,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X9,X30,X2)
| c_lessequals(X9,X30,X2) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_980,plain,
! [X9,X7,X2] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),X2)
| ~ c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_981,axiom,
! [X1,X2] : hAPP(c_Set_Ovimage(c_COMBI(X2),X2,X2),X1) = X1,
c_0_448 ).
fof(c_0_982,axiom,
! [X1,X2] : hAPP(c_Set_Oimage(c_COMBI(X2),X2,X2),X1) = X1,
c_0_449 ).
fof(c_0_983,plain,
! [X1,X73,X2] :
( X73 = X1
| ~ hBOOL(hAPP(c_fequal(X73,X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_984,axiom,
! [X39,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X39,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
c_0_451 ).
fof(c_0_985,axiom,
! [X7,X2] : c_HOL_Ominus__class_Ominus(X7,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X7,
c_0_452 ).
fof(c_0_986,axiom,
! [X7,X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X7,tc_fun(X2,tc_bool)),
c_0_453 ).
fof(c_0_987,axiom,
! [X9,X7,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X9),X7) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_454 ).
fof(c_0_988,axiom,
! [X9,X7,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X2),X9),X7),
c_0_455 ).
fof(c_0_989,axiom,
! [X24,X21,X11,X2] : hAPP(c_COMBK(X21,X2,X11),X24) = X21,
c_0_456 ).
fof(c_0_990,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X20,X6,X2)
| c_lessequals(X6,X20,X2) ),
inference(fof_simplification,[status(thm)],[c_0_457]) ).
fof(c_0_991,plain,
! [X6,X21,X2] :
( c_Collect(X21,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_992,plain,
! [X6,X21,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Collect(X21,X2)
| ~ hBOOL(hAPP(X21,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_993,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X6) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_994,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X20),X6) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_995,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X6) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_996,plain,
! [X20,X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X20),X6) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_997,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
c_0_464 ).
fof(c_0_998,axiom,
! [X3,X36,X4,X34,X35] : c_Com_Ocom_OWhile(X3,X4) != c_Com_Ocom_OCond(X36,X35,X34),
c_0_465 ).
fof(c_0_999,axiom,
! [X3,X31,X34,X32,X35] : c_Com_Ocom_OCond(X3,X32,X31) != c_Com_Ocom_OSemi(X35,X34),
c_0_466 ).
fof(c_0_1000,axiom,
! [X3,X36,X4,X34,X35] : c_Com_Ocom_OCond(X36,X35,X34) != c_Com_Ocom_OWhile(X3,X4),
c_0_467 ).
fof(c_0_1001,axiom,
! [X3,X31,X34,X32,X35] : c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OCond(X3,X32,X31),
c_0_468 ).
fof(c_0_1002,axiom,
! [X7,X2] : c_HOL_Ominus__class_Ominus(X7,X7,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_469 ).
fof(c_0_1003,plain,
! [X33,X30,X9,X2] :
( hAPP(hAPP(X33,X9),X30) = hAPP(hAPP(X33,X30),X9)
| ~ c_OrderedGroup_Oab__semigroup__mult(X33,X2) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1004,plain,
! [X10,X7,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X7),X10) != c_Orderings_Obot__class_Obot(X2)
| X10 = c_Orderings_Obot__class_Obot(X2) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1005,plain,
! [X10,X7,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X7),X10) != c_Orderings_Obot__class_Obot(X2)
| X7 = c_Orderings_Obot__class_Obot(X2) ),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1006,axiom,
! [X3,X31,X32] : c_Com_Ocom_OCond(X3,X32,X31) != c_Com_Ocom_OSKIP,
c_0_473 ).
fof(c_0_1007,axiom,
! [X3,X31,X32] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X3,X32,X31),
c_0_474 ).
fof(c_0_1008,axiom,
! [X2] : c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X2),X2,tc_fun(X2,tc_bool)),
c_0_475 ).
fof(c_0_1009,axiom,
! [X6,X2] : hBOOL(hAPP(c_fequal(X6,X2),X6)),
c_0_476 ).
fof(c_0_1010,axiom,
! [X7,X2] : c_lessequals(X7,X7,tc_fun(X2,tc_bool)),
c_0_477 ).
fof(c_0_1011,axiom,
! [X6,X2] : c_lessequals(X6,X6,tc_fun(X2,tc_bool)),
c_0_478 ).
fof(c_0_1012,plain,
! [X2] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = c_Orderings_Obot__class_Obot(X2) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1013,plain,
! [X11] :
( ~ class_Orderings_Obot(X11)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X11)),v_x) = c_Orderings_Obot__class_Obot(X11) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1014,plain,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),c_Orderings_Obot__class_Obot(X2)),X6) = c_Orderings_Obot__class_Obot(X2) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1015,plain,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2)),X6) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1016,plain,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),c_Orderings_Obot__class_Obot(X2)) = c_Orderings_Obot__class_Obot(X2) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1017,plain,
! [X6,X2] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1018,plain,
! [X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X2),X2,X2) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1019,plain,
! [X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X2),X2,X2) ),
inference(fof_simplification,[status(thm)],[c_0_486]) ).
fof(c_0_1020,plain,
! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),c_Orderings_Obot__class_Obot(X2)) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1021,axiom,
! [X2] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_488 ).
fof(c_0_1022,plain,
! [X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1023,plain,
! [X6,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X6,X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1024,plain,
! [X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X6),X6) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1025,plain,
! [X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X6),X6) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1026,plain,
! [X20,X6,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_SetInterval_Oord__class_OlessThan(X6,X2) != c_SetInterval_Oord__class_OlessThan(X20,X2)
| X6 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1027,axiom,
! [X3,X36,X4,X51] :
( c_Com_Ocom_OWhile(X36,X51) != c_Com_Ocom_OWhile(X3,X4)
| X51 = X4 ),
c_0_494 ).
fof(c_0_1028,axiom,
! [X3,X36,X4,X51] :
( c_Com_Ocom_OWhile(X36,X51) != c_Com_Ocom_OWhile(X3,X4)
| X36 = X3 ),
c_0_495 ).
fof(c_0_1029,axiom,
! [X31,X34,X32,X35] :
( c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OSemi(X32,X31)
| X35 = X32 ),
c_0_496 ).
fof(c_0_1030,axiom,
! [X31,X34,X32,X35] :
( c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OSemi(X32,X31)
| X34 = X31 ),
c_0_497 ).
fof(c_0_1031,plain,
! [X71,X72] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X71,X72))
| ~ class_Finite__Set_Ofinite_Ofinite(X72)
| ~ class_Finite__Set_Ofinite_Ofinite(X71) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1032,axiom,
! [X3,X4,X34,X35] : c_Com_Ocom_OWhile(X3,X4) != c_Com_Ocom_OSemi(X35,X34),
c_0_499 ).
fof(c_0_1033,axiom,
! [X3,X4,X34,X35] : c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OWhile(X3,X4),
c_0_500 ).
fof(c_0_1034,axiom,
! [X6,X2] : c_The(c_fequal(X6,X2),X2) = X6,
c_0_501 ).
fof(c_0_1035,plain,
! [X71,X72] :
( class_HOL_Oord(tc_fun(X71,X72))
| ~ class_HOL_Oord(X72) ),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1036,plain,
! [X71,X72] :
( class_HOL_Ominus(tc_fun(X71,X72))
| ~ class_HOL_Ominus(X72) ),
inference(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1037,plain,
! [X71,X72] :
( class_Orderings_Obot(tc_fun(X71,X72))
| ~ class_Orderings_Obot(X72) ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1038,plain,
! [X71,X72] :
( class_Orderings_Oorder(tc_fun(X71,X72))
| ~ class_Orderings_Oorder(X72) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1039,plain,
! [X71,X72] :
( class_Lattices_Olattice(tc_fun(X71,X72))
| ~ class_Lattices_Olattice(X72) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1040,plain,
! [X71,X72] :
( class_Orderings_Opreorder(tc_fun(X71,X72))
| ~ class_Orderings_Opreorder(X72) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1041,plain,
! [X71,X72] :
( class_Lattices_Obounded__lattice(tc_fun(X71,X72))
| ~ class_Lattices_Obounded__lattice(X72) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1042,plain,
! [X71,X72] :
( class_Lattices_Odistrib__lattice(tc_fun(X71,X72))
| ~ class_Lattices_Odistrib__lattice(X72) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1043,plain,
! [X71,X72] :
( class_Lattices_Olower__semilattice(tc_fun(X71,X72))
| ~ class_Lattices_Olattice(X72) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1044,plain,
! [X71,X72] :
( class_Lattices_Oupper__semilattice(tc_fun(X71,X72))
| ~ class_Lattices_Olattice(X72) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1045,plain,
! [X71,X72] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X71,X72))
| ~ class_Complete__Lattice_Ocomplete__lattice(X72) ),
inference(fof_simplification,[status(thm)],[c_0_512]) ).
fof(c_0_1046,axiom,
! [X31,X32] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X32,X31),
c_0_513 ).
fof(c_0_1047,axiom,
! [X31,X32] : c_Com_Ocom_OSemi(X32,X31) != c_Com_Ocom_OSKIP,
c_0_514 ).
fof(c_0_1048,axiom,
! [X3,X4] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X3,X4),
c_0_515 ).
fof(c_0_1049,axiom,
! [X3,X4] : c_Com_Ocom_OWhile(X3,X4) != c_Com_Ocom_OSKIP,
c_0_516 ).
fof(c_0_1050,plain,
! [X7,X2] :
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1051,axiom,
! [X21,X2] : hAPP(c_COMBI(X2),X21) = X21,
c_0_518 ).
fof(c_0_1052,axiom,
hAPP(c_COMBI(t_a),v_P) = v_P,
c_0_519 ).
fof(c_0_1053,axiom,
! [X21,X2] : c_Collect(X21,X2) = X21,
c_0_520 ).
fof(c_0_1054,axiom,
class_HOL_Oord(tc_bool),
c_0_521 ).
fof(c_0_1055,axiom,
class_HOL_Ominus(tc_bool),
c_0_522 ).
fof(c_0_1056,axiom,
class_Orderings_Obot(tc_bool),
c_0_523 ).
fof(c_0_1057,axiom,
class_Orderings_Oorder(tc_bool),
c_0_524 ).
fof(c_0_1058,axiom,
class_Lattices_Olattice(tc_bool),
c_0_525 ).
fof(c_0_1059,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_526 ).
fof(c_0_1060,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_527 ).
fof(c_0_1061,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_528 ).
fof(c_0_1062,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
c_0_529 ).
fof(c_0_1063,axiom,
class_Lattices_Olower__semilattice(tc_bool),
c_0_530 ).
fof(c_0_1064,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_531 ).
fof(c_0_1065,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_532 ).
fof(c_0_1066,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60,X61] :
( hAPP(X59,hAPP(hAPP(c_Set_Oinsert(X61),X58),hAPP(hAPP(c_Set_Oinsert(X61),X57),c_Orderings_Obot__class_Obot(tc_fun(X61,tc_bool))))) = hAPP(hAPP(X52,X58),X57)
| ~ c_Complete__Lattice_Ocomplete__lattice(X60,X59,X53,X54,X55,X52,X56,X51,X61) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_1067,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60,X61] :
( hAPP(X60,hAPP(hAPP(c_Set_Oinsert(X61),X58),hAPP(hAPP(c_Set_Oinsert(X61),X57),c_Orderings_Obot__class_Obot(tc_fun(X61,tc_bool))))) = hAPP(hAPP(X55,X58),X57)
| ~ c_Complete__Lattice_Ocomplete__lattice(X60,X59,X53,X54,X55,X52,X56,X51,X61) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_1068,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60,X61] :
( hBOOL(hAPP(hAPP(X54,hAPP(X59,X60)),X51))
| ~ hBOOL(c_in(X51,X60,X61))
| ~ c_Complete__Lattice_Ocomplete__lattice(X59,X58,X54,X55,X56,X53,X57,X52,X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_535])])]) ).
fof(c_0_1069,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60,X61] :
( hBOOL(hAPP(hAPP(X54,X51),hAPP(X58,X60)))
| ~ hBOOL(c_in(X51,X60,X61))
| ~ c_Complete__Lattice_Ocomplete__lattice(X59,X58,X54,X55,X56,X53,X57,X52,X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_536])])]) ).
fof(c_0_1070,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60] :
( hAPP(X58,hAPP(hAPP(c_Set_Oinsert(X60),X57),c_Orderings_Obot__class_Obot(tc_fun(X60,tc_bool)))) = X57
| ~ c_Complete__Lattice_Ocomplete__lattice(X59,X58,X53,X54,X55,X52,X56,X51,X60) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_1071,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60] :
( hAPP(X59,hAPP(hAPP(c_Set_Oinsert(X60),X57),c_Orderings_Obot__class_Obot(tc_fun(X60,tc_bool)))) = X57
| ~ c_Complete__Lattice_Ocomplete__lattice(X59,X58,X53,X54,X55,X52,X56,X51,X60) ),
inference(variable_rename,[status(thm)],[c_0_538]) ).
fof(c_0_1072,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60,X61] :
( hAPP(X58,hAPP(hAPP(c_Set_Oinsert(X61),X57),X60)) = hAPP(hAPP(X52,X57),hAPP(X58,X60))
| ~ c_Complete__Lattice_Ocomplete__lattice(X59,X58,X53,X54,X55,X52,X56,X51,X61) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_1073,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59,X60,X61] :
( hAPP(X59,hAPP(hAPP(c_Set_Oinsert(X61),X57),X60)) = hAPP(hAPP(X55,X57),hAPP(X59,X60))
| ~ c_Complete__Lattice_Ocomplete__lattice(X59,X58,X53,X54,X55,X52,X56,X51,X61) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_1074,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59] :
( hAPP(X57,c_Orderings_Obot__class_Obot(tc_fun(X59,tc_bool))) = X56
| ~ c_Complete__Lattice_Ocomplete__lattice(X58,X57,X53,X54,X55,X52,X56,X51,X59) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_1075,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58,X59] :
( hAPP(X58,c_Orderings_Obot__class_Obot(tc_fun(X59,tc_bool))) = X51
| ~ c_Complete__Lattice_Ocomplete__lattice(X58,X57,X53,X54,X55,X52,X56,X51,X59) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_1076,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Hoare__Mirabelle_Ohoare__derivs(X47,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X48)),c_Hoare__Mirabelle_Otriple_Otriple(X46,c_Com_Ocom_OCond(X44,X43,X42),X45,X48)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X48),tc_bool))),X48)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X47,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X48)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X46,c_Fun_Ocomp(c_Not,X44,tc_bool,tc_bool,tc_Com_Ostate),X48),X42,X45,X48)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X48),tc_bool))),X48)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X47,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X48)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X46,X44,X48),X43,X45,X48)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X48),tc_bool))),X48) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_1077,plain,
! [X40,X41,X42,X43,X44] :
( c_Hoare__Mirabelle_Ohoare__derivs(X43,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X44)),c_Hoare__Mirabelle_Otriple_Otriple(X42,c_Com_Ocom_OWhile(X41,X40),c_Hoare__Mirabelle_Opeek__and(X42,c_Fun_Ocomp(c_Not,X41,tc_bool,tc_bool,tc_Com_Ostate),X44),X44)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X44),tc_bool))),X44)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X43,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X44)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X42,X41,X44),X40,X42,X44)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X44),tc_bool))),X44) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_1078,plain,
! [X40,X41,X42,X43,X44,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X44,X42,X43,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X43,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X45,X44,X43,X42)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X45,X44,X43,X42,X41,X40)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X41,X42,X40,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_1079,plain,
! [X40,X41,X42,X43,X44,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X44,X42,X43,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X43,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X45,X44,X43,X42)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X45,X44,X43,X42,X41,X40)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X41,X42,X40,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_1080,plain,
! [X68,X69,X70,X71,X72,X73,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X73,X70,X72,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X68,X71),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X73,X72,X70,X69,X68)))
| ~ hBOOL(hAPP(hAPP(X69,X71),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X73,X72,X70)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X69,X70,X68,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_1081,plain,
! [X68,X69,X70,X71,X72,X73,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X73,X70,X72,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X68,X71),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X73,X72,X70,X69,X68)))
| ~ hBOOL(hAPP(hAPP(X69,X71),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X73,X72,X70)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X69,X70,X68,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_1082,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Hoare__Mirabelle_Ohoare__derivs(X47,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X48)),c_Hoare__Mirabelle_Otriple_Otriple(X46,c_Com_Ocom_OSemi(X43,X42),X44,X48)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X48),tc_bool))),X48)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X47,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X48)),c_Hoare__Mirabelle_Otriple_Otriple(X45,X42,X44,X48)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X48),tc_bool))),X48)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X47,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X48)),c_Hoare__Mirabelle_Otriple_Otriple(X46,X43,X45,X48)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X48),tc_bool))),X48) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_1083,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X16),X18)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X16),X18)),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_1084,plain,
! [X54,X55,X56,X57,X58,X59,X60] : c_Fun_Ocomp(X56,c_Fun_Ocomp(X55,X54,X57,X58,X60),X58,X59,X60) = c_Fun_Ocomp(c_Fun_Ocomp(X56,X55,X58,X59,X57),X54,X57,X59,X60),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_1085,plain,
! [X25,X26,X27,X28,X29,X30] : c_COMBS(X27,X26,X25,X29,X28,X30) = hAPP(hAPP(X27,X25),hAPP(X26,X25)),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_1086,axiom,
c_COMBS(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
c_0_553 ).
fof(c_0_1087,plain,
! [X25,X26,X27,X28,X29,X30] : c_COMBC(X27,X26,X25,X29,X28,X30) = hAPP(hAPP(X27,X25),X26),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_1088,axiom,
c_COMBC(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),v_Q),
c_0_555 ).
fof(c_0_1089,plain,
! [X40,X41,X42,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X43,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X42,X40,X41,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X42,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X43,X42,X41,X40)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X43,X42,X41,X40))) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_1090,plain,
! [X40,X41,X42,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X43,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X42,X40,X41,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X42,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X43,X42,X41,X40)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X43,X42,X41,X40))) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_1091,plain,
! [X55,X56,X57,X58,X59,X60] : hAPP(c_Set_Oimage(c_Fun_Ocomp(X57,X56,X58,X60,X59),X59,X60),X55) = hAPP(c_Set_Oimage(X57,X58,X60),hAPP(c_Set_Oimage(X56,X59,X58),X55)),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_1092,plain,
! [X19,X20,X21,X22,X23,X24] : hAPP(c_Set_Oimage(X20,X23,X24),hAPP(c_Set_Oimage(X19,X22,X23),X21)) = hAPP(c_Set_Oimage(c_COMBB(X20,X19,X23,X24,X22),X22,X24),X21),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_1093,plain,
! [X19,X20,X21,X22,X23,X24] : hAPP(c_Set_Ovimage(c_Fun_Ocomp(X20,X21,X22,X23,X24),X24,X23),X19) = hAPP(c_Set_Ovimage(X21,X24,X22),hAPP(c_Set_Ovimage(X20,X22,X23),X19)),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_1094,plain,
! [X13,X14,X15,X16,X17] :
( ~ hBOOL(c_in(hAPP(X13,X14),hAPP(c_Set_Oimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X15,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X16))
| ~ c_Fun_Oinj__on(X13,hAPP(hAPP(c_Set_Oinsert(X17),X14),X15),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_1095,plain,
! [X65,X66,X67,X68,X69] :
( ~ hBOOL(hAPP(X69,c_Hoare__Mirabelle_Otriple_Otriple__case(X67,c_Hoare__Mirabelle_Otriple_Otriple(X66,X68,X65,t_b),t_b,t_a)))
| hBOOL(hAPP(X69,hAPP(hAPP(hAPP(X67,X66),X68),X65))) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_1096,plain,
! [X63,X64,X65,X66,X67] :
( ~ hBOOL(hAPP(X67,c_Hoare__Mirabelle_Otriple_Otriple__case(X66,c_Hoare__Mirabelle_Otriple_Otriple(X65,X64,X63,t_b),t_b,t_a)))
| hBOOL(hAPP(X67,hAPP(hAPP(hAPP(X66,X65),X64),X63))) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_1097,plain,
! [X59,X60,X61,X62,X63,X64,X65,X66,X67,X68,X69] :
( hAPP(X64,hAPP(X62,X60)) != hAPP(X63,hAPP(X61,X59))
| hAPP(c_Fun_Ocomp(X64,X62,X68,X69,X67),X60) = hAPP(c_Fun_Ocomp(X63,X61,X66,X69,X65),X59) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_564])])]) ).
fof(c_0_1098,plain,
! [X19,X20,X21,X22,X23,X24] :
( c_Fun_Oinj__on(X19,hAPP(c_Set_Oimage(X20,X24,X22),X21),X22,X23)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X19,X20,X22,X23,X24),X21,X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_1099,plain,
! [X13,X14,X15,X16,X17] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),hAPP(c_Set_Oimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X17,tc_bool)))),hAPP(c_Set_Oimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X14,X15,tc_fun(X17,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Fun_Oinj__on(X13,X14,X17,X16)
| ~ c_Fun_Oinj__on(X13,X15,X17,X16)
| c_Fun_Oinj__on(X13,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X15),X14),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_1100,plain,
! [X54,X55,X56,X57,X58,X59,X60,X61,X62] :
( c_Fun_Ocomp(X58,X57,X60,X61,X62) != c_Fun_Ocomp(X56,X55,X59,X61,X62)
| hAPP(X58,hAPP(X57,X54)) = hAPP(X56,hAPP(X55,X54)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_567])])]) ).
fof(c_0_1101,plain,
! [X19,X20,X21,X22,X23,X24] :
( c_Fun_Oinj__on(c_Fun_Ocomp(X19,X20,X23,X22,X24),X21,X24,X22)
| ~ c_Fun_Oinj__on(X19,hAPP(c_Set_Oimage(X20,X24,X23),X21),X23,X22)
| ~ c_Fun_Oinj__on(X20,X21,X24,X23) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_1102,plain,
! [X16,X17,X18,X19,X20] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X17,X19,tc_fun(X20,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X18),X17,tc_fun(X20,tc_bool),tc_fun(X20,tc_bool),X19),X19,tc_fun(X20,tc_bool))
| X16 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_569])])]) ).
fof(c_0_1103,plain,
! [X16,X17,X18,X19,X20] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X18),X17,tc_fun(X20,tc_bool),tc_fun(X20,tc_bool),X19),X19,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X17,X19,tc_fun(X20,tc_bool)))
| X16 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_570])])]) ).
fof(c_0_1104,plain,
! [X16,X17,X18,X19,X20] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X17,X19,tc_fun(X20,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X18),X17,tc_fun(X20,tc_bool),tc_fun(X20,tc_bool),X19),X19,tc_fun(X20,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_1105,plain,
! [X38,X39,X40,X41,X42] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X42,tc_bool)),X39),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,X40,X41,tc_fun(X42,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X38,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X42,tc_bool)),X39),X40,tc_fun(X42,tc_bool),tc_fun(X42,tc_bool),X41),X41,tc_fun(X42,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_1106,plain,
! [X16,X17,X18,X19,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X18),X17,tc_fun(X20,tc_bool),tc_fun(X20,tc_bool),X19),X19,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X17,X19,tc_fun(X20,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_1107,plain,
! [X13,X14,X15,X16,X17] :
( c_Fun_Oinj__on(X13,hAPP(hAPP(c_Set_Oinsert(X17),X14),X15),X17,X16)
| hBOOL(c_in(hAPP(X13,X14),hAPP(c_Set_Oimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X15,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X16))
| ~ c_Fun_Oinj__on(X13,X15,X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_1108,plain,
! [X19,X20,X21,X22,X23,X24] : hAPP(c_Set_Ovimage(X19,X24,X23),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,X20,X22,tc_fun(X23,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,c_COMBB(c_Set_Ovimage(X19,X24,X23),X20,tc_fun(X23,tc_bool),tc_fun(X24,tc_bool),X22),X22,tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1109,plain,
! [X19,X20,X21,X22,X23,X24] : hAPP(c_Set_Oimage(X19,X23,X24),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,X20,X22,tc_fun(X23,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,c_COMBB(c_Set_Oimage(X19,X23,X24),X20,tc_fun(X23,tc_bool),tc_fun(X24,tc_bool),X22),X22,tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1110,plain,
! [X12,X13,X14,X15,X16,X17] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,c_COMBB(hAPP(c_Set_Oinsert(X16),X13),X14,tc_fun(X16,tc_bool),tc_fun(X16,tc_bool),X17),X17,tc_fun(X16,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X16),X13),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15,X14,X17,tc_fun(X16,tc_bool)))
| ~ hBOOL(c_in(X12,X15,X17)) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_1111,plain,
! [X16,X17,X18,X19,X20] :
( hAPP(hAPP(c_Set_Oinsert(X20),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X18,X19,tc_fun(X20,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,c_COMBB(hAPP(c_Set_Oinsert(X20),X16),X18,tc_fun(X20,tc_bool),tc_fun(X20,tc_bool),X19),X19,tc_fun(X20,tc_bool))
| X17 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_578])])]) ).
fof(c_0_1112,plain,
! [X16,X17,X18,X19,X20] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,c_COMBB(hAPP(c_Set_Oinsert(X20),X16),X18,tc_fun(X20,tc_bool),tc_fun(X20,tc_bool),X19),X19,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X20),X16),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X18,X19,tc_fun(X20,tc_bool)))
| X17 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_579])])]) ).
fof(c_0_1113,plain,
! [X19,X20,X21,X22,X23,X24] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X19,X22,X23),X21),X20,X23,tc_fun(X24,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,c_COMBB(X20,X19,X23,tc_fun(X24,tc_bool),X22),X22,tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_1114,plain,
! [X19,X20,X21,X22,X23,X24] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X21,c_COMBB(X20,X19,X22,tc_fun(X24,tc_bool),X23),X23,tc_fun(X24,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X19,X23,X22),X21),X20,X22,tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_1115,plain,
! [X12,X13,X14,X15] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X15,tc_bool)),X13),X12,tc_fun(X15,tc_bool),tc_fun(X15,tc_bool),X14),X14,tc_fun(X15,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_1116,plain,
! [X12,X13,X14,X15] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X15),X12),X13,tc_fun(X15,tc_bool),tc_fun(X15,tc_bool),X14),X14,tc_fun(X15,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_1117,plain,
! [X13,X14,X15,X16,X17] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),hAPP(c_Set_Oimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X17,tc_bool)))),hAPP(c_Set_Oimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X14,X15,tc_fun(X17,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Fun_Oinj__on(X13,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X15),X14),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1118,plain,
! [X19,X20,X21,X22] : hAPP(c_Fun_Ocomp(c_COMBK(X20,X22,X21),X19,X21,X22,t_a),v_x) = X20,
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1119,plain,
! [X13,X14,X15,X16,X17] : c_lessequals(hAPP(c_Set_Oimage(X13,X16,X17),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),hAPP(c_Set_Oimage(X13,X16,X17),X15)),hAPP(c_Set_Oimage(X13,X16,X17),X14)),tc_fun(X17,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1120,plain,
! [X19,X20,X21,X22,X23] :
( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X20,X19,X23,tc_fun(X22,X22),X21),X21,X22)
| ~ c_Finite__Set_Ofun__left__comm__idem(X20,X23,X22) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_1121,plain,
! [X43,X44,X45,X46,X47,X48] : hAPP(X45,hAPP(X44,X43)) = hAPP(c_Fun_Ocomp(X45,X44,X46,X47,X48),X43),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_1122,plain,
! [X19,X20,X21,X22,X23,X24] : hAPP(c_Fun_Ocomp(X21,X20,X23,X24,X22),X19) = hAPP(X21,hAPP(X20,X19)),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_1123,plain,
! [X25,X26,X27,X28,X29,X30] : hAPP(c_COMBB(X27,X26,X29,X30,X28),X25) = hAPP(X27,hAPP(X26,X25)),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1124,plain,
! [X19,X20,X21,X22] : hAPP(c_Fun_Ocomp(X20,X19,X21,X22,t_a),v_x) = hAPP(X20,hAPP(X19,v_x)),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_1125,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
c_0_592 ).
fof(c_0_1126,plain,
! [X40,X41,X42] : c_Hoare__Mirabelle_Ohoare__derivs(X41,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X42)),c_Hoare__Mirabelle_Otriple_Otriple(X40,c_Com_Ocom_OSKIP,X40,X42)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X42),tc_bool))),X42),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1127,plain,
! [X15,X16,X17,X18,X19] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X18,tc_bool)),X17),X16),X15,X18,tc_fun(X19,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X15,X18,tc_fun(X19,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,X15,X18,tc_fun(X19,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1128,plain,
! [X31,X32,X33,X34,X35] :
( hAPP(X31,X33) = X32
| ~ hBOOL(c_in(X33,hAPP(c_Set_Ovimage(X31,X35,X34),hAPP(hAPP(c_Set_Oinsert(X34),X32),c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool)))),X35)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_595])])]) ).
fof(c_0_1129,plain,
! [X13,X14,X15,X16,X17] : hAPP(c_Set_Ovimage(X13,X17,X16),hAPP(hAPP(c_Set_Oinsert(X16),X14),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),hAPP(c_Set_Ovimage(X13,X17,X16),hAPP(hAPP(c_Set_Oinsert(X16),X14),c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))))),hAPP(c_Set_Ovimage(X13,X17,X16),X15)),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1130,plain,
! [X16,X17,X18,X19,X20,X21] :
( hAPP(c_Set_Oimage(X16,X21,X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X21,tc_bool)),X19),X18)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),hAPP(c_Set_Oimage(X16,X21,X20),X19)),hAPP(c_Set_Oimage(X16,X21,X20),X18))
| ~ c_lessequals(X18,X17,tc_fun(X21,tc_bool))
| ~ c_lessequals(X19,X17,tc_fun(X21,tc_bool))
| ~ c_Fun_Oinj__on(X16,X17,X21,X20) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1131,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17)),X16) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16))
| c_lessequals(X16,X18,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1132,plain,
! [X53,X54,X55,X56] : hBOOL(c_in(X54,hAPP(c_Set_Ovimage(X53,X55,X56),hAPP(hAPP(c_Set_Oinsert(X56),hAPP(X53,X54)),c_Orderings_Obot__class_Obot(tc_fun(X56,tc_bool)))),X55)),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1133,plain,
! [X13,X14,X15,X16,X17] : c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X13,X16,X17),X15),hAPP(c_Set_Oimage(X13,X16,X17),X14),tc_fun(X17,tc_bool)),hAPP(c_Set_Oimage(X13,X16,X17),c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X16,tc_bool))),tc_fun(X17,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1134,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16)),X18) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X18)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X16),X18)),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1135,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16)),X18) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X18)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X16),X18)),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1136,plain,
! [X31,X32,X33,X34] :
( X33 = X32
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,hAPP(hAPP(c_Set_Oinsert(X34),X33),c_Orderings_Obot__class_Obot(tc_fun(X34,tc_bool))),X34),X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_603])])]) ).
fof(c_0_1137,plain,
! [X31,X32,X33,X34,X35,X36] :
( hBOOL(c_in(X31,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34,X33,X36,tc_fun(X35,tc_bool)),X35))
| ~ hBOOL(c_in(X31,hAPP(X33,X32),X35))
| ~ hBOOL(c_in(X32,X34,X36)) ),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_1138,plain,
! [X31,X32,X33,X34,X35,X36] :
( hBOOL(c_in(X32,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34,X33,X35,tc_fun(X36,tc_bool)),X36))
| ~ hBOOL(c_in(X32,hAPP(X33,X31),X36))
| ~ hBOOL(c_in(X31,X34,X35)) ),
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_1139,plain,
! [X16,X17,X18,X19,X20,X21] :
( hAPP(c_Set_Oimage(X16,X21,X20),c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X21,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X16,X21,X20),X19),hAPP(c_Set_Oimage(X16,X21,X20),X18),tc_fun(X20,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X21,tc_bool))
| ~ c_lessequals(X19,X17,tc_fun(X21,tc_bool))
| ~ c_Fun_Oinj__on(X16,X17,X21,X20) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1140,plain,
! [X12,X13,X14,X15] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X15,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X13,X14,tc_fun(X15,tc_bool))),X12) = X12,
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1141,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X16)),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_1142,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X16)),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1143,plain,
! [X31,X32,X33,X34,X35,X36] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34,X33,X36,tc_fun(X35,tc_bool)),X31))
| ~ hBOOL(hAPP(hAPP(X33,X32),X31))
| ~ hBOOL(c_in(X32,X34,X36)) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1144,plain,
! [X31,X32,X33,X34,X35,X36] :
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34,X33,X36,tc_fun(X35,tc_bool)),X32))
| ~ hBOOL(hAPP(hAPP(X33,X31),X32))
| ~ hBOOL(c_in(X31,X34,X36)) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1145,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X11,X13,X14))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),tc_fun(X14,tc_bool)),X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1146,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X11,X13,X14))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),tc_fun(X14,tc_bool)),X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1147,plain,
! [X13,X14,X15,X16] :
( c_Fun_Ocomp(hAPP(X14,X13),hAPP(X14,X13),X15,X15,X15) = hAPP(X14,X13)
| ~ c_Finite__Set_Ofun__left__comm__idem(X14,X16,X15) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_614])])]) ).
fof(c_0_1148,plain,
! [X22,X23,X24,X25] :
( hBOOL(c_in(X22,X24,X25))
| ~ hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X25,tc_bool)),X24),c_Collect(X23,X25)),X25)) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1149,plain,
! [X7,X8] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X8),X7),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X8),X7),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X8))),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1150,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),tc_fun(X14,tc_bool)),X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1151,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,X18,X20))
| hBOOL(c_in(X17,X19,X20))
| ~ hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X19),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1152,plain,
! [X13,X14,X15,X16,X17] : hAPP(c_Set_Oimage(X13,X16,X17),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),hAPP(c_Set_Oimage(X13,X16,X17),X15)),hAPP(c_Set_Oimage(X13,X16,X17),X14)),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1153,plain,
! [X13,X14,X15,X16,X17] : hAPP(c_Set_Ovimage(X13,X17,X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),hAPP(c_Set_Ovimage(X13,X17,X16),X15)),hAPP(c_Set_Ovimage(X13,X17,X16),X14)),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1154,plain,
! [X13,X14,X15,X16,X17] : hAPP(c_Set_Ovimage(X13,X17,X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),hAPP(c_Set_Ovimage(X13,X17,X16),X15)),hAPP(c_Set_Ovimage(X13,X17,X16),X14)),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1155,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17)),X16) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16))
| ~ c_lessequals(X16,X18,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1156,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X23,X22))
| ~ hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X25,tc_bool)),X24),c_Collect(X23,X25)),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_623])])]) ).
fof(c_0_1157,plain,
! [X38,X39,X40,X41,X42,X43] :
( c_lessequals(hAPP(X41,X38),X40,tc_fun(X43,tc_bool))
| ~ hBOOL(c_in(X38,X39,X42))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X39,X41,X42,tc_fun(X43,tc_bool)),X40,tc_fun(X43,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1158,plain,
! [X13,X14,X15,X16,X17] :
( hAPP(c_Set_Oimage(X13,X17,X16),X15) != hAPP(c_Set_Oimage(X13,X17,X16),X14)
| ~ c_Fun_Oinj__on(X13,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X15),X14),X17,X16)
| X15 = X14 ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1159,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,X19,X20))
| ~ hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X19),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1160,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X19),X18),X20)) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1161,plain,
! [X39,X40,X41,X42,X43] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X42,tc_bool)),hAPP(X41,X39)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X40,X41,X43,tc_fun(X42,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X40,X41,X43,tc_fun(X42,tc_bool))
| ~ hBOOL(c_in(X39,X40,X43)) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1162,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17)),X16) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16)),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1163,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17)),X16) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16)),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1164,plain,
! [X12,X13,X14,X15,X16] :
( c_Finite__Set_Ofinite(hAPP(X13,X12),X15)
| ~ hBOOL(c_in(X12,X14,X16))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14,X13,X16,tc_fun(X15,tc_bool)),X15)
| ~ c_Finite__Set_Ofinite(X14,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_631])])]) ).
fof(c_0_1165,plain,
! [X12,X13,X14,X15,X16] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X15),X12),X14),X13,X15,tc_fun(X16,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),hAPP(X13,X12)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14,X13,X15,tc_fun(X16,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1166,plain,
! [X11,X12,X13,X14] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),tc_fun(X14,tc_bool)),X12,tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X11,X13,X14))
| ~ c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1167,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool))),X16) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16),tc_fun(X19,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1168,plain,
! [X34,X35,X36,X37] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X37,tc_bool)),X36),X35) != c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool))
| X35 = c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool))
| ~ c_Finite__Set_Ofinite(X35,X37)
| X36 = c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool))
| ~ c_Finite__Set_Ofinite(X36,X37)
| ~ c_OrderedGroup_Oab__semigroup__mult(X34,X37)
| c_Finite__Set_Ofold1(X34,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X37,tc_bool)),X36),X35),X37) = hAPP(hAPP(X34,c_Finite__Set_Ofold1(X34,X36,X37)),c_Finite__Set_Ofold1(X34,X35,X37)) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1169,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(hAPP(X13,X14),X15,X16))
| ~ hBOOL(c_in(X14,hAPP(c_Set_Ovimage(X13,X17,X16),X15),X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_636])])]) ).
fof(c_0_1170,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(hAPP(X13,X14),X15,X16))
| ~ hBOOL(c_in(X14,hAPP(c_Set_Ovimage(X13,X17,X16),X15),X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_637])])]) ).
fof(c_0_1171,plain,
! [X13,X14,X15,X16,X17] :
( c_Fun_Oinj__on(X13,X15,X17,X16)
| ~ c_Fun_Oinj__on(X13,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X15),X14),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1172,plain,
! [X13,X14,X15,X16,X17] :
( c_Fun_Oinj__on(X13,X14,X17,X16)
| ~ c_Fun_Oinj__on(X13,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X15),X14),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1173,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X21)),X24) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1174,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X22)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X21)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)),X24) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1175,plain,
! [X13,X14,X15] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X14,hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),X15),X13)),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1176,plain,
! [X13,X14,X15] :
( hAPP(c_Set_Oimage(X13,X15,X15),X14) = X14
| ~ c_Fun_Oinj__on(X13,X14,X15,X15)
| ~ c_lessequals(hAPP(c_Set_Oimage(X13,X15,X15),X14),X14,tc_fun(X15,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1177,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X19),X18),X20))
| ~ hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1178,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X19),X18),X20))
| ~ hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1179,plain,
! [X16,X17,X18,X19] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16),tc_fun(X19,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X16),X17,tc_fun(X19,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1180,plain,
! [X22,X23,X24,X25] :
( hBOOL(c_in(X22,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X25,tc_bool)),X24),c_Collect(X23,X25)),X25))
| ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(c_in(X22,X24,X25)) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1181,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(X12,X11))
| hBOOL(hAPP(X13,X11))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X14,tc_bool)),X13),X12),X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_648])])]) ).
fof(c_0_1182,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(X13,X11))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12),X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_649])])]) ).
fof(c_0_1183,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(X12,X11))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12),X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_650])])]) ).
fof(c_0_1184,plain,
! [X16,X17,X18,X19] : c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16),tc_fun(X19,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool))),c_HOL_Ominus__class_Ominus(X18,X16,tc_fun(X19,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1185,plain,
! [X16,X17,X18,X19] : c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16),tc_fun(X19,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool))),c_HOL_Ominus__class_Ominus(X18,X16,tc_fun(X19,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1186,plain,
! [X16,X17,X18,X19] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17),X16,tc_fun(X19,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),c_HOL_Ominus__class_Ominus(X18,X16,tc_fun(X19,tc_bool))),c_HOL_Ominus__class_Ominus(X17,X16,tc_fun(X19,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1187,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X16),c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X16),X18),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X16),X17),tc_fun(X19,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1188,plain,
! [X21,X22,X23] :
( X21 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X23),X22),c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool))),X23)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X23),X22),c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool))),X21)) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1189,plain,
! [X44,X45,X46,X47,X48] :
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X48,tc_bool)),X47),X46),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X48,tc_bool)),X45),X44),tc_fun(X48,tc_bool))
| ~ c_lessequals(X46,X44,tc_fun(X48,tc_bool))
| ~ c_lessequals(X47,X45,tc_fun(X48,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1190,plain,
! [X44,X45,X46,X47,X48] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X48,tc_bool)),X47),X46),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X48,tc_bool)),X45),X44),tc_fun(X48,tc_bool))
| ~ c_lessequals(X46,X44,tc_fun(X48,tc_bool))
| ~ c_lessequals(X47,X45,tc_fun(X48,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1191,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(hAPP(X15,hAPP(X14,X13)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X14,X17,X16),X15),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_658])])]) ).
fof(c_0_1192,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X19),X16),X18)),X17) = hAPP(hAPP(c_Set_Oinsert(X19),X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17))
| ~ hBOOL(c_in(X16,X17,X19)) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1193,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),X16)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X17),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X16)),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1194,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X16)),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1195,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X19),X18),X20))
| ~ hBOOL(c_in(X17,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1196,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X19),X18),X20))
| ~ hBOOL(c_in(X17,X18,X20)) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1197,plain,
! [X67,X68,X69,X70] :
( c_Hoare__Mirabelle_Ohoare__derivs(X69,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X70)),X68),X67),X70)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X69,X67,X70)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X69,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X70)),X68),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X70),tc_bool))),X70) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1198,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(X14,hAPP(c_Set_Ovimage(X13,X16,X17),X15),X16))
| ~ hBOOL(c_in(hAPP(X13,X14),X15,X17)) ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1199,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(X14,hAPP(c_Set_Ovimage(X13,X16,X17),X15),X16))
| ~ hBOOL(c_in(hAPP(X13,X14),X15,X17)) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1200,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(X14,hAPP(c_Set_Ovimage(X13,X17,X16),X15),X17))
| ~ hBOOL(c_in(hAPP(X13,X14),X15,X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_667])])]) ).
fof(c_0_1201,plain,
! [X13,X14,X15,X16,X17,X18] :
( hBOOL(c_in(hAPP(X14,X13),X15,X18))
| ~ hBOOL(c_in(X13,X16,X17))
| ~ c_lessequals(hAPP(c_Set_Oimage(X14,X17,X18),X16),X15,tc_fun(X18,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1202,plain,
! [X65,X66,X67,X68,X69,X70] : c_Hoare__Mirabelle_Otriple_Otriple__case(X67,c_Hoare__Mirabelle_Otriple_Otriple(X66,X68,X65,X69),X69,X70) = hAPP(hAPP(hAPP(X67,X66),X68),X65),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1203,plain,
! [X65,X66,X67,X68,X69,X70] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X67,c_Hoare__Mirabelle_Otriple_Otriple(X66,X68,X65,X69),X69,X70) = hAPP(hAPP(hAPP(X67,X66),X68),X65),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1204,plain,
! [X13,X14,X15,X16,X17] : hAPP(c_Set_Ovimage(X13,X17,X16),c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X16,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X13,X17,X16),X15),hAPP(c_Set_Ovimage(X13,X17,X16),X14),tc_fun(X17,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1205,plain,
! [X17,X18,X19,X20] :
( ~ hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X20,tc_bool)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1206,plain,
! [X31,X32,X33] :
( X31 = X32
| ~ hBOOL(c_in(X31,hAPP(hAPP(c_Set_Oinsert(X33),X32),c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool))),X33)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_673])])]) ).
fof(c_0_1207,plain,
! [X11,X12,X13,X14] : c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),tc_fun(X14,tc_bool)),X12,tc_fun(X14,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1208,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(hAPP(X14,X13),hAPP(c_Set_Oimage(X14,X17,X16),X15),X16))
| ~ hBOOL(c_in(X13,X15,X17)) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1209,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(c_in(hAPP(X14,X13),hAPP(c_Set_Oimage(X14,X16,X17),X15),X17))
| ~ hBOOL(c_in(X13,X15,X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_676])])]) ).
fof(c_0_1210,plain,
! [X13,X14,X15,X16,X17] :
( ~ hBOOL(c_in(X13,X15,X16))
| hBOOL(c_in(hAPP(X14,X13),hAPP(c_Set_Oimage(X14,X16,X17),X15),X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_677])])]) ).
fof(c_0_1211,plain,
! [X53,X54,X55,X56,X57] :
( ~ hBOOL(c_in(X53,X55,X56))
| hBOOL(c_in(hAPP(X54,X53),hAPP(c_Set_Oimage(X54,X56,X57),X55),X57)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_678])])]) ).
fof(c_0_1212,plain,
! [X12,X13,X14,X15,X16] :
( c_lessequals(hAPP(X13,X12),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14,X13,X16,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool))
| ~ hBOOL(c_in(X12,X14,X16)) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1213,plain,
! [X42,X43,X44,X45,X46] :
( hAPP(hAPP(c_Set_Oinsert(X46),X45),hAPP(hAPP(c_Set_Oinsert(X46),X44),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X46),X43),hAPP(hAPP(c_Set_Oinsert(X46),X42),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool))))
| X45 = X42
| X45 = X43 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_680])])]) ).
fof(c_0_1214,plain,
! [X42,X43,X44,X45,X46] :
( hAPP(hAPP(c_Set_Oinsert(X46),X45),hAPP(hAPP(c_Set_Oinsert(X46),X44),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X46),X43),hAPP(hAPP(c_Set_Oinsert(X46),X42),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool))))
| X44 = X43
| X45 = X43 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_681])])]) ).
fof(c_0_1215,plain,
! [X42,X43,X44,X45,X46] :
( hAPP(hAPP(c_Set_Oinsert(X46),X45),hAPP(hAPP(c_Set_Oinsert(X46),X44),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X46),X43),hAPP(hAPP(c_Set_Oinsert(X46),X42),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool))))
| X45 = X42
| X44 = X42 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_682])])]) ).
fof(c_0_1216,plain,
! [X42,X43,X44,X45,X46] :
( hAPP(hAPP(c_Set_Oinsert(X46),X45),hAPP(hAPP(c_Set_Oinsert(X46),X44),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X46),X43),hAPP(hAPP(c_Set_Oinsert(X46),X42),c_Orderings_Obot__class_Obot(tc_fun(X46,tc_bool))))
| X44 = X43
| X44 = X42 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_683])])]) ).
fof(c_0_1217,plain,
! [X13,X14,X15,X16] :
( c_Finite__Set_Ofinite(X14,X15)
| ~ c_Fun_Oinj__on(X13,X14,X15,X16)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X13,X15,X16),X14),X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_684])])]) ).
fof(c_0_1218,plain,
! [X16,X17,X18,X19] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool)),X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16),tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1219,plain,
! [X12,X13,X14,X15] : hAPP(hAPP(c_Set_Oinsert(X15),X12),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X13,X14,tc_fun(X15,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X15),X12),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1220,plain,
! [X13,X14,X15,X16,X17] :
( c_Fun_Oinj__on(X13,X15,X17,X16)
| ~ c_Fun_Oinj__on(X13,hAPP(hAPP(c_Set_Oinsert(X17),X14),X15),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1221,plain,
! [X13,X14,X15,X16] : c_lessequals(hAPP(c_Set_Oimage(X13,X15,X16),hAPP(c_Set_Ovimage(X13,X15,X16),X14)),X14,tc_fun(X16,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1222,plain,
! [X10,X11,X12] :
( hAPP(hAPP(c_Set_Oinsert(X12),X10),c_HOL_Ominus__class_Ominus(X11,hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),tc_fun(X12,tc_bool))) = X11
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1223,plain,
! [X13,X14,X15,X16,X17] :
( c_Fun_Oinj__on(X13,c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X17,tc_bool)),X17,X16)
| ~ c_Fun_Oinj__on(X13,X15,X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1224,plain,
! [X11,X12,X13,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X14),X11),X13)),hAPP(hAPP(c_Set_Oinsert(X14),X11),X12)) = hAPP(hAPP(c_Set_Oinsert(X14),X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12)),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1225,plain,
! [X12,X13,X14,X15] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X15,tc_bool)),X13),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X12,X14,tc_fun(X15,tc_bool))) = X13,
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1226,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ c_Fun_Oinj__on(X23,X24,X26,X25)
| X22 = X21
| ~ hBOOL(c_in(X21,X24,X26))
| ~ hBOOL(c_in(X22,X24,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_693])])]) ).
fof(c_0_1227,plain,
! [X13,X14,X15,X16,X17,X18] :
( hAPP(X15,X14) != hAPP(X15,X13)
| ~ hBOOL(c_in(X13,X16,X18))
| ~ hBOOL(c_in(X14,X16,X18))
| ~ c_Fun_Oinj__on(X15,X16,X18,X17)
| X14 = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_694])])]) ).
fof(c_0_1228,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ hBOOL(c_in(X21,X24,X26))
| ~ hBOOL(c_in(X22,X24,X26))
| ~ c_Fun_Oinj__on(X23,X24,X26,X25)
| X22 = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_695])])]) ).
fof(c_0_1229,plain,
! [X21,X22,X23,X24,X25,X26] :
( hAPP(X23,X22) != hAPP(X23,X21)
| ~ hBOOL(c_in(X21,X24,X26))
| ~ hBOOL(c_in(X22,X24,X26))
| X22 = X21
| ~ c_Fun_Oinj__on(X23,X24,X26,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_696])])]) ).
fof(c_0_1230,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( c_Hoare__Mirabelle_Otriple_Otriple(X74,X76,X72,X77) != c_Hoare__Mirabelle_Otriple_Otriple(X73,X75,X71,X77)
| X74 = X73 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_697])])]) ).
fof(c_0_1231,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( c_Hoare__Mirabelle_Otriple_Otriple(X74,X76,X72,X77) != c_Hoare__Mirabelle_Otriple_Otriple(X73,X75,X71,X77)
| X76 = X75 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_698])])]) ).
fof(c_0_1232,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( c_Hoare__Mirabelle_Otriple_Otriple(X74,X76,X72,X77) != c_Hoare__Mirabelle_Otriple_Otriple(X73,X75,X71,X77)
| X72 = X71 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_699])])]) ).
fof(c_0_1233,plain,
! [X13,X14,X15] :
( c_Fun_Oinj__on(X13,X14,X15,X15)
| ~ c_lessequals(X14,hAPP(c_Set_Oimage(X13,X15,X15),X14),tc_fun(X15,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1234,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,X19,X20))
| ~ hBOOL(c_in(X17,c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X20,tc_bool)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1235,plain,
! [X13,X14,X15,X16,X17] :
( c_Fun_Oinj__on(X13,X15,X17,X16)
| ~ c_lessequals(X15,X14,tc_fun(X17,tc_bool))
| ~ c_Fun_Oinj__on(X13,X14,X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1236,plain,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),hAPP(hAPP(c_Set_Oinsert(X14),X11),X12)) = hAPP(hAPP(c_Set_Oinsert(X14),X11),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12))
| ~ hBOOL(c_in(X11,X13,X14)) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1237,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X18)
| c_lessequals(hAPP(X16,X15),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17,X16,X19,X18),X18)
| ~ hBOOL(c_in(X15,X17,X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_704])])]) ).
fof(c_0_1238,plain,
! [X11,X12,X13,X14] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool)),X14) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1239,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11)) = X12,
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1240,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X18,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X17),X16),tc_fun(X19,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X17,tc_fun(X19,tc_bool)),X16,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1241,plain,
! [X12,X13,X14,X15] : c_HOL_Ominus__class_Ominus(X13,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X12,X14,tc_fun(X15,tc_bool)),tc_fun(X15,tc_bool)) = X13,
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1242,plain,
! [X13,X14,X15] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X14,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15),X13)),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1243,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X20,tc_bool)),X20))
| hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1244,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,c_HOL_Ominus__class_Ominus(X19,X18,tc_fun(X20,tc_bool)),X20))
| hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,X19,X20)) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1245,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12),X11))
| ~ hBOOL(hAPP(X12,X11))
| ~ hBOOL(hAPP(X13,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_712])])]) ).
fof(c_0_1246,plain,
! [X16,X17,X18,X19] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X19),X16),X18)),X17) = hAPP(hAPP(c_Set_Oinsert(X19),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17)),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1247,plain,
! [X12,X13,X14,X15,X16] :
( c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14,X13,X15,tc_fun(X16,tc_bool))
| hAPP(X13,X12) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1248,plain,
! [X12,X13,X14,X15,X16] :
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14,X13,X15,tc_fun(X16,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| hAPP(X13,X12) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ hBOOL(c_in(X12,X14,X15)) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1249,plain,
! [X13,X14,X15,X16,X17] :
( ~ c_lessequals(X13,X15,tc_fun(X16,tc_bool))
| c_lessequals(hAPP(c_Set_Oimage(X14,X16,X17),X13),hAPP(c_Set_Oimage(X14,X16,X17),X15),tc_fun(X17,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_716])])]) ).
fof(c_0_1250,plain,
! [X13,X14,X15,X16,X17] :
( c_lessequals(hAPP(c_Set_Oimage(X13,X17,X16),X15),hAPP(c_Set_Oimage(X13,X17,X16),X14),tc_fun(X16,tc_bool))
| ~ c_lessequals(X15,X14,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1251,plain,
! [X13,X14,X15,X16,X17] :
( c_lessequals(hAPP(c_Set_Ovimage(X13,X16,X17),X15),hAPP(c_Set_Ovimage(X13,X16,X17),X14),tc_fun(X16,tc_bool))
| ~ c_lessequals(X15,X14,tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1252,plain,
! [X10,X11,X12] : hAPP(hAPP(c_Set_Oinsert(X12),X10),c_HOL_Ominus__class_Ominus(X11,hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),tc_fun(X12,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1253,plain,
! [X16,X17,X18,X19] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17),X16,tc_fun(X19,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),c_HOL_Ominus__class_Ominus(X17,X16,tc_fun(X19,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1254,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X14,tc_bool)),X13),X12),X11))
| ~ hBOOL(hAPP(X13,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_721])])]) ).
fof(c_0_1255,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X14,tc_bool)),X13),X12),X11))
| ~ hBOOL(hAPP(X12,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_722])])]) ).
fof(c_0_1256,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X17,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17),X16,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1257,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X18,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17),X16,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1258,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X16,X18,tc_fun(X19,tc_bool))
| ~ c_lessequals(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17),tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1259,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X16,X17,tc_fun(X19,tc_bool))
| ~ c_lessequals(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17),tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1260,plain,
! [X13,X14,X15,X16,X17] :
( hAPP(hAPP(c_Set_Oinsert(X16),hAPP(X14,X13)),hAPP(c_Set_Oimage(X14,X17,X16),X15)) = hAPP(c_Set_Oimage(X14,X17,X16),X15)
| ~ hBOOL(c_in(X13,X15,X17)) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1261,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X14,X17,X16),X15),X13))
| ~ hBOOL(hAPP(X15,hAPP(X14,X13))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_728])])]) ).
fof(c_0_1262,plain,
! [X11,X12,X13,X14] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool)),X14)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)),X14) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1263,plain,
! [X44,X45,X46,X47,X48] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X47,X46,tc_fun(X48,tc_bool)),c_HOL_Ominus__class_Ominus(X45,X44,tc_fun(X48,tc_bool)),tc_fun(X48,tc_bool))
| ~ c_lessequals(X44,X46,tc_fun(X48,tc_bool))
| ~ c_lessequals(X47,X45,tc_fun(X48,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1264,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)),X23) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X23)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X21),X23)) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1265,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)),X23) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X23)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X21),X23)) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1266,plain,
! [X11,X12,X13,X14] :
( ~ hBOOL(c_in(X11,X12,X14))
| ~ hBOOL(c_in(X11,X13,X14))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12) != c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1267,plain,
! [X11,X12,X13,X14] : c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X14),X11),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),tc_fun(X14,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1268,plain,
! [X17,X18,X19,X20,X21] :
( hAPP(c_Set_Oimage(c_COMBK(X18,X20,X21),X21,X20),X19) = hAPP(hAPP(c_Set_Oinsert(X20),X18),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)))
| ~ hBOOL(c_in(X17,X19,X21)) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1269,plain,
! [X31,X32,X33,X34] :
( hBOOL(c_in(X32,X33,X34))
| X32 = X31
| ~ hBOOL(c_in(X32,hAPP(hAPP(c_Set_Oinsert(X34),X31),X33),X34)) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1270,plain,
! [X10,X11,X12] : hAPP(hAPP(c_Set_Oinsert(X12),X10),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X12,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)))),X11),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1271,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17),tc_fun(X19,tc_bool))
| ~ c_lessequals(X16,X17,tc_fun(X19,tc_bool))
| ~ c_lessequals(X16,X18,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1272,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X16,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17),tc_fun(X19,tc_bool))
| ~ c_lessequals(X16,X17,tc_fun(X19,tc_bool))
| ~ c_lessequals(X16,X18,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1273,plain,
! [X16,X17,X18,X19] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17),X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,X16,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1274,plain,
! [X16,X17,X18,X19] :
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X19,tc_bool)),X18),X17),X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,X16,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1275,plain,
! [X42,X43,X44,X45,X46] :
( ~ class_Orderings_Oorder(X46)
| c_lessequals(X43,X45,X46)
| ~ c_lessequals(X45,X44,X46)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X45,X44,X46),c_SetInterval_Oord__class_OatLeastAtMost(X43,X42,X46),tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1276,plain,
! [X42,X43,X44,X45,X46] :
( ~ class_Orderings_Oorder(X46)
| c_lessequals(X44,X42,X46)
| ~ c_lessequals(X45,X44,X46)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X45,X44,X46),c_SetInterval_Oord__class_OatLeastAtMost(X43,X42,X46),tc_fun(X46,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1277,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X19),X16),X18)),X17) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X19,tc_bool)),X18),X17)
| hBOOL(c_in(X16,X17,X19)) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1278,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),c_HOL_Ominus__class_Ominus(X11,X12,tc_fun(X13,tc_bool))),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X11),X12),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1279,plain,
! [X31,X32,X33] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X33),X32),hAPP(hAPP(c_Set_Oinsert(X33),X31),c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool)))),X33) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X33),X32),X31) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1280,plain,
! [X31,X32,X33] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X33),X32),hAPP(hAPP(c_Set_Oinsert(X33),X31),c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool)))),X33) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X33),X32),X31) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1281,plain,
! [X11,X12,X13,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X14,tc_bool)),X13),hAPP(hAPP(c_Set_Oinsert(X14),X11),X12)) = hAPP(hAPP(c_Set_Oinsert(X14),X11),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X14,tc_bool)),X13),X12)),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1282,plain,
! [X8,X9,X10] :
( X9 = hAPP(hAPP(c_Set_Oinsert(X10),X8),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))
| ~ c_lessequals(X9,hAPP(hAPP(c_Set_Oinsert(X10),X8),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))),tc_fun(X10,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1283,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1284,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1285,plain,
! [X13,X14,X15,X16,X17] : hAPP(c_Set_Oimage(X13,X16,X17),hAPP(hAPP(c_Set_Oinsert(X16),X14),X15)) = hAPP(hAPP(c_Set_Oinsert(X17),hAPP(X13,X14)),hAPP(c_Set_Oimage(X13,X16,X17),X15)),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1286,plain,
! [X8,X9,X10,X11] :
( ~ class_Lattices_Olower__semilattice(X11)
| c_lessequals(X9,X8,X11)
| ~ hBOOL(c_in(X8,X10,X11))
| ~ c_lessequals(X9,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X11),X10,X11),X11)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1287,plain,
! [X13,X14,X15,X16,X17] :
( c_Finite__Set_Ofinite(X14,X16)
| ~ c_lessequals(X14,hAPP(c_Set_Oimage(X13,X17,X16),X15),tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_754])])]) ).
fof(c_0_1288,plain,
! [X7,X8] : hBOOL(c_in(X7,hAPP(hAPP(c_Set_Oinsert(X8),X7),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X8)),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1289,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X21)) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1290,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X22)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X21)) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1291,plain,
! [X7,X8,X9] : hAPP(hAPP(c_Set_Oinsert(X9),X7),hAPP(hAPP(c_Set_Oinsert(X9),X8),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X9),X8),hAPP(hAPP(c_Set_Oinsert(X9),X7),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1292,plain,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),hAPP(hAPP(c_Set_Oinsert(X14),X11),X12)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X14,tc_bool)),X13),X12)
| hBOOL(c_in(X11,X13,X14)) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1293,plain,
! [X8,X9,X10] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X10),X8),X9),hAPP(hAPP(c_Set_Oinsert(X10),X8),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))),tc_fun(X10,tc_bool)) = X9
| hBOOL(c_in(X8,X9,X10)) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1294,plain,
! [X11,X12,X13,X14] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X14),X11),X13),X12,tc_fun(X14,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X14),X11),c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool)))
| hBOOL(c_in(X11,X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1295,plain,
! [X31,X32,X33,X34] :
( hBOOL(c_in(X32,hAPP(hAPP(c_Set_Oinsert(X34),X31),X33),X34))
| ~ hBOOL(c_in(X32,X33,X34)) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1296,plain,
! [X31,X32,X33,X34] :
( hBOOL(c_in(X32,hAPP(hAPP(c_Set_Oinsert(X34),X31),X33),X34))
| ~ hBOOL(c_in(X32,X33,X34)) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1297,plain,
! [X34,X35,X36,X37] :
( c_Finite__Set_Ofold1(X35,hAPP(hAPP(c_Set_Oinsert(X37),X34),X36),X37) = hAPP(hAPP(X35,X34),c_Finite__Set_Ofold1(X35,X36,X37))
| hBOOL(c_in(X34,X36,X37))
| ~ c_Finite__Set_Ofinite(X36,X37)
| X36 = c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X35,X37) ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1298,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(X41,X43)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X43,tc_bool)),X42),X41),X43) ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1299,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(X42,X43)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X43,tc_bool)),X42),X41),X43) ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1300,plain,
! [X11,X12,X13,X14] :
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X14),X11),X13),X12,tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X11,X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1301,plain,
! [X16,X17,X18,X19] :
( c_HOL_Ominus__class_Ominus(X17,c_HOL_Ominus__class_Ominus(X16,X18,tc_fun(X19,tc_bool)),tc_fun(X19,tc_bool)) = X18
| ~ c_lessequals(X17,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1302,plain,
! [X17,X18,X19,X20] :
( hAPP(c_Set_Ovimage(c_COMBK(X17,X19,X20),X20,X19),X18) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| hBOOL(c_in(X17,X18,X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_769])])]) ).
fof(c_0_1303,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool))
| hBOOL(c_in(X11,X13,X14)) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1304,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| hBOOL(c_in(X11,X13,X14))
| ~ c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1305,plain,
! [X42,X43,X44,X45,X46] :
( ~ class_Orderings_Oorder(X46)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X45,X44,X46),c_SetInterval_Oord__class_OatLeastAtMost(X43,X42,X46),tc_fun(X46,tc_bool))
| ~ c_lessequals(X44,X42,X46)
| ~ c_lessequals(X43,X45,X46) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1306,plain,
! [X17,X18,X19,X20] :
( hAPP(c_Set_Oimage(c_COMBK(X17,X20,X19),X19,X20),X18) = hAPP(hAPP(c_Set_Oinsert(X20),X17),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)))
| X18 = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_773])])]) ).
fof(c_0_1307,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),c_HOL_Ominus__class_Ominus(X11,X12,tc_fun(X13,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1308,plain,
! [X11,X12,X13,X14] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X14),X11),X13),X12,tc_fun(X14,tc_bool)) = c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X11,X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1309,plain,
! [X18,X19,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X19),X18),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X19,v_x)),hAPP(X18,v_x)) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1310,plain,
! [X18,X19,X20] :
( ~ class_Lattices_Olattice(X20)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X20)),X19),X18),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X20),hAPP(X19,v_x)),hAPP(X18,v_x)) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1311,plain,
! [X39,X40] :
( ~ class_Orderings_Oorder(X40)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X40),X39),c_Orderings_Obot__class_Obot(tc_fun(X40,tc_bool))),c_SetInterval_Oord__class_OlessThan(X39,X40),tc_fun(X40,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X40),X39),c_Orderings_Obot__class_Obot(tc_fun(X40,tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1312,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),c_HOL_Ominus__class_Ominus(X11,X12,tc_fun(X13,tc_bool))) = X11
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1313,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X22)),X21) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1314,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X22)),X21) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1315,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22)),X21) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1316,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22)),X21) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1317,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| hBOOL(c_in(X11,X13,X14)) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1318,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,hAPP(hAPP(c_Set_Oinsert(X14),X11),X12),tc_fun(X14,tc_bool))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| hBOOL(c_in(X11,X13,X14)) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1319,plain,
! [X17,X18,X19] : hAPP(c_Set_Oimage(c_COMBK(X17,X19,X18),X18,X19),c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X19,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1320,plain,
! [X56,X57,X58,X59] :
( hBOOL(c_in(X56,X57,X59))
| ~ hBOOL(c_in(X56,X58,X59))
| ~ c_lessequals(X58,X57,tc_fun(X59,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1321,plain,
! [X11,X12,X13,X14] :
( hBOOL(c_in(X11,X12,X14))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ hBOOL(c_in(X11,X13,X14)) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1322,plain,
! [X17,X18,X19,X20] :
( hBOOL(c_in(X17,X18,X20))
| ~ hBOOL(c_in(X17,X19,X20))
| ~ c_lessequals(X19,X18,tc_fun(X20,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1323,plain,
! [X11,X12,X13,X14] :
( hBOOL(c_in(X11,X12,X14))
| ~ hBOOL(c_in(X11,X13,X14))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1324,plain,
! [X44,X45,X46,X47] :
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X47),X44),X46),hAPP(hAPP(c_Set_Oinsert(X47),X44),X45),tc_fun(X47,tc_bool))
| ~ c_lessequals(X46,X45,tc_fun(X47,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1325,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(X23,X22))
| X21 = X22
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X24),X21),X23),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_792])])]) ).
fof(c_0_1326,plain,
! [X11,X12,X13,X14] :
( hBOOL(c_in(X11,X12,X14))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X14),X11),X13),X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1327,plain,
! [X15,X16,X17,X18] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X17)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16,c_COMBK(X15,X17,X18),X18,X17) = X15
| X16 = c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_794])])]) ).
fof(c_0_1328,plain,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Set_Oinsert(X14),X11),X13) != hAPP(hAPP(c_Set_Oinsert(X14),X11),X12)
| hBOOL(c_in(X11,X12,X14))
| hBOOL(c_in(X11,X13,X14))
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1329,plain,
! [X22,X23,X24] :
( ~ hBOOL(hAPP(X23,X22))
| ~ hBOOL(c_in(X22,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_796])])]) ).
fof(c_0_1330,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X12),X11,X12),X10,X12)
| ~ hBOOL(c_in(X10,X11,X12))
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1331,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(X23,X22))
| ~ hBOOL(c_in(X22,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_798])])]) ).
fof(c_0_1332,plain,
! [X11,X12,X13] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11),X11,tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1333,plain,
! [X11,X12,X13] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11),X12,tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1334,plain,
! [X11,X12,X13] : c_lessequals(X12,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11),tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1335,plain,
! [X11,X12,X13] : c_lessequals(X11,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11),tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1336,plain,
! [X11,X12,X13,X14] :
( c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X14),X11),X13),X12,tc_fun(X14,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1337,plain,
! [X42,X43,X44,X45,X46] :
( ~ class_Orderings_Oorder(X46)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X45,X44,X46),c_SetInterval_Oord__class_OatLeastAtMost(X43,X42,X46),tc_fun(X46,tc_bool))
| c_lessequals(X45,X44,X46) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1338,plain,
! [X30,X31,X32,X33,X34,X35] :
( ~ c_Orderings_Olinorder(X30,X31,X32)
| c_Finite__Set_Ofold1(X33,hAPP(hAPP(c_Set_Oinsert(X35),X34),c_Orderings_Obot__class_Obot(tc_fun(X35,tc_bool))),X35) = X34 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_805])])]) ).
fof(c_0_1339,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11) != c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))
| c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)) = X12 ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1340,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X43,tc_bool)),X42),X41),X43)
| ~ c_Finite__Set_Ofinite(X41,X43)
| ~ c_Finite__Set_Ofinite(X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1341,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X43,tc_bool)),X42),X41),X43)
| ~ c_Finite__Set_Ofinite(X41,X43)
| ~ c_Finite__Set_Ofinite(X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1342,plain,
! [X30,X31,X32,X33] :
( ~ hBOOL(hAPP(hAPP(X31,X30),X30))
| ~ c_Orderings_Olinorder(X31,X32,X33)
| ~ hBOOL(hAPP(hAPP(X32,X30),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_809])])]) ).
fof(c_0_1343,plain,
! [X30,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(X32,X31),X30))
| ~ hBOOL(hAPP(hAPP(X33,X30),X31))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_810])])]) ).
fof(c_0_1344,plain,
! [X30,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ hBOOL(hAPP(hAPP(X32,X30),X31))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_811])])]) ).
fof(c_0_1345,plain,
! [X30,X31,X32,X33,X34] :
( ~ hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ hBOOL(hAPP(hAPP(X33,X30),X31))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_812])])]) ).
fof(c_0_1346,plain,
! [X10,X11] : ~ hBOOL(c_in(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11)),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1347,plain,
! [X17,X18] : ~ hBOOL(c_in(X17,c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool)),X18)),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1348,plain,
! [X7,X8] : ~ hBOOL(c_in(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8)),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1349,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Olower__semilattice(X34)
| c_lessequals(X31,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X34),X33),X32),X34)
| ~ c_lessequals(X31,X32,X34)
| ~ c_lessequals(X31,X33,X34) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1350,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21),X24)
| ~ c_lessequals(X23,X21,X24)
| ~ c_lessequals(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1351,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21),X24)
| ~ c_lessequals(X23,X21,X24)
| ~ c_lessequals(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1352,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22),X21,X24)
| ~ c_lessequals(X22,X21,X24)
| ~ c_lessequals(X23,X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1353,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21),X23,X24)
| ~ c_lessequals(X21,X23,X24)
| ~ c_lessequals(X22,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1354,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Oupper__semilattice(X34)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X34),X33),X32),X31,X34)
| ~ c_lessequals(X32,X31,X34)
| ~ c_lessequals(X33,X31,X34) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1355,plain,
! [X60,X61,X62] :
( ~ class_Orderings_Oorder(X62)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),c_SetInterval_Oord__class_OlessThan(X61,X62)),c_SetInterval_Oord__class_OatLeastAtMost(X61,X60,X62)) = c_Orderings_Obot__class_Obot(tc_fun(X62,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1356,plain,
! [X34,X35,X36,X37,X38] :
( hAPP(hAPP(X34,hAPP(hAPP(X34,X37),X36)),X35) = hAPP(hAPP(X34,X37),hAPP(hAPP(X34,X36),X35))
| ~ c_OrderedGroup_Oab__semigroup__mult(X34,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_823])])]) ).
fof(c_0_1357,plain,
! [X31,X32,X33] :
( hAPP(hAPP(c_Set_Oinsert(X33),X32),c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X33),X31),c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool)))
| X32 = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_824])])]) ).
fof(c_0_1358,plain,
! [X3] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1359,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),c_HOL_Ominus__class_Ominus(X11,X12,tc_fun(X13,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1360,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X43,tc_bool)),X42),X41),X43)
| ~ c_Finite__Set_Ofinite(X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1361,plain,
! [X41,X42,X43] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X43,tc_bool)),X42),X41),X43)
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1362,plain,
! [X16,X17,X18,X19] :
( c_lessequals(X18,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(X19,tc_bool))
| ~ c_lessequals(X18,X17,tc_fun(X19,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1363,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
| c_HOL_Ominus__class_Ominus(X30,X28,X31) != c_HOL_Ominus__class_Ominus(X29,X27,X31)
| c_lessequals(X28,X30,X31)
| ~ c_lessequals(X27,X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1364,plain,
! [X27,X28,X29,X30,X31] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
| c_HOL_Ominus__class_Ominus(X30,X28,X31) != c_HOL_Ominus__class_Ominus(X29,X27,X31)
| c_lessequals(X27,X29,X31)
| ~ c_lessequals(X28,X30,X31) ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1365,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X21)) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1366,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X23),X21)) ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1367,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X21)) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1368,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),X21)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X22),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X21)) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1369,plain,
! [X11,X12,X13] : hBOOL(c_in(X11,hAPP(hAPP(c_Set_Oinsert(X13),X11),X12),X13)),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1370,plain,
! [X11,X12,X13] : hBOOL(c_in(X11,hAPP(hAPP(c_Set_Oinsert(X13),X11),X12),X13)),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1371,plain,
! [X8,X9,X10] : hBOOL(c_in(X8,hAPP(hAPP(c_Set_Oinsert(X10),X8),X9),X10)),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1372,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Oupper__semilattice(X34)
| c_lessequals(X33,X31,X34)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X34),X33),X32),X31,X34) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1373,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Oupper__semilattice(X34)
| c_lessequals(X32,X31,X34)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X34),X33),X32),X31,X34) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1374,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(X23,X21,X24)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22),X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1375,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(X22,X21,X24)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X24),X23),X22),X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1376,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,X21,X24)
| ~ c_lessequals(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21),X24) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1377,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,X22,X24)
| ~ c_lessequals(X23,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X24),X22),X21),X24) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1378,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Olower__semilattice(X34)
| c_lessequals(X31,X32,X34)
| ~ c_lessequals(X31,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X34),X33),X32),X34) ),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1379,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Olower__semilattice(X34)
| c_lessequals(X31,X33,X34)
| ~ c_lessequals(X31,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X34),X33),X32),X34) ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1380,plain,
! [X21,X22,X23,X24] : hAPP(hAPP(c_Set_Oinsert(X24),X22),hAPP(hAPP(c_Set_Oinsert(X24),X21),X23)) = hAPP(hAPP(c_Set_Oinsert(X24),X21),hAPP(hAPP(c_Set_Oinsert(X24),X22),X23)),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1381,plain,
! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X11,tc_fun(X13,tc_bool)) = c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1382,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11) != X11
| c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1383,plain,
! [X31,X32,X33,X34] :
( c_lessequals(X33,hAPP(hAPP(c_Set_Oinsert(X34),X31),X32),tc_fun(X34,tc_bool))
| ~ c_lessequals(X33,X32,tc_fun(X34,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1384,plain,
! [X30,X31,X32,X33,X34] :
( X31 = X30
| ~ hBOOL(hAPP(hAPP(X32,X31),X30))
| hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_851])])]) ).
fof(c_0_1385,plain,
! [X30,X31,X32,X33,X34] :
( X31 = X30
| hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ hBOOL(hAPP(hAPP(X32,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_852])])]) ).
fof(c_0_1386,plain,
! [X13,X14,X15] : c_Fun_Oinj__on(X13,c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),X15,X14),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1387,plain,
! [X11,X12,X13] :
( c_Finite__Set_Ofinite(X12,X13)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13)
| ~ c_Finite__Set_Ofinite(X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1388,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11) != c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))
| X12 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1389,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11) != c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))
| X11 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1390,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X11),X12),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1391,plain,
! [X11,X12,X13] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X11),X12),
inference(variable_rename,[status(thm)],[c_0_858]) ).
fof(c_0_1392,plain,
! [X28,X29,X30] :
( ~ class_Orderings_Olinorder(X30)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X28,X30),c_Finite__Set_Olinorder__class_OMin(X29,X30),X30)
| ~ c_Finite__Set_Ofinite(X28,X30)
| X29 = c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool))
| ~ c_lessequals(X29,X28,tc_fun(X30,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_859]) ).
fof(c_0_1393,plain,
! [X28,X29,X30] :
( ~ class_Orderings_Olinorder(X30)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X29,X30),c_Finite__Set_Olinorder__class_OMax(X28,X30),X30)
| ~ c_Finite__Set_Ofinite(X28,X30)
| X29 = c_Orderings_Obot__class_Obot(tc_fun(X30,tc_bool))
| ~ c_lessequals(X29,X28,tc_fun(X30,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1394,plain,
! [X22,X23,X24] :
( hBOOL(hAPP(X23,X22))
| ~ hBOOL(c_in(X22,c_Collect(X23,X24),X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_861])])]) ).
fof(c_0_1395,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X8,c_Finite__Set_Olinorder__class_OMax(X9,X10),X10)
| ~ hBOOL(c_in(X8,X9,X10))
| ~ c_Finite__Set_Ofinite(X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_862]) ).
fof(c_0_1396,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X9,X10),X8,X10)
| ~ hBOOL(c_in(X8,X9,X10))
| ~ c_Finite__Set_Ofinite(X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_863]) ).
fof(c_0_1397,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X24),X21),X23),X22))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_864])])]) ).
fof(c_0_1398,plain,
! [X67,X68,X69,X70] :
( c_Hoare__Mirabelle_Ohoare__derivs(X69,X68,X70)
| ~ c_lessequals(X68,X67,tc_fun(tc_Hoare__Mirabelle_Otriple(X70),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X69,X67,X70) ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1399,plain,
! [X45,X46,X47,X48] :
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X45,X48,X47),X46),X47)
| ~ c_Finite__Set_Ofinite(X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1400,plain,
! [X11,X12] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X12,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),X11) = c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1401,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ominus(X14)
| hAPP(c_HOL_Ominus__class_Ominus(X13,X12,tc_fun(t_a,X14)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X13,v_x),hAPP(X12,v_x),X14) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1402,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11) = X12
| ~ c_lessequals(X11,X12,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1403,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X13,tc_bool)),X12),X11) = X11
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1404,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11) = X11
| ~ c_lessequals(X11,X12,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1405,plain,
! [X11,X12,X13] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X13,tc_bool)),X12),X11) = X12
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1406,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X22,X21,X23)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X22,X23),c_SetInterval_Oord__class_OlessThan(X21,X23),tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1407,plain,
! [X8,X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| c_lessequals(X8,c_Complete__Lattice_OSup__class_OSup(X9,X10),X10)
| ~ hBOOL(c_in(X8,X9,X10)) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1408,plain,
! [X8,X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X9,X10),X8,X10)
| ~ hBOOL(c_in(X8,X9,X10)) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1409,plain,
! [X13,X14,X15] : c_Finite__Set_Ofold1(X13,hAPP(hAPP(c_Set_Oinsert(X15),X14),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),X15) = X14,
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1410,plain,
! [X13,X14,X15,X16] :
( c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool)) != hAPP(c_Set_Oimage(X13,X15,X16),X14)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_877])])]) ).
fof(c_0_1411,plain,
! [X13,X14,X15,X16] :
( hAPP(c_Set_Oimage(X13,X15,X16),X14) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_878])])]) ).
fof(c_0_1412,plain,
! [X34,X35,X36,X37,X38] :
( hAPP(hAPP(c_Set_Oinsert(X37),X35),X34) != c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool))
| hBOOL(c_in(X35,X34,X37))
| ~ c_OrderedGroup_Oab__semigroup__mult(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_879])])]) ).
fof(c_0_1413,plain,
! [X34,X35,X36,X37,X38] :
( hAPP(hAPP(X34,X37),hAPP(hAPP(X34,X36),X35)) = hAPP(hAPP(X34,X36),hAPP(hAPP(X34,X37),X35))
| ~ c_OrderedGroup_Oab__semigroup__mult(X34,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_880])])]) ).
fof(c_0_1414,plain,
! [X8,X9] : c_Fun_Oinj__on(c_COMBI(X9),X8,X9,X9),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1415,plain,
! [X30,X31,X32,X33,X34] :
( X31 = X30
| hBOOL(hAPP(hAPP(X33,X31),X30))
| hBOOL(hAPP(hAPP(X33,X30),X31))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_882])])]) ).
fof(c_0_1416,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(X33,X30),X31))
| X31 = X30
| hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_883])])]) ).
fof(c_0_1417,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(X33,X30),X31))
| hBOOL(hAPP(hAPP(X33,X31),X30))
| X31 = X30
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_884])])]) ).
fof(c_0_1418,plain,
! [X30,X31,X32,X33,X34] :
( X31 = X30
| hBOOL(hAPP(hAPP(X33,X30),X31))
| hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_885])])]) ).
fof(c_0_1419,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(hAPP(X32,X30),X30))
| ~ c_Orderings_Olinorder(X31,X32,X33)
| hBOOL(hAPP(hAPP(X31,X30),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_886])])]) ).
fof(c_0_1420,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(X33,X31),X30))
| hBOOL(hAPP(hAPP(X32,X30),X31))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_887])])]) ).
fof(c_0_1421,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(X33,X30),X31))
| hBOOL(hAPP(hAPP(X32,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_888])])]) ).
fof(c_0_1422,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(X32,X30),X31))
| hBOOL(hAPP(hAPP(X32,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_889])])]) ).
fof(c_0_1423,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(hAPP(X32,X30),X31))
| hBOOL(hAPP(hAPP(X33,X31),X30))
| ~ c_Orderings_Olinorder(X32,X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_890])])]) ).
fof(c_0_1424,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Oupper__semilattice(X34)
| c_lessequals(X31,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X34),X33),X32),X34)
| ~ c_lessequals(X31,X33,X34) ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1425,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Oupper__semilattice(X34)
| c_lessequals(X31,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X34),X33),X32),X34)
| ~ c_lessequals(X31,X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1426,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Olower__semilattice(X34)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X34),X33),X32),X31,X34)
| ~ c_lessequals(X32,X31,X34) ),
inference(variable_rename,[status(thm)],[c_0_893]) ).
fof(c_0_1427,plain,
! [X31,X32,X33,X34] :
( ~ class_Lattices_Olower__semilattice(X34)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X34),X33),X32),X31,X34)
| ~ c_lessequals(X33,X31,X34) ),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1428,plain,
! [X11,X12] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X12,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),X11) = X11,
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1429,plain,
! [X11,X12,X13] :
( X12 = X11
| ~ c_lessequals(X11,X12,tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_896])])]) ).
fof(c_0_1430,plain,
! [X11,X12,X13] :
( X12 = X11
| ~ c_lessequals(X11,X12,tc_fun(X13,tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_897])])]) ).
fof(c_0_1431,plain,
! [X20,X21,X22,X23,X24] :
( hAPP(hAPP(X22,X21),hAPP(hAPP(X22,X21),X20)) = hAPP(hAPP(X22,X21),X20)
| ~ c_Finite__Set_Ofun__left__comm__idem(X22,X24,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_898])])]) ).
fof(c_0_1432,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_HOL_Oord(X21)
| c_lessequals(hAPP(X20,X18),hAPP(X19,X18),X21)
| ~ c_lessequals(X20,X19,tc_fun(X22,X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_899])])]) ).
fof(c_0_1433,plain,
! [X7,X8,X9] :
( hAPP(hAPP(c_Set_Oinsert(X9),X8),X7) != c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| hBOOL(c_in(X8,X7,X9)) ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1434,plain,
! [X8,X9,X10] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X10),X8),X9),X8)),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1435,plain,
! [X21,X22,X23,X24] :
( ~ class_Orderings_Opreorder(X24)
| c_lessequals(X23,X21,X24)
| ~ c_lessequals(X22,X21,X24)
| ~ c_lessequals(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1436,plain,
! [X21,X22,X23,X24] :
( ~ class_Orderings_Oorder(X24)
| c_lessequals(X21,X23,X24)
| ~ c_lessequals(X21,X22,X24)
| ~ c_lessequals(X22,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1437,plain,
! [X8,X9] :
( X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_904]) ).
fof(c_0_1438,plain,
! [X11,X12,X13] : c_lessequals(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X12,tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1439,plain,
! [X10,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X11),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1440,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X11),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_907]) ).
fof(c_0_1441,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X11),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_908]) ).
fof(c_0_1442,plain,
! [X10,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X11),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1443,plain,
! [X10,X11,X12] :
( hAPP(hAPP(c_Set_Oinsert(X12),X10),X11) = X11
| ~ hBOOL(c_in(X10,X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1444,plain,
! [X69,X70,X71,X72] :
( c_Hoare__Mirabelle_Ohoare__derivs(X71,X69,X72)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X71,X70,X72)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X70,X69,X72) ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1445,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X22,X23),c_SetInterval_Oord__class_OlessThan(X21,X23),tc_fun(X23,tc_bool))
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1446,plain,
! [X8,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X9,tc_bool)),X8),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1447,plain,
! [X31,X32,X33] :
( ~ class_Orderings_Oorder(X33)
| c_SetInterval_Oord__class_OatLeastAtMost(X32,X31,X33) != c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool))
| ~ c_lessequals(X32,X31,X33) ),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1448,plain,
! [X31,X32,X33] :
( ~ class_Orderings_Oorder(X33)
| c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X32,X31,X33)
| ~ c_lessequals(X32,X31,X33) ),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1449,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X8,X9),X8,X9))
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1450,plain,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X9)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X8,X9),X8,X9))
| X8 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_917]) ).
fof(c_0_1451,plain,
! [X7,X8] : c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X8),X7),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X8) = X7,
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1452,plain,
! [X7,X8] : c_The(hAPP(hAPP(c_Set_Oinsert(X8),X7),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool))),X8) = X7,
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1453,plain,
! [X30,X31,X32,X33] :
( ~ c_Orderings_Olinorder(X31,X32,X33)
| ~ hBOOL(hAPP(hAPP(X32,X30),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_920])])]) ).
fof(c_0_1454,plain,
! [X30,X31,X32,X33] :
( ~ hBOOL(hAPP(hAPP(X32,X30),X30))
| ~ c_Orderings_Olinorder(X31,X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_921])])]) ).
fof(c_0_1455,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1456,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) ),
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1457,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) ),
inference(variable_rename,[status(thm)],[c_0_924]) ).
fof(c_0_1458,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) ),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1459,plain,
! [X11,X12,X13] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13)
| ~ c_Finite__Set_Ofinite(X12,X13)
| ~ c_Finite__Set_Ofinite(X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1460,plain,
! [X22,X23,X24] :
( hBOOL(c_in(X22,c_Collect(X23,X24),X24))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_927])])]) ).
fof(c_0_1461,plain,
! [X7,X8] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X7)),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1462,plain,
! [X8,X9,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X8),hAPP(hAPP(c_Set_Oinsert(X10),X8),X9)) = hAPP(hAPP(c_Set_Oinsert(X10),X8),X9),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1463,plain,
! [X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| ~ hBOOL(c_in(X23,X24,X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_930])])]) ).
fof(c_0_1464,plain,
! [X10,X11,X12] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12),X10),c_Complete__Lattice_OSup__class_OSup(X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1465,plain,
! [X10,X11,X12] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12),X10),c_Complete__Lattice_OInf__class_OInf(X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_932]) ).
fof(c_0_1466,plain,
! [X25,X26,X27,X28] :
( hBOOL(hAPP(X26,X25))
| ~ c_lessequals(X27,X26,tc_fun(X28,tc_bool))
| ~ hBOOL(hAPP(X27,X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_933])])]) ).
fof(c_0_1467,plain,
! [X25,X26,X27,X28] :
( hBOOL(hAPP(X26,X25))
| ~ hBOOL(hAPP(X27,X25))
| ~ c_lessequals(X27,X26,tc_fun(X28,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_934])])]) ).
fof(c_0_1468,plain,
! [X13,X14,X15] : c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) = hAPP(c_Set_Oimage(X13,X14,X15),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_935]) ).
fof(c_0_1469,plain,
! [X13,X14,X15] : hAPP(c_Set_Oimage(X13,X14,X15),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_936]) ).
fof(c_0_1470,plain,
! [X13,X14,X15] : hAPP(c_Set_Ovimage(X13,X15,X14),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_937]) ).
fof(c_0_1471,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(X11,X12)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12) ),
inference(variable_rename,[status(thm)],[c_0_938]) ).
fof(c_0_1472,plain,
! [X8,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X9,tc_bool)),X8),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8,
inference(variable_rename,[status(thm)],[c_0_939]) ).
fof(c_0_1473,plain,
! [X67,X68,X69] :
( c_Hoare__Mirabelle_Ohoare__derivs(X68,X67,X69)
| ~ c_lessequals(X67,X68,tc_fun(tc_Hoare__Mirabelle_Otriple(X69),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_940]) ).
fof(c_0_1474,plain,
! [X11,X12,X13] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X12,X11,tc_fun(X13,tc_bool)),X13)
| ~ c_Finite__Set_Ofinite(X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_941]) ).
fof(c_0_1475,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| X22 = X21
| ~ c_lessequals(X22,X21,X23)
| ~ c_lessequals(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_942]) ).
fof(c_0_1476,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| X22 = X21
| ~ c_lessequals(X21,X22,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1477,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| X22 = X21
| ~ c_lessequals(X21,X22,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_944]) ).
fof(c_0_1478,plain,
! [X3] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1479,plain,
! [X27,X28,X29,X30] :
( ~ class_OrderedGroup_Oab__group__add(X30)
| c_HOL_Ominus__class_Ominus(X29,X29,X30) != c_HOL_Ominus__class_Ominus(X28,X27,X30)
| X28 = X27 ),
inference(variable_rename,[status(thm)],[c_0_946]) ).
fof(c_0_1480,plain,
! [X21,X22,X23,X24] :
( ~ class_OrderedGroup_Oab__group__add(X24)
| c_HOL_Ominus__class_Ominus(X22,X21,X24) != c_HOL_Ominus__class_Ominus(X23,X23,X24)
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1481,plain,
! [X11,X12,X13] : c_lessequals(X12,hAPP(hAPP(c_Set_Oinsert(X13),X11),X12),tc_fun(X13,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1482,plain,
! [X13,X14,X15] : c_Finite__Set_Ofold1(X13,X14,X15) = c_The(c_Finite__Set_Ofold1Set(X13,X14,X15),X15),
inference(variable_rename,[status(thm)],[c_0_949]) ).
fof(c_0_1483,plain,
! [X37,X38,X39,X40,X41,X42] :
( c_Com_Ocom_OCond(X38,X42,X40) != c_Com_Ocom_OCond(X37,X41,X39)
| X38 = X37 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_950])])]) ).
fof(c_0_1484,plain,
! [X37,X38,X39,X40,X41,X42] :
( c_Com_Ocom_OCond(X38,X42,X40) != c_Com_Ocom_OCond(X37,X41,X39)
| X42 = X41 ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1485,plain,
! [X37,X38,X39,X40,X41,X42] :
( c_Com_Ocom_OCond(X38,X42,X40) != c_Com_Ocom_OCond(X37,X41,X39)
| X40 = X39 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_952])])]) ).
fof(c_0_1486,plain,
! [X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_SetInterval_Oord__class_OatLeastAtMost(X10,X10,X11) = hAPP(hAPP(c_Set_Oinsert(X11),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1487,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21),X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1488,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21),X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1489,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21),X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1490,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21),X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1491,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_lessequals(X22,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21),X23) ),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1492,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_lessequals(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21),X23) ),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1493,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_lessequals(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21),X23) ),
inference(variable_rename,[status(thm)],[c_0_960]) ).
fof(c_0_1494,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_lessequals(X22,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21),X23) ),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1495,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)) = X22 ),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1496,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)) = X22 ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1497,plain,
! [X11,X12,X13] :
( c_Finite__Set_Ofinite(X12,X13)
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_Finite__Set_Ofinite(X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1498,plain,
! [X11,X12,X13] :
( c_Finite__Set_Ofinite(X12,X13)
| ~ c_Finite__Set_Ofinite(X11,X13)
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_965]) ).
fof(c_0_1499,plain,
! [X23,X24,X25] :
( hBOOL(c_in(X23,X24,X25))
| ~ hBOOL(hAPP(X24,X23)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_966])])]) ).
fof(c_0_1500,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X8,tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_967]) ).
fof(c_0_1501,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
c_0_968 ).
fof(c_0_1502,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) = X21
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1503,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) = X22
| ~ c_lessequals(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1504,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) = X21
| ~ c_lessequals(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1505,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) = X22
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1506,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) != X21
| c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1507,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) != X22
| c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1508,plain,
! [X8,X9] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X9,tc_bool)),X8),X8) = X8,
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1509,plain,
! [X8,X9] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X9,tc_bool)),X8),X8) = X8,
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1510,plain,
! [X10,X11] : c_Collect(c_fequal(X10,X11),X11) = hAPP(hAPP(c_Set_Oinsert(X11),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1511,plain,
! [X31,X32,X33] :
( ~ class_Orderings_Oorder(X33)
| c_SetInterval_Oord__class_OatLeastAtMost(X32,X31,X33) = c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool))
| c_lessequals(X32,X31,X33) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1512,plain,
! [X31,X32,X33] :
( ~ class_Orderings_Oorder(X33)
| c_Orderings_Obot__class_Obot(tc_fun(X33,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X32,X31,X33)
| c_lessequals(X32,X31,X33) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1513,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_980]) ).
fof(c_0_1514,plain,
! [X3,X4] : hAPP(c_Set_Ovimage(c_COMBI(X4),X4,X4),X3) = X3,
inference(variable_rename,[status(thm)],[c_0_981]) ).
fof(c_0_1515,plain,
! [X3,X4] : hAPP(c_Set_Oimage(c_COMBI(X4),X4,X4),X3) = X3,
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1516,plain,
! [X74,X75,X76] :
( X75 = X74
| ~ hBOOL(hAPP(c_fequal(X75,X76),X74)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_983])])]) ).
fof(c_0_1517,plain,
! [X40,X41] : c_Hoare__Mirabelle_Ohoare__derivs(X40,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X41),tc_bool)),X41),
inference(variable_rename,[status(thm)],[c_0_984]) ).
fof(c_0_1518,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),tc_fun(X9,tc_bool)) = X8,
inference(variable_rename,[status(thm)],[c_0_985]) ).
fof(c_0_1519,plain,
! [X8,X9] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X8,tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_986]) ).
fof(c_0_1520,plain,
! [X10,X11,X12] : hAPP(hAPP(c_Set_Oinsert(X12),X10),X11) != c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_987]) ).
fof(c_0_1521,plain,
! [X10,X11,X12] : c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1522,plain,
! [X25,X26,X27,X28] : hAPP(c_COMBK(X26,X28,X27),X25) = X26,
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1523,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X21,X22,X23)
| c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1524,plain,
! [X22,X23,X24] :
( c_Collect(X23,X24) != c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool))
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_991])])]) ).
fof(c_0_1525,plain,
! [X22,X23,X24] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) != c_Collect(X23,X24)
| ~ hBOOL(hAPP(X23,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_992])])]) ).
fof(c_0_1526,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X21),X22) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1527,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X21),X22) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1528,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X21),X22) ),
inference(variable_rename,[status(thm)],[c_0_995]) ).
fof(c_0_1529,plain,
! [X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X21),X22) ),
inference(variable_rename,[status(thm)],[c_0_996]) ).
fof(c_0_1530,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
c_0_997 ).
fof(c_0_1531,plain,
! [X37,X38,X39,X40,X41] : c_Com_Ocom_OWhile(X37,X39) != c_Com_Ocom_OCond(X38,X41,X40),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1532,plain,
! [X36,X37,X38,X39,X40] : c_Com_Ocom_OCond(X36,X39,X37) != c_Com_Ocom_OSemi(X40,X38),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1533,plain,
! [X37,X38,X39,X40,X41] : c_Com_Ocom_OCond(X38,X41,X40) != c_Com_Ocom_OWhile(X37,X39),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1534,plain,
! [X36,X37,X38,X39,X40] : c_Com_Ocom_OSemi(X40,X38) != c_Com_Ocom_OCond(X36,X39,X37),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1535,plain,
! [X8,X9] : c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X9,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1536,plain,
! [X34,X35,X36,X37] :
( hAPP(hAPP(X34,X36),X35) = hAPP(hAPP(X34,X35),X36)
| ~ c_OrderedGroup_Oab__semigroup__mult(X34,X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1003])])]) ).
fof(c_0_1537,plain,
! [X11,X12,X13] :
( ~ class_Lattices_Obounded__lattice(X13)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13),X12),X11) != c_Orderings_Obot__class_Obot(X13)
| X11 = c_Orderings_Obot__class_Obot(X13) ),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1538,plain,
! [X11,X12,X13] :
( ~ class_Lattices_Obounded__lattice(X13)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13),X12),X11) != c_Orderings_Obot__class_Obot(X13)
| X12 = c_Orderings_Obot__class_Obot(X13) ),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1539,plain,
! [X33,X34,X35] : c_Com_Ocom_OCond(X33,X35,X34) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1540,plain,
! [X33,X34,X35] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X33,X35,X34),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1541,plain,
! [X3] : c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X3),X3,tc_fun(X3,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1542,plain,
! [X7,X8] : hBOOL(hAPP(c_fequal(X7,X8),X7)),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1543,plain,
! [X8,X9] : c_lessequals(X8,X8,tc_fun(X9,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1544,plain,
! [X7,X8] : c_lessequals(X7,X7,tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1011]) ).
fof(c_0_1545,plain,
! [X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) = c_Orderings_Obot__class_Obot(X3) ),
inference(variable_rename,[status(thm)],[c_0_1012]) ).
fof(c_0_1546,plain,
! [X12] :
( ~ class_Orderings_Obot(X12)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X12)),v_x) = c_Orderings_Obot__class_Obot(X12) ),
inference(variable_rename,[status(thm)],[c_0_1013]) ).
fof(c_0_1547,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X8),c_Orderings_Obot__class_Obot(X8)),X7) = c_Orderings_Obot__class_Obot(X8) ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1548,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8),c_Orderings_Obot__class_Obot(X8)),X7) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1549,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X8),X7),c_Orderings_Obot__class_Obot(X8)) = c_Orderings_Obot__class_Obot(X8) ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1550,plain,
! [X7,X8] :
( ~ class_Orderings_Obot(X8)
| c_lessequals(c_Orderings_Obot__class_Obot(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1551,plain,
! [X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X3),X3,X3) ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1552,plain,
! [X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X3),X3,X3) ),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1553,plain,
! [X7,X8] :
( ~ class_Lattices_Obounded__lattice(X8)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8),X7),c_Orderings_Obot__class_Obot(X8)) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1020]) ).
fof(c_0_1554,plain,
! [X3] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1555,plain,
! [X7,X8] :
( ~ class_Orderings_Opreorder(X8)
| c_lessequals(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1556,plain,
! [X7,X8] :
( ~ class_Orderings_Oorder(X8)
| c_lessequals(X7,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1023]) ).
fof(c_0_1557,plain,
! [X7,X8] :
( ~ class_Lattices_Olower__semilattice(X8)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X8),X7),X7) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1558,plain,
! [X7,X8] :
( ~ class_Lattices_Oupper__semilattice(X8)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8),X7),X7) = X7 ),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1559,plain,
! [X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_SetInterval_Oord__class_OlessThan(X22,X23) != c_SetInterval_Oord__class_OlessThan(X21,X23)
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1560,plain,
! [X52,X53,X54,X55] :
( c_Com_Ocom_OWhile(X53,X55) != c_Com_Ocom_OWhile(X52,X54)
| X55 = X54 ),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1561,plain,
! [X52,X53,X54,X55] :
( c_Com_Ocom_OWhile(X53,X55) != c_Com_Ocom_OWhile(X52,X54)
| X53 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1028])])]) ).
fof(c_0_1562,plain,
! [X36,X37,X38,X39] :
( c_Com_Ocom_OSemi(X39,X37) != c_Com_Ocom_OSemi(X38,X36)
| X39 = X38 ),
inference(variable_rename,[status(thm)],[c_0_1029]) ).
fof(c_0_1563,plain,
! [X36,X37,X38,X39] :
( c_Com_Ocom_OSemi(X39,X37) != c_Com_Ocom_OSemi(X38,X36)
| X37 = X36 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1030])])]) ).
fof(c_0_1564,plain,
! [X73,X74] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X73,X74))
| ~ class_Finite__Set_Ofinite_Ofinite(X74)
| ~ class_Finite__Set_Ofinite_Ofinite(X73) ),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1565,plain,
! [X36,X37,X38,X39] : c_Com_Ocom_OWhile(X36,X37) != c_Com_Ocom_OSemi(X39,X38),
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1566,plain,
! [X36,X37,X38,X39] : c_Com_Ocom_OSemi(X39,X38) != c_Com_Ocom_OWhile(X36,X37),
inference(variable_rename,[status(thm)],[c_0_1033]) ).
fof(c_0_1567,plain,
! [X7,X8] : c_The(c_fequal(X7,X8),X8) = X7,
inference(variable_rename,[status(thm)],[c_0_1034]) ).
fof(c_0_1568,plain,
! [X73,X74] :
( class_HOL_Oord(tc_fun(X73,X74))
| ~ class_HOL_Oord(X74) ),
inference(variable_rename,[status(thm)],[c_0_1035]) ).
fof(c_0_1569,plain,
! [X73,X74] :
( class_HOL_Ominus(tc_fun(X73,X74))
| ~ class_HOL_Ominus(X74) ),
inference(variable_rename,[status(thm)],[c_0_1036]) ).
fof(c_0_1570,plain,
! [X73,X74] :
( class_Orderings_Obot(tc_fun(X73,X74))
| ~ class_Orderings_Obot(X74) ),
inference(variable_rename,[status(thm)],[c_0_1037]) ).
fof(c_0_1571,plain,
! [X73,X74] :
( class_Orderings_Oorder(tc_fun(X73,X74))
| ~ class_Orderings_Oorder(X74) ),
inference(variable_rename,[status(thm)],[c_0_1038]) ).
fof(c_0_1572,plain,
! [X73,X74] :
( class_Lattices_Olattice(tc_fun(X73,X74))
| ~ class_Lattices_Olattice(X74) ),
inference(variable_rename,[status(thm)],[c_0_1039]) ).
fof(c_0_1573,plain,
! [X73,X74] :
( class_Orderings_Opreorder(tc_fun(X73,X74))
| ~ class_Orderings_Opreorder(X74) ),
inference(variable_rename,[status(thm)],[c_0_1040]) ).
fof(c_0_1574,plain,
! [X73,X74] :
( class_Lattices_Obounded__lattice(tc_fun(X73,X74))
| ~ class_Lattices_Obounded__lattice(X74) ),
inference(variable_rename,[status(thm)],[c_0_1041]) ).
fof(c_0_1575,plain,
! [X73,X74] :
( class_Lattices_Odistrib__lattice(tc_fun(X73,X74))
| ~ class_Lattices_Odistrib__lattice(X74) ),
inference(variable_rename,[status(thm)],[c_0_1042]) ).
fof(c_0_1576,plain,
! [X73,X74] :
( class_Lattices_Olower__semilattice(tc_fun(X73,X74))
| ~ class_Lattices_Olattice(X74) ),
inference(variable_rename,[status(thm)],[c_0_1043]) ).
fof(c_0_1577,plain,
! [X73,X74] :
( class_Lattices_Oupper__semilattice(tc_fun(X73,X74))
| ~ class_Lattices_Olattice(X74) ),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_1578,plain,
! [X73,X74] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X73,X74))
| ~ class_Complete__Lattice_Ocomplete__lattice(X74) ),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1579,plain,
! [X33,X34] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X34,X33),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_1580,plain,
! [X33,X34] : c_Com_Ocom_OSemi(X34,X33) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[c_0_1047]) ).
fof(c_0_1581,plain,
! [X5,X6] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X5,X6),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_1582,plain,
! [X5,X6] : c_Com_Ocom_OWhile(X5,X6) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_1583,plain,
! [X8,X9] :
( ~ class_Finite__Set_Ofinite_Ofinite(X9)
| c_Finite__Set_Ofinite(X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1584,plain,
! [X22,X23] : hAPP(c_COMBI(X23),X22) = X22,
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_1585,axiom,
hAPP(c_COMBI(t_a),v_P) = v_P,
c_0_1052 ).
fof(c_0_1586,plain,
! [X22,X23] : c_Collect(X22,X23) = X22,
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_1587,axiom,
class_HOL_Oord(tc_bool),
c_0_1054 ).
fof(c_0_1588,axiom,
class_HOL_Ominus(tc_bool),
c_0_1055 ).
fof(c_0_1589,axiom,
class_Orderings_Obot(tc_bool),
c_0_1056 ).
fof(c_0_1590,axiom,
class_Orderings_Oorder(tc_bool),
c_0_1057 ).
fof(c_0_1591,axiom,
class_Lattices_Olattice(tc_bool),
c_0_1058 ).
fof(c_0_1592,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_1059 ).
fof(c_0_1593,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_1060 ).
fof(c_0_1594,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_1061 ).
fof(c_0_1595,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
c_0_1062 ).
fof(c_0_1596,axiom,
class_Lattices_Olower__semilattice(tc_bool),
c_0_1063 ).
fof(c_0_1597,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_1064 ).
fof(c_0_1598,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_1065 ).
cnf(c_0_1599,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1600,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1601,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1602,plain,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1603,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1604,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1605,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1606,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1607,plain,
( hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1608,plain,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1609,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OCond(X4,X5,X7),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X7,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1610,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OWhile(X4,X5),c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1611,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1612,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1613,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1614,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1615,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1616,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1617,plain,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1618,plain,
c_COMBS(X1,X2,X3,X4,X5,X6) = hAPP(hAPP(X1,X3),hAPP(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1619,plain,
c_COMBS(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1620,plain,
c_COMBC(X1,X2,X3,X4,X5,X6) = hAPP(hAPP(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1621,plain,
c_COMBC(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),v_Q),
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1622,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1623,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1624,plain,
hAPP(c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4),X6) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(c_Set_Oimage(X2,X5,X3),X6)),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1625,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X5,X2),X6)) = hAPP(c_Set_Oimage(c_COMBB(X1,X4,X2,X3,X5),X5,X3),X6),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1626,plain,
hAPP(c_Set_Ovimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4),X6) = hAPP(c_Set_Ovimage(X2,X5,X3),hAPP(c_Set_Ovimage(X1,X3,X4),X6)),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1627,plain,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5)
| ~ hBOOL(c_in(hAPP(X1,X3),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1628,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1629,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1630,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1631,plain,
( c_Fun_Oinj__on(X1,hAPP(c_Set_Oimage(X2,X5,X3),X6),X3,X4)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1632,plain,
( c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5)
| ~ c_Fun_Oinj__on(X1,X4,X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1633,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1634,plain,
( c_Fun_Oinj__on(c_Fun_Ocomp(X5,X1,X4,X6,X3),X2,X3,X6)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X1,X3,X4),X2),X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1635,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1636,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1637,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1638,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1639,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1640,plain,
( hBOOL(c_in(hAPP(X1,X5),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4))
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1641,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Ovimage(X1,X2,X3),X5,tc_fun(X3,tc_bool),tc_fun(X2,tc_bool),X6),X6,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1642,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Oimage(X1,X2,X3),X5,tc_fun(X2,tc_bool),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1643,plain,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBB(hAPP(c_Set_Oinsert(X4),X5),X6,tc_fun(X4,tc_bool),tc_fun(X4,tc_bool),X3),X3,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X6,X3,tc_fun(X4,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1644,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1645,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1646,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,X3,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(X5,X1,X3,tc_fun(X6,tc_bool),X2),X2,tc_fun(X6,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1647,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(X2,X3,X4,tc_fun(X5,tc_bool),X6),X6,tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X3,X6,X4),X1),X2,X4,tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1648,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1649,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1650,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1651,plain,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1652,plain,
c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X4),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1653,plain,
( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X1,X4,X2,tc_fun(X3,X3),X5),X5,X3)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1654,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1655,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1656,plain,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1657,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1658,plain,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1659,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSKIP,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1660,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X1,tc_fun(X5,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1661,plain,
( hAPP(X2,X1) = X5
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1662,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1663,plain,
( hAPP(c_Set_Oimage(X1,X3,X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X5),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_Set_Oimage(X1,X3,X4),X5)),hAPP(c_Set_Oimage(X1,X3,X4),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1664,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1665,plain,
hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1666,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1667,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1668,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1669,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1670,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1671,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1672,plain,
( hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X3,X4),X5),hAPP(c_Set_Oimage(X1,X3,X4),X6),tc_fun(X4,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1673,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X1,tc_bool))),X4) = X4,
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1674,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1675,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1676,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1677,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1678,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1679,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1680,plain,
( c_Fun_Ocomp(hAPP(X1,X4),hAPP(X1,X4),X3,X3,X3) = hAPP(X1,X4)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1681,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1682,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1))),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1683,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1684,plain,
( hBOOL(c_in(X1,X3,X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1685,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1686,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1687,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1688,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1689,plain,
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1690,plain,
( c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1691,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X2),X4,X5)
| hAPP(c_Set_Oimage(X3,X4,X5),X1) != hAPP(c_Set_Oimage(X3,X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1692,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1693,plain,
( hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1694,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1695,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1696,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1697,plain,
( c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1698,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),hAPP(X4,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1699,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1700,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1701,plain,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1702,plain,
( hBOOL(c_in(hAPP(X2,X1),X5,X4))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1703,plain,
( hBOOL(c_in(hAPP(X2,X1),X5,X4))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1704,plain,
( c_Fun_Oinj__on(X1,X3,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1705,plain,
( c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1706,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1707,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1708,plain,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1709,plain,
( hAPP(c_Set_Oimage(X3,X2,X2),X1) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(hAPP(c_Set_Oimage(X3,X2,X2),X1),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1710,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1711,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1712,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1713,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1714,plain,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1715,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1716,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1717,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1718,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1719,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1720,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1721,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1722,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),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_1189]) ).
cnf(c_0_1723,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),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_1190]) ).
cnf(c_0_1724,plain,
( hBOOL(hAPP(X4,hAPP(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1725,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1726,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1727,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1728,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1729,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1730,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1731,plain,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1732,plain,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1733,plain,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1734,plain,
( hBOOL(c_in(hAPP(X1,X6),X5,X3))
| ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1735,plain,
c_Hoare__Mirabelle_Otriple_Otriple__case(X1,c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),X5,X6) = hAPP(hAPP(hAPP(X1,X2),X3),X4),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1736,plain,
c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),X5,X6) = hAPP(hAPP(hAPP(X1,X2),X3),X4),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1737,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1738,plain,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1739,plain,
( X1 = X3
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1740,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1741,plain,
( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1742,plain,
( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1743,plain,
( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1744,plain,
( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1745,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1746,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1747,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1748,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1749,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1750,plain,
( c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
| ~ c_Fun_Oinj__on(X1,X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1751,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1752,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1753,plain,
( c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1754,plain,
c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X4,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1755,plain,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1756,plain,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1757,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1758,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = X2,
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1759,plain,
( X1 = X4
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(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_1226]) ).
cnf(c_0_1760,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1761,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1228]) ).
cnf(c_0_1762,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,X2,X3))
| ~ hBOOL(c_in(X6,X2,X3))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1763,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1230]) ).
cnf(c_0_1764,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1765,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1766,plain,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X2,X2),X1),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1767,plain,
( hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1768,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_1235]) ).
cnf(c_0_1769,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1770,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1771,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1772,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1773,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1774,plain,
c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1775,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1776,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1777,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1778,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1245]) ).
cnf(c_0_1779,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1246]) ).
cnf(c_0_1780,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1781,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1782,plain,
( c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1783,plain,
( c_lessequals(hAPP(c_Set_Oimage(X4,X3,X5),X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1784,plain,
( c_lessequals(hAPP(c_Set_Ovimage(X4,X5,X3),X1),hAPP(c_Set_Ovimage(X4,X5,X3),X2),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1251]) ).
cnf(c_0_1785,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1252]) ).
cnf(c_0_1786,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1253]) ).
cnf(c_0_1787,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1788,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1255]) ).
cnf(c_0_1789,plain,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1790,plain,
( c_lessequals(X2,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1791,plain,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1792,plain,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1259]) ).
cnf(c_0_1793,plain,
( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X1)),hAPP(c_Set_Oimage(X5,X3,X4),X2)) = hAPP(c_Set_Oimage(X5,X3,X4),X2)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1260]) ).
cnf(c_0_1794,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1261]) ).
cnf(c_0_1795,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1796,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,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_1263]) ).
cnf(c_0_1797,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1798,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1799,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X4,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1800,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1801,plain,
( hAPP(c_Set_Oimage(c_COMBK(X4,X5,X3),X3,X5),X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1802,plain,
( X1 = X3
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1803,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X3),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1804,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),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(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1805,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),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(split_conjunct,[status(thm)],[c_0_1272]) ).
cnf(c_0_1806,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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_1273]) ).
cnf(c_0_1807,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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_1274]) ).
cnf(c_0_1808,plain,
( c_lessequals(X4,X1,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1809,plain,
( c_lessequals(X2,X5,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1276]) ).
cnf(c_0_1810,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1277]) ).
cnf(c_0_1811,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1278]) ).
cnf(c_0_1812,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1279]) ).
cnf(c_0_1813,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1814,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1815,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1816,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1283]) ).
cnf(c_0_1817,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1818,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X1,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
inference(split_conjunct,[status(thm)],[c_0_1285]) ).
cnf(c_0_1819,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1286]) ).
cnf(c_0_1820,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,hAPP(c_Set_Oimage(X4,X2,X5),X1),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1821,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)),
inference(split_conjunct,[status(thm)],[c_0_1288]) ).
cnf(c_0_1822,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1289]) ).
cnf(c_0_1823,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1290]) ).
cnf(c_0_1824,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(split_conjunct,[status(thm)],[c_0_1291]) ).
cnf(c_0_1825,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1292]) ).
cnf(c_0_1826,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_1293]) ).
cnf(c_0_1827,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_1294]) ).
cnf(c_0_1828,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1295]) ).
cnf(c_0_1829,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1296]) ).
cnf(c_0_1830,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X4,X3,X2))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1831,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1832,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1299]) ).
cnf(c_0_1833,plain,
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1300]) ).
cnf(c_0_1834,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ 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_1301]) ).
cnf(c_0_1835,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(c_Set_Ovimage(c_COMBK(X1,X3,X4),X4,X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1302]) ).
cnf(c_0_1836,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1303]) ).
cnf(c_0_1837,plain,
( hBOOL(c_in(X3,X1,X2))
| c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1304]) ).
cnf(c_0_1838,plain,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1305]) ).
cnf(c_0_1839,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(c_COMBK(X3,X4,X2),X2,X4),X1) = hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1840,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1307]) ).
cnf(c_0_1841,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1308]) ).
cnf(c_0_1842,plain,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1309]) ).
cnf(c_0_1843,plain,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1310]) ).
cnf(c_0_1844,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1845,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1846,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1847,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1848,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1849,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1850,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1851,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1852,plain,
hAPP(c_Set_Oimage(c_COMBK(X1,X2,X3),X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1853,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1854,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1855,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1856,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1857,plain,
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1858,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1859,plain,
( hBOOL(c_in(X2,X4,X1))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1860,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1861,plain,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| hAPP(hAPP(c_Set_Oinsert(X4),X3),X1) != hAPP(hAPP(c_Set_Oinsert(X4),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_1862,plain,
( ~ hBOOL(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_1329]) ).
cnf(c_0_1863,plain,
( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_1864,plain,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1865,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_1866,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X2,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_1867,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_1868,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_1869,plain,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_1870,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_1871,plain,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3
| ~ c_Orderings_Olinorder(X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1338]) ).
cnf(c_0_1872,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1339]) ).
cnf(c_0_1873,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1340]) ).
cnf(c_0_1874,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_1875,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1876,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_1877,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1878,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1879,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_1880,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_1881,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1348]) ).
cnf(c_0_1882,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1349]) ).
cnf(c_0_1883,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1884,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1885,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1886,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_1887,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1888,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1889,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1890,plain,
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_1891,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1358]) ).
cnf(c_0_1892,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_1893,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_1894,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1895,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_1362]) ).
cnf(c_0_1896,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1897,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1898,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_1899,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1366]) ).
cnf(c_0_1900,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1367]) ).
cnf(c_0_1901,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_1902,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_1903,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_1904,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_1905,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_1906,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_1907,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1374]) ).
cnf(c_0_1908,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_1909,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_1910,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_1911,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_1912,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_1913,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1380]) ).
cnf(c_0_1914,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_1915,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_1916,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_1917,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_1918,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1385]) ).
cnf(c_0_1919,plain,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1386]) ).
cnf(c_0_1920,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_1921,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1388]) ).
cnf(c_0_1922,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1389]) ).
cnf(c_0_1923,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_1924,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_1925,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_1926,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1393]) ).
cnf(c_0_1927,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1394]) ).
cnf(c_0_1928,plain,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1395]) ).
cnf(c_0_1929,plain,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1396]) ).
cnf(c_0_1930,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1397]) ).
cnf(c_0_1931,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_1398]) ).
cnf(c_0_1932,plain,
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X2,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_1933,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1400]) ).
cnf(c_0_1934,plain,
( hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3)
| ~ class_HOL_Ominus(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1401]) ).
cnf(c_0_1935,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1402]) ).
cnf(c_0_1936,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1403]) ).
cnf(c_0_1937,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_1938,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_1939,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X2),c_SetInterval_Oord__class_OlessThan(X3,X2),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_1940,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_1941,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_1942,plain,
c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_1943,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != hAPP(c_Set_Oimage(X4,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_1944,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(X3,X2,X4),X1) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_1945,plain,
( hBOOL(c_in(X3,X4,X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(c_Set_Oinsert(X5),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_1946,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_1947,plain,
c_Fun_Oinj__on(c_COMBI(X1),X2,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_1948,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_1949,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_1950,plain,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_1951,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_1952,plain,
( hBOOL(hAPP(hAPP(X1,X2),X2))
| hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_1953,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_1954,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_1955,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_1956,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_1957,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_1958,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_1959,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_1960,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_1961,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_1962,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_1429]) ).
cnf(c_0_1963,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_1430]) ).
cnf(c_0_1964,plain,
( hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),X5)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1431]) ).
cnf(c_0_1965,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_1432]) ).
cnf(c_0_1966,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1433]) ).
cnf(c_0_1967,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_1968,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_1435]) ).
cnf(c_0_1969,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_1436]) ).
cnf(c_0_1970,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_1437]) ).
cnf(c_0_1971,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1438]) ).
cnf(c_0_1972,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1439]) ).
cnf(c_0_1973,plain,
( c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_1974,plain,
( c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_1975,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1442]) ).
cnf(c_0_1976,plain,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_1977,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_1444]) ).
cnf(c_0_1978,plain,
( c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X3),c_SetInterval_Oord__class_OlessThan(X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_1979,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1446]) ).
cnf(c_0_1980,plain,
( ~ c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_1981,plain,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1448]) ).
cnf(c_0_1982,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_1983,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_1984,plain,
c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_1985,plain,
c_The(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_1986,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1453]) ).
cnf(c_0_1987,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1454]) ).
cnf(c_0_1988,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_1989,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_1990,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_1991,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_1992,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,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_1459]) ).
cnf(c_0_1993,plain,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_1994,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_1995,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_1996,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_1997,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_1998,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_1999,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_1466]) ).
cnf(c_0_2000,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_1467]) ).
cnf(c_0_2001,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2002,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2003,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2004,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2005,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_2006,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_1473]) ).
cnf(c_0_2007,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2008,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2009,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2010,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2011,plain,
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(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2012,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2013,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2014,plain,
c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1481]) ).
cnf(c_0_2015,plain,
c_Finite__Set_Ofold1(X1,X2,X3) = c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1482]) ).
cnf(c_0_2016,plain,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1483]) ).
cnf(c_0_2017,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1484]) ).
cnf(c_0_2018,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1485]) ).
cnf(c_0_2019,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2020,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2021,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1488]) ).
cnf(c_0_2022,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2023,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2024,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1491]) ).
cnf(c_0_2025,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2026,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2027,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2028,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1495]) ).
cnf(c_0_2029,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1496]) ).
cnf(c_0_2030,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_1497]) ).
cnf(c_0_2031,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_1498]) ).
cnf(c_0_2032,plain,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2033,plain,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2034,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2035,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2036,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X1) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2037,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2038,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2039,plain,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2040,plain,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2041,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1508]) ).
cnf(c_0_2042,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2043,plain,
c_Collect(c_fequal(X1,X2),X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2044,plain,
( c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1511]) ).
cnf(c_0_2045,plain,
( c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2046,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2047,plain,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2048,plain,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1515]) ).
cnf(c_0_2049,plain,
( X1 = X3
| ~ hBOOL(hAPP(c_fequal(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2050,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2051,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1518]) ).
cnf(c_0_2052,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1519]) ).
cnf(c_0_2053,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1520]) ).
cnf(c_0_2054,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1521]) ).
cnf(c_0_2055,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2056,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2057,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1524]) ).
cnf(c_0_2058,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1525]) ).
cnf(c_0_2059,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2060,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2061,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1528]) ).
cnf(c_0_2062,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1529]) ).
cnf(c_0_2063,plain,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
inference(split_conjunct,[status(thm)],[c_0_1530]) ).
cnf(c_0_2064,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_1531]) ).
cnf(c_0_2065,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[c_0_1532]) ).
cnf(c_0_2066,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2067,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2068,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2069,plain,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2070,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1537]) ).
cnf(c_0_2071,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2072,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2073,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1540]) ).
cnf(c_0_2074,plain,
c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1541]) ).
cnf(c_0_2075,plain,
hBOOL(hAPP(c_fequal(X1,X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2076,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2077,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2078,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1545]) ).
cnf(c_0_2079,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1546]) ).
cnf(c_0_2080,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1547]) ).
cnf(c_0_2081,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1548]) ).
cnf(c_0_2082,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1549]) ).
cnf(c_0_2083,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1550]) ).
cnf(c_0_2084,plain,
( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1551]) ).
cnf(c_0_2085,plain,
( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1552]) ).
cnf(c_0_2086,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2087,plain,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2088,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2089,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2090,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2091,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2092,plain,
( X1 = X2
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2093,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1560]) ).
cnf(c_0_2094,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2095,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2096,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1563]) ).
cnf(c_0_2097,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_1564]) ).
cnf(c_0_2098,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2099,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2100,plain,
c_The(c_fequal(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1567]) ).
cnf(c_0_2101,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1568]) ).
cnf(c_0_2102,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2103,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2104,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2105,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2106,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2107,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2108,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1575]) ).
cnf(c_0_2109,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1576]) ).
cnf(c_0_2110,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1577]) ).
cnf(c_0_2111,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1578]) ).
cnf(c_0_2112,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2113,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[c_0_1580]) ).
cnf(c_0_2114,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2115,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2116,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1583]) ).
cnf(c_0_2117,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1584]) ).
cnf(c_0_2118,plain,
hAPP(c_COMBI(t_a),v_P) = v_P,
inference(split_conjunct,[status(thm)],[c_0_1585]) ).
cnf(c_0_2119,plain,
c_Collect(X1,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2120,plain,
class_HOL_Oord(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2121,plain,
class_HOL_Ominus(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1588]) ).
cnf(c_0_2122,plain,
class_Orderings_Obot(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1589]) ).
cnf(c_0_2123,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1590]) ).
cnf(c_0_2124,plain,
class_Lattices_Olattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1591]) ).
cnf(c_0_2125,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1592]) ).
cnf(c_0_2126,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1593]) ).
cnf(c_0_2127,plain,
class_Lattices_Obounded__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2128,plain,
class_Lattices_Odistrib__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2129,plain,
class_Lattices_Olower__semilattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2130,plain,
class_Lattices_Oupper__semilattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2131,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2132,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1599,
[final] ).
cnf(c_0_2133,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1600,
[final] ).
cnf(c_0_2134,plain,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
c_0_1601,
[final] ).
cnf(c_0_2135,plain,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
c_0_1602,
[final] ).
cnf(c_0_2136,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1603,
[final] ).
cnf(c_0_2137,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1604,
[final] ).
cnf(c_0_2138,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1605,
[final] ).
cnf(c_0_2139,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1606,
[final] ).
cnf(c_0_2140,plain,
( hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1607,
[final] ).
cnf(c_0_2141,plain,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_1608,
[final] ).
cnf(c_0_2142,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OCond(X4,X5,X7),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X7,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
c_0_1609,
[final] ).
cnf(c_0_2143,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OWhile(X4,X5),c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
c_0_1610,
[final] ).
cnf(c_0_2144,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
c_0_1611,
[final] ).
cnf(c_0_2145,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
c_0_1612,
[final] ).
cnf(c_0_2146,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
c_0_1613,
[final] ).
cnf(c_0_2147,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
c_0_1614,
[final] ).
cnf(c_0_2148,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
c_0_1615,
[final] ).
cnf(c_0_2149,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),
c_0_1616,
[final] ).
cnf(c_0_2150,plain,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
c_0_1617,
[final] ).
cnf(c_0_2151,plain,
c_COMBS(X1,X2,X3,X4,X5,X6) = hAPP(hAPP(X1,X3),hAPP(X2,X3)),
c_0_1618,
[final] ).
cnf(c_0_2152,plain,
c_COMBS(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
c_0_1619,
[final] ).
cnf(c_0_2153,plain,
c_COMBC(X1,X2,X3,X4,X5,X6) = hAPP(hAPP(X1,X3),X2),
c_0_1620,
[final] ).
cnf(c_0_2154,plain,
c_COMBC(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),v_Q),
c_0_1621,
[final] ).
cnf(c_0_2155,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_1622,
[final] ).
cnf(c_0_2156,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_1623,
[final] ).
cnf(c_0_2157,plain,
hAPP(c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4),X6) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(c_Set_Oimage(X2,X5,X3),X6)),
c_0_1624,
[final] ).
cnf(c_0_2158,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X5,X2),X6)) = hAPP(c_Set_Oimage(c_COMBB(X1,X4,X2,X3,X5),X5,X3),X6),
c_0_1625,
[final] ).
cnf(c_0_2159,plain,
hAPP(c_Set_Ovimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4),X6) = hAPP(c_Set_Ovimage(X2,X5,X3),hAPP(c_Set_Ovimage(X1,X3,X4),X6)),
c_0_1626,
[final] ).
cnf(c_0_2160,plain,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5)
| ~ hBOOL(c_in(hAPP(X1,X3),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X5)) ),
c_0_1627,
[final] ).
cnf(c_0_2161,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a))) ),
c_0_1628,
[final] ).
cnf(c_0_2162,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a))) ),
c_0_1629,
[final] ).
cnf(c_0_2163,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
c_0_1630,
[final] ).
cnf(c_0_2164,plain,
( c_Fun_Oinj__on(X1,hAPP(c_Set_Oimage(X2,X5,X3),X6),X3,X4)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) ),
c_0_1631,
[final] ).
cnf(c_0_2165,plain,
( c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5)
| ~ c_Fun_Oinj__on(X1,X4,X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1632,
[final] ).
cnf(c_0_2166,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
c_0_1633,
[final] ).
cnf(c_0_2167,plain,
( c_Fun_Oinj__on(c_Fun_Ocomp(X5,X1,X4,X6,X3),X2,X3,X6)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X1,X3,X4),X2),X4,X6) ),
c_0_1634,
[final] ).
cnf(c_0_2168,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
c_0_1635,
[final] ).
cnf(c_0_2169,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
c_0_1636,
[final] ).
cnf(c_0_2170,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))),
c_0_1637,
[final] ).
cnf(c_0_2171,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))),
c_0_1638,
[final] ).
cnf(c_0_2172,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool))),
c_0_1639,
[final] ).
cnf(c_0_2173,plain,
( hBOOL(c_in(hAPP(X1,X5),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4))
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_1640,
[final] ).
cnf(c_0_2174,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Ovimage(X1,X2,X3),X5,tc_fun(X3,tc_bool),tc_fun(X2,tc_bool),X6),X6,tc_fun(X2,tc_bool)) = hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X3,tc_bool))),
c_0_1641,
[final] ).
cnf(c_0_2175,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Oimage(X1,X2,X3),X5,tc_fun(X2,tc_bool),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X2,tc_bool))),
c_0_1642,
[final] ).
cnf(c_0_2176,plain,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBB(hAPP(c_Set_Oinsert(X4),X5),X6,tc_fun(X4,tc_bool),tc_fun(X4,tc_bool),X3),X3,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X6,X3,tc_fun(X4,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1643,
[final] ).
cnf(c_0_2177,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
c_0_1644,
[final] ).
cnf(c_0_2178,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
c_0_1645,
[final] ).
cnf(c_0_2179,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,X3,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(X5,X1,X3,tc_fun(X6,tc_bool),X2),X2,tc_fun(X6,tc_bool)),
c_0_1646,
[final] ).
cnf(c_0_2180,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(X2,X3,X4,tc_fun(X5,tc_bool),X6),X6,tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X3,X6,X4),X1),X2,X4,tc_fun(X5,tc_bool)),
c_0_1647,
[final] ).
cnf(c_0_2181,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_1648,
[final] ).
cnf(c_0_2182,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_1649,
[final] ).
cnf(c_0_2183,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
c_0_1650,
[final] ).
cnf(c_0_2184,plain,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
c_0_1651,
[final] ).
cnf(c_0_2185,plain,
c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X4),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),tc_fun(X3,tc_bool)),
c_0_1652,
[final] ).
cnf(c_0_2186,plain,
( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X1,X4,X2,tc_fun(X3,X3),X5),X5,X3)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
c_0_1653,
[final] ).
cnf(c_0_2187,plain,
hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3) = hAPP(X1,hAPP(X2,X3)),
c_0_1654,
[final] ).
cnf(c_0_2188,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
c_0_1655,
[final] ).
cnf(c_0_2189,plain,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
c_0_1656,
[final] ).
cnf(c_0_2190,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
c_0_1657,
[final] ).
cnf(c_0_2191,plain,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
c_0_1658,
[final] ).
cnf(c_0_2192,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSKIP,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
c_0_1659,
[final] ).
cnf(c_0_2193,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X1,tc_fun(X5,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,X1,tc_fun(X5,tc_bool)),
c_0_1660,
[final] ).
cnf(c_0_2194,plain,
( hAPP(X2,X1) = X5
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)) ),
c_0_1661,
[final] ).
cnf(c_0_2195,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)) = hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)),
c_0_1662,
[final] ).
cnf(c_0_2196,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_Set_Oimage(X1,X3,X4),X5)),hAPP(c_Set_Oimage(X1,X3,X4),X6)) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X5),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
c_0_1663,
[final] ).
cnf(c_0_2197,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1)) ),
c_0_1664,
[final] ).
cnf(c_0_2198,plain,
hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)),
c_0_1665,
[final] ).
cnf(c_0_2199,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))),tc_fun(X3,tc_bool)),
c_0_1666,
[final] ).
cnf(c_0_2200,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4),
c_0_1667,
[final] ).
cnf(c_0_2201,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4),
c_0_1668,
[final] ).
cnf(c_0_2202,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4)) ),
c_0_1669,
[final] ).
cnf(c_0_2203,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
c_0_1670,
[final] ).
cnf(c_0_2204,plain,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
c_0_1671,
[final] ).
cnf(c_0_2205,plain,
( c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X3,X4),X5),hAPP(c_Set_Oimage(X1,X3,X4),X6),tc_fun(X4,tc_bool)) = hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
c_0_1672,
[final] ).
cnf(c_0_2206,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X1,tc_bool))),X4) = X4,
c_0_1673,
[final] ).
cnf(c_0_2207,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
c_0_1674,
[final] ).
cnf(c_0_2208,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
c_0_1675,
[final] ).
cnf(c_0_2209,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
c_0_1676,
[final] ).
cnf(c_0_2210,plain,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
c_0_1677,
[final] ).
cnf(c_0_2211,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
c_0_1678,
[final] ).
cnf(c_0_2212,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
c_0_1679,
[final] ).
cnf(c_0_2213,plain,
( c_Fun_Ocomp(hAPP(X1,X4),hAPP(X1,X4),X3,X3,X3) = hAPP(X1,X4)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
c_0_1680,
[final] ).
cnf(c_0_2214,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
c_0_1681,
[final] ).
cnf(c_0_2215,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1))),
c_0_1682,
[final] ).
cnf(c_0_2216,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
c_0_1683,
[final] ).
cnf(c_0_2217,plain,
( hBOOL(c_in(X1,X3,X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
c_0_1684,
[final] ).
cnf(c_0_2218,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)) = hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5)),
c_0_1685,
[final] ).
cnf(c_0_2219,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)) = hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5)),
c_0_1686,
[final] ).
cnf(c_0_2220,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)) = hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5)),
c_0_1687,
[final] ).
cnf(c_0_2221,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1688,
[final] ).
cnf(c_0_2222,plain,
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
c_0_1689,
[final] ).
cnf(c_0_2223,plain,
( c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
c_0_1690,
[final] ).
cnf(c_0_2224,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X2),X4,X5)
| hAPP(c_Set_Oimage(X3,X4,X5),X1) != hAPP(c_Set_Oimage(X3,X4,X5),X2) ),
c_0_1691,
[final] ).
cnf(c_0_2225,plain,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
c_0_1692,
[final] ).
cnf(c_0_2226,plain,
( hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
c_0_1693,
[final] ).
cnf(c_0_2227,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1694,
[final] ).
cnf(c_0_2228,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
c_0_1695,
[final] ).
cnf(c_0_2229,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
c_0_1696,
[final] ).
cnf(c_0_2230,plain,
( c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
c_0_1697,
[final] ).
cnf(c_0_2231,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),hAPP(X4,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
c_0_1698,
[final] ).
cnf(c_0_2232,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
c_0_1699,
[final] ).
cnf(c_0_2233,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4),
c_0_1700,
[final] ).
cnf(c_0_2234,plain,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1701,
[final] ).
cnf(c_0_2235,plain,
( hBOOL(c_in(hAPP(X2,X1),X5,X4))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3)) ),
c_0_1702,
[final] ).
cnf(c_0_2236,plain,
( hBOOL(c_in(hAPP(X2,X1),X5,X4))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3)) ),
c_0_1703,
[final] ).
cnf(c_0_2237,plain,
( c_Fun_Oinj__on(X1,X3,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
c_0_1704,
[final] ).
cnf(c_0_2238,plain,
( c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
c_0_1705,
[final] ).
cnf(c_0_2239,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_1706,
[final] ).
cnf(c_0_2240,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)),X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_1707,
[final] ).
cnf(c_0_2241,plain,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X3)),
c_0_1708,
[final] ).
cnf(c_0_2242,plain,
( hAPP(c_Set_Oimage(X3,X2,X2),X1) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(hAPP(c_Set_Oimage(X3,X2,X2),X1),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
c_0_1709,
[final] ).
cnf(c_0_2243,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
c_0_1710,
[final] ).
cnf(c_0_2244,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
c_0_1711,
[final] ).
cnf(c_0_2245,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
c_0_1712,
[final] ).
cnf(c_0_2246,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
c_0_1713,
[final] ).
cnf(c_0_2247,plain,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_1714,
[final] ).
cnf(c_0_2248,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_1715,
[final] ).
cnf(c_0_2249,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_1716,
[final] ).
cnf(c_0_2250,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)),
c_0_1717,
[final] ).
cnf(c_0_2251,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)),
c_0_1718,
[final] ).
cnf(c_0_2252,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
c_0_1719,
[final] ).
cnf(c_0_2253,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
c_0_1720,
[final] ).
cnf(c_0_2254,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3)) ),
c_0_1721,
[final] ).
cnf(c_0_2255,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),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_1722,
[final] ).
cnf(c_0_2256,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),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_1723,
[final] ).
cnf(c_0_2257,plain,
( hBOOL(hAPP(X4,hAPP(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5)) ),
c_0_1724,
[final] ).
cnf(c_0_2258,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1725,
[final] ).
cnf(c_0_2259,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
c_0_1726,
[final] ).
cnf(c_0_2260,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
c_0_1727,
[final] ).
cnf(c_0_2261,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1728,
[final] ).
cnf(c_0_2262,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1729,
[final] ).
cnf(c_0_2263,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
c_0_1730,
[final] ).
cnf(c_0_2264,plain,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
c_0_1731,
[final] ).
cnf(c_0_2265,plain,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
c_0_1732,
[final] ).
cnf(c_0_2266,plain,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
c_0_1733,
[final] ).
cnf(c_0_2267,plain,
( hBOOL(c_in(hAPP(X1,X6),X5,X3))
| ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X6,X4,X2)) ),
c_0_1734,
[final] ).
cnf(c_0_2268,plain,
c_Hoare__Mirabelle_Otriple_Otriple__case(X1,c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),X5,X6) = hAPP(hAPP(hAPP(X1,X2),X3),X4),
c_0_1735,
[final] ).
cnf(c_0_2269,plain,
c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),X5,X6) = hAPP(hAPP(hAPP(X1,X2),X3),X4),
c_0_1736,
[final] ).
cnf(c_0_2270,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool)) = hAPP(c_Set_Ovimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool))),
c_0_1737,
[final] ).
cnf(c_0_2271,plain,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
c_0_1738,
[final] ).
cnf(c_0_2272,plain,
( X1 = X3
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)) ),
c_0_1739,
[final] ).
cnf(c_0_2273,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),
c_0_1740,
[final] ).
cnf(c_0_2274,plain,
( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1741,
[final] ).
cnf(c_0_2275,plain,
( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1742,
[final] ).
cnf(c_0_2276,plain,
( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
| ~ hBOOL(c_in(X2,X5,X3)) ),
c_0_1743,
[final] ).
cnf(c_0_2277,plain,
( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
| ~ hBOOL(c_in(X2,X5,X3)) ),
c_0_1744,
[final] ).
cnf(c_0_2278,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1745,
[final] ).
cnf(c_0_2279,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_1746,
[final] ).
cnf(c_0_2280,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_1747,
[final] ).
cnf(c_0_2281,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_1748,
[final] ).
cnf(c_0_2282,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_1749,
[final] ).
cnf(c_0_2283,plain,
( c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
| ~ c_Fun_Oinj__on(X1,X4,X2,X3) ),
c_0_1750,
[final] ).
cnf(c_0_2284,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
c_0_1751,
[final] ).
cnf(c_0_2285,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
c_0_1752,
[final] ).
cnf(c_0_2286,plain,
( c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5) ),
c_0_1753,
[final] ).
cnf(c_0_2287,plain,
c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X4,tc_fun(X3,tc_bool)),
c_0_1754,
[final] ).
cnf(c_0_2288,plain,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1755,
[final] ).
cnf(c_0_2289,plain,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
c_0_1756,
[final] ).
cnf(c_0_2290,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
c_0_1757,
[final] ).
cnf(c_0_2291,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = X2,
c_0_1758,
[final] ).
cnf(c_0_2292,plain,
( X1 = X4
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,X2,X3))
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| hAPP(X5,X1) != hAPP(X5,X4) ),
c_0_1759,
[final] ).
cnf(c_0_2293,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_1760,
[final] ).
cnf(c_0_2294,plain,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
c_0_1761,
[final] ).
cnf(c_0_2295,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,X2,X3))
| ~ hBOOL(c_in(X6,X2,X3))
| hAPP(X1,X5) != hAPP(X1,X6) ),
c_0_1762,
[final] ).
cnf(c_0_2296,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
c_0_1763,
[final] ).
cnf(c_0_2297,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
c_0_1764,
[final] ).
cnf(c_0_2298,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
c_0_1765,
[final] ).
cnf(c_0_2299,plain,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X2,X2),X1),tc_fun(X2,tc_bool)) ),
c_0_1766,
[final] ).
cnf(c_0_2300,plain,
( hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
c_0_1767,
[final] ).
cnf(c_0_2301,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_1768,
[final] ).
cnf(c_0_2302,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1769,
[final] ).
cnf(c_0_2303,plain,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
c_0_1770,
[final] ).
cnf(c_0_2304,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2) ),
c_0_1771,
[final] ).
cnf(c_0_2305,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
c_0_1772,
[final] ).
cnf(c_0_2306,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_1773,
[final] ).
cnf(c_0_2307,plain,
c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
c_0_1774,
[final] ).
cnf(c_0_2308,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)),
c_0_1775,
[final] ).
cnf(c_0_2309,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1776,
[final] ).
cnf(c_0_2310,plain,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1777,
[final] ).
cnf(c_0_2311,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_1778,
[final] ).
cnf(c_0_2312,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
c_0_1779,
[final] ).
cnf(c_0_2313,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1780,
[final] ).
cnf(c_0_2314,plain,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1781,
[final] ).
cnf(c_0_2315,plain,
( c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
c_0_1782,
[final] ).
cnf(c_0_2316,plain,
( c_lessequals(hAPP(c_Set_Oimage(X4,X3,X5),X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1783,
[final] ).
cnf(c_0_2317,plain,
( c_lessequals(hAPP(c_Set_Ovimage(X4,X5,X3),X1),hAPP(c_Set_Ovimage(X4,X5,X3),X2),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1784,
[final] ).
cnf(c_0_2318,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
c_0_1785,
[final] ).
cnf(c_0_2319,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
c_0_1786,
[final] ).
cnf(c_0_2320,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1787,
[final] ).
cnf(c_0_2321,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1788,
[final] ).
cnf(c_0_2322,plain,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) ),
c_0_1789,
[final] ).
cnf(c_0_2323,plain,
( c_lessequals(X2,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) ),
c_0_1790,
[final] ).
cnf(c_0_2324,plain,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
c_0_1791,
[final] ).
cnf(c_0_2325,plain,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
c_0_1792,
[final] ).
cnf(c_0_2326,plain,
( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X1)),hAPP(c_Set_Oimage(X5,X3,X4),X2)) = hAPP(c_Set_Oimage(X5,X3,X4),X2)
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1793,
[final] ).
cnf(c_0_2327,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
c_0_1794,
[final] ).
cnf(c_0_2328,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1795,
[final] ).
cnf(c_0_2329,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,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_1796,
[final] ).
cnf(c_0_2330,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1797,
[final] ).
cnf(c_0_2331,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1798,
[final] ).
cnf(c_0_2332,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X4,X3,X1)) ),
c_0_1799,
[final] ).
cnf(c_0_2333,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),
c_0_1800,
[final] ).
cnf(c_0_2334,plain,
( hAPP(c_Set_Oimage(c_COMBK(X4,X5,X3),X3,X5),X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1801,
[final] ).
cnf(c_0_2335,plain,
( X1 = X3
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2)) ),
c_0_1802,
[final] ).
cnf(c_0_2336,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
c_0_1803,
[final] ).
cnf(c_0_2337,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),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)) ),
c_0_1804,
[final] ).
cnf(c_0_2338,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),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)) ),
c_0_1805,
[final] ).
cnf(c_0_2339,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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_1806,
[final] ).
cnf(c_0_2340,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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_1807,
[final] ).
cnf(c_0_2341,plain,
( c_lessequals(X4,X1,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1808,
[final] ).
cnf(c_0_2342,plain,
( c_lessequals(X2,X5,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1809,
[final] ).
cnf(c_0_2343,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) ),
c_0_1810,
[final] ).
cnf(c_0_2344,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
c_0_1811,
[final] ).
cnf(c_0_2345,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1812,
[final] ).
cnf(c_0_2346,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1813,
[final] ).
cnf(c_0_2347,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
c_0_1814,
[final] ).
cnf(c_0_2348,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
c_0_1815,
[final] ).
cnf(c_0_2349,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
c_0_1816,
[final] ).
cnf(c_0_2350,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
c_0_1817,
[final] ).
cnf(c_0_2351,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X1,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
c_0_1818,
[final] ).
cnf(c_0_2352,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1819,
[final] ).
cnf(c_0_2353,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,hAPP(c_Set_Oimage(X4,X2,X5),X1),tc_fun(X5,tc_bool)) ),
c_0_1820,
[final] ).
cnf(c_0_2354,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)),
c_0_1821,
[final] ).
cnf(c_0_2355,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1822,
[final] ).
cnf(c_0_2356,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1823,
[final] ).
cnf(c_0_2357,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
c_0_1824,
[final] ).
cnf(c_0_2358,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4) ),
c_0_1825,
[final] ).
cnf(c_0_2359,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)) = X2 ),
c_0_1826,
[final] ).
cnf(c_0_2360,plain,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))) ),
c_0_1827,
[final] ).
cnf(c_0_2361,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1828,
[final] ).
cnf(c_0_2362,plain,
( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1829,
[final] ).
cnf(c_0_2363,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X4,X3,X2))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1830,
[final] ).
cnf(c_0_2364,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
c_0_1831,
[final] ).
cnf(c_0_2365,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
c_0_1832,
[final] ).
cnf(c_0_2366,plain,
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1833,
[final] ).
cnf(c_0_2367,plain,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1834,
[final] ).
cnf(c_0_2368,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(c_Set_Ovimage(c_COMBK(X1,X3,X4),X4,X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_1835,
[final] ).
cnf(c_0_2369,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool)) ),
c_0_1836,
[final] ).
cnf(c_0_2370,plain,
( hBOOL(c_in(X3,X1,X2))
| c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
c_0_1837,
[final] ).
cnf(c_0_2371,plain,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1838,
[final] ).
cnf(c_0_2372,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(c_COMBK(X3,X4,X2),X2,X4),X1) = hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) ),
c_0_1839,
[final] ).
cnf(c_0_2373,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
c_0_1840,
[final] ).
cnf(c_0_2374,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1841,
[final] ).
cnf(c_0_2375,plain,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
c_0_1842,
[final] ).
cnf(c_0_2376,plain,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
c_0_1843,
[final] ).
cnf(c_0_2377,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ class_Orderings_Oorder(X1) ),
c_0_1844,
[final] ).
cnf(c_0_2378,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1845,
[final] ).
cnf(c_0_2379,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1846,
[final] ).
cnf(c_0_2380,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_1847,
[final] ).
cnf(c_0_2381,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_1848,
[final] ).
cnf(c_0_2382,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1849,
[final] ).
cnf(c_0_2383,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1850,
[final] ).
cnf(c_0_2384,plain,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1851,
[final] ).
cnf(c_0_2385,plain,
hAPP(c_Set_Oimage(c_COMBK(X1,X2,X3),X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_1852,
[final] ).
cnf(c_0_2386,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1853,
[final] ).
cnf(c_0_2387,plain,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1854,
[final] ).
cnf(c_0_2388,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1855,
[final] ).
cnf(c_0_2389,plain,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
c_0_1856,
[final] ).
cnf(c_0_2390,plain,
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1857,
[final] ).
cnf(c_0_2391,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
c_0_1858,
[final] ).
cnf(c_0_2392,plain,
( hBOOL(c_in(X2,X4,X1))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) ),
c_0_1859,
[final] ).
cnf(c_0_2393,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
c_0_1860,
[final] ).
cnf(c_0_2394,plain,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| hAPP(hAPP(c_Set_Oinsert(X4),X3),X1) != hAPP(hAPP(c_Set_Oinsert(X4),X3),X2) ),
c_0_1861,
[final] ).
cnf(c_0_2395,plain,
( ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X1)) ),
c_0_1862,
[final] ).
cnf(c_0_2396,plain,
( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1863,
[final] ).
cnf(c_0_2397,plain,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
c_0_1864,
[final] ).
cnf(c_0_2398,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
c_0_1865,
[final] ).
cnf(c_0_2399,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X2,tc_fun(X1,tc_bool)),
c_0_1866,
[final] ).
cnf(c_0_2400,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),tc_fun(X2,tc_bool)),
c_0_1867,
[final] ).
cnf(c_0_2401,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),tc_fun(X2,tc_bool)),
c_0_1868,
[final] ).
cnf(c_0_2402,plain,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) ),
c_0_1869,
[final] ).
cnf(c_0_2403,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1870,
[final] ).
cnf(c_0_2404,plain,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3
| ~ c_Orderings_Olinorder(X4,X5,X6) ),
c_0_1871,
[final] ).
cnf(c_0_2405,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1872,
[final] ).
cnf(c_0_2406,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1873,
[final] ).
cnf(c_0_2407,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1874,
[final] ).
cnf(c_0_2408,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
c_0_1875,
[final] ).
cnf(c_0_2409,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
c_0_1876,
[final] ).
cnf(c_0_2410,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
c_0_1877,
[final] ).
cnf(c_0_2411,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
c_0_1878,
[final] ).
cnf(c_0_2412,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_1879,
[final] ).
cnf(c_0_2413,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_1880,
[final] ).
cnf(c_0_2414,plain,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
c_0_1881,
[final] ).
cnf(c_0_2415,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1882,
[final] ).
cnf(c_0_2416,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1883,
[final] ).
cnf(c_0_2417,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1884,
[final] ).
cnf(c_0_2418,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1885,
[final] ).
cnf(c_0_2419,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1886,
[final] ).
cnf(c_0_2420,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1887,
[final] ).
cnf(c_0_2421,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
c_0_1888,
[final] ).
cnf(c_0_2422,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_1889,
[final] ).
cnf(c_0_2423,plain,
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
c_0_1890,
[final] ).
cnf(c_0_2424,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_1891,
[final] ).
cnf(c_0_2425,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_1892,
[final] ).
cnf(c_0_2426,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1893,
[final] ).
cnf(c_0_2427,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1894,
[final] ).
cnf(c_0_2428,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_1895,
[final] ).
cnf(c_0_2429,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1896,
[final] ).
cnf(c_0_2430,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1897,
[final] ).
cnf(c_0_2431,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1898,
[final] ).
cnf(c_0_2432,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_1899,
[final] ).
cnf(c_0_2433,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_1900,
[final] ).
cnf(c_0_2434,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1901,
[final] ).
cnf(c_0_2435,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
c_0_1902,
[final] ).
cnf(c_0_2436,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
c_0_1903,
[final] ).
cnf(c_0_2437,plain,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
c_0_1904,
[final] ).
cnf(c_0_2438,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1905,
[final] ).
cnf(c_0_2439,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1906,
[final] ).
cnf(c_0_2440,plain,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1907,
[final] ).
cnf(c_0_2441,plain,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1908,
[final] ).
cnf(c_0_2442,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1909,
[final] ).
cnf(c_0_2443,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1910,
[final] ).
cnf(c_0_2444,plain,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1911,
[final] ).
cnf(c_0_2445,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1912,
[final] ).
cnf(c_0_2446,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
c_0_1913,
[final] ).
cnf(c_0_2447,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
c_0_1914,
[final] ).
cnf(c_0_2448,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) != X2 ),
c_0_1915,
[final] ).
cnf(c_0_2449,plain,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1916,
[final] ).
cnf(c_0_2450,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_1917,
[final] ).
cnf(c_0_2451,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_1918,
[final] ).
cnf(c_0_2452,plain,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
c_0_1919,
[final] ).
cnf(c_0_2453,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
c_0_1920,
[final] ).
cnf(c_0_2454,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1921,
[final] ).
cnf(c_0_2455,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_1922,
[final] ).
cnf(c_0_2456,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
c_0_1923,
[final] ).
cnf(c_0_2457,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
c_0_1924,
[final] ).
cnf(c_0_2458,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1925,
[final] ).
cnf(c_0_2459,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1926,
[final] ).
cnf(c_0_2460,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
c_0_1927,
[final] ).
cnf(c_0_2461,plain,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1928,
[final] ).
cnf(c_0_2462,plain,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1929,
[final] ).
cnf(c_0_2463,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1930,
[final] ).
cnf(c_0_2464,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_1931,
[final] ).
cnf(c_0_2465,plain,
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X2,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1932,
[final] ).
cnf(c_0_2466,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_1933,
[final] ).
cnf(c_0_2467,plain,
( c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_HOL_Ominus(X3) ),
c_0_1934,
[final] ).
cnf(c_0_2468,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1935,
[final] ).
cnf(c_0_2469,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1936,
[final] ).
cnf(c_0_2470,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1937,
[final] ).
cnf(c_0_2471,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1938,
[final] ).
cnf(c_0_2472,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X2),c_SetInterval_Oord__class_OlessThan(X3,X2),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
c_0_1939,
[final] ).
cnf(c_0_2473,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1940,
[final] ).
cnf(c_0_2474,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1941,
[final] ).
cnf(c_0_2475,plain,
c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3,
c_0_1942,
[final] ).
cnf(c_0_2476,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(X4,X2,X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1943,
[final] ).
cnf(c_0_2477,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(X3,X2,X4),X1) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_1944,
[final] ).
cnf(c_0_2478,plain,
( hBOOL(c_in(X3,X4,X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(c_Set_Oinsert(X5),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
c_0_1945,
[final] ).
cnf(c_0_2479,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_1946,
[final] ).
cnf(c_0_2480,plain,
c_Fun_Oinj__on(c_COMBI(X1),X2,X1,X1),
c_0_1947,
[final] ).
cnf(c_0_2481,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1948,
[final] ).
cnf(c_0_2482,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1949,
[final] ).
cnf(c_0_2483,plain,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1950,
[final] ).
cnf(c_0_2484,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1951,
[final] ).
cnf(c_0_2485,plain,
( hBOOL(hAPP(hAPP(X1,X2),X2))
| hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
c_0_1952,
[final] ).
cnf(c_0_2486,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1953,
[final] ).
cnf(c_0_2487,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1954,
[final] ).
cnf(c_0_2488,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1955,
[final] ).
cnf(c_0_2489,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_1956,
[final] ).
cnf(c_0_2490,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1957,
[final] ).
cnf(c_0_2491,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1958,
[final] ).
cnf(c_0_2492,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1959,
[final] ).
cnf(c_0_2493,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1960,
[final] ).
cnf(c_0_2494,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
c_0_1961,
[final] ).
cnf(c_0_2495,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1962,
[final] ).
cnf(c_0_2496,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1963,
[final] ).
cnf(c_0_2497,plain,
( hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),X5)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
c_0_1964,
[final] ).
cnf(c_0_2498,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_1965,
[final] ).
cnf(c_0_2499,plain,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_1966,
[final] ).
cnf(c_0_2500,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
c_0_1967,
[final] ).
cnf(c_0_2501,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1968,
[final] ).
cnf(c_0_2502,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1969,
[final] ).
cnf(c_0_2503,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_1970,
[final] ).
cnf(c_0_2504,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
c_0_1971,
[final] ).
cnf(c_0_2505,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1972,
[final] ).
cnf(c_0_2506,plain,
( c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_1973,
[final] ).
cnf(c_0_2507,plain,
( c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_1974,
[final] ).
cnf(c_0_2508,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1975,
[final] ).
cnf(c_0_2509,plain,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1976,
[final] ).
cnf(c_0_2510,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_1977,
[final] ).
cnf(c_0_2511,plain,
( c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X3),c_SetInterval_Oord__class_OlessThan(X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1978,
[final] ).
cnf(c_0_2512,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_1979,
[final] ).
cnf(c_0_2513,plain,
( ~ c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_1980,
[final] ).
cnf(c_0_2514,plain,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1981,
[final] ).
cnf(c_0_2515,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1982,
[final] ).
cnf(c_0_2516,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1983,
[final] ).
cnf(c_0_2517,plain,
c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
c_0_1984,
[final] ).
cnf(c_0_2518,plain,
c_The(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
c_0_1985,
[final] ).
cnf(c_0_2519,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4) ),
c_0_1986,
[final] ).
cnf(c_0_2520,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
c_0_1987,
[final] ).
cnf(c_0_2521,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_1988,
[final] ).
cnf(c_0_2522,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
c_0_1989,
[final] ).
cnf(c_0_2523,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
c_0_1990,
[final] ).
cnf(c_0_2524,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_1991,
[final] ).
cnf(c_0_2525,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1992,
[final] ).
cnf(c_0_2526,plain,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1993,
[final] ).
cnf(c_0_2527,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_1994,
[final] ).
cnf(c_0_2528,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
c_0_1995,
[final] ).
cnf(c_0_2529,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
c_0_1996,
[final] ).
cnf(c_0_2530,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1997,
[final] ).
cnf(c_0_2531,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1998,
[final] ).
cnf(c_0_2532,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_1999,
[final] ).
cnf(c_0_2533,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_2000,
[final] ).
cnf(c_0_2534,plain,
hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2001,
[final] ).
cnf(c_0_2535,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_2002,
[final] ).
cnf(c_0_2536,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_2003,
[final] ).
cnf(c_0_2537,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) ),
c_0_2004,
[final] ).
cnf(c_0_2538,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
c_0_2005,
[final] ).
cnf(c_0_2539,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
c_0_2006,
[final] ).
cnf(c_0_2540,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_2007,
[final] ).
cnf(c_0_2541,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2008,
[final] ).
cnf(c_0_2542,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2009,
[final] ).
cnf(c_0_2543,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2010,
[final] ).
cnf(c_0_2544,plain,
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)),
c_0_2011,
[final] ).
cnf(c_0_2545,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_2012,
[final] ).
cnf(c_0_2546,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_2013,
[final] ).
cnf(c_0_2547,plain,
c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),tc_fun(X2,tc_bool)),
c_0_2014,
[final] ).
cnf(c_0_2548,plain,
c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3) = c_Finite__Set_Ofold1(X1,X2,X3),
c_0_2015,
[final] ).
cnf(c_0_2549,plain,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
c_0_2016,
[final] ).
cnf(c_0_2550,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
c_0_2017,
[final] ).
cnf(c_0_2551,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
c_0_2018,
[final] ).
cnf(c_0_2552,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ class_Orderings_Oorder(X2) ),
c_0_2019,
[final] ).
cnf(c_0_2553,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_2020,
[final] ).
cnf(c_0_2554,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_2021,
[final] ).
cnf(c_0_2555,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_2022,
[final] ).
cnf(c_0_2556,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_2023,
[final] ).
cnf(c_0_2557,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2)
| ~ class_Lattices_Olattice(X2) ),
c_0_2024,
[final] ).
cnf(c_0_2558,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2)
| ~ class_Lattices_Olattice(X2) ),
c_0_2025,
[final] ).
cnf(c_0_2559,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_2026,
[final] ).
cnf(c_0_2560,plain,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_2027,
[final] ).
cnf(c_0_2561,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
c_0_2028,
[final] ).
cnf(c_0_2562,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
c_0_2029,
[final] ).
cnf(c_0_2563,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_2030,
[final] ).
cnf(c_0_2564,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
c_0_2031,
[final] ).
cnf(c_0_2565,plain,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2032,
[final] ).
cnf(c_0_2566,plain,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2033,
[final] ).
cnf(c_0_2567,plain,
c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x),
c_0_2034,
[final] ).
cnf(c_0_2568,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2035,
[final] ).
cnf(c_0_2569,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X1) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2036,
[final] ).
cnf(c_0_2570,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2037,
[final] ).
cnf(c_0_2571,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2038,
[final] ).
cnf(c_0_2572,plain,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2039,
[final] ).
cnf(c_0_2573,plain,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2040,
[final] ).
cnf(c_0_2574,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
c_0_2041,
[final] ).
cnf(c_0_2575,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
c_0_2042,
[final] ).
cnf(c_0_2576,plain,
hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Collect(c_fequal(X1,X2),X2),
c_0_2043,
[final] ).
cnf(c_0_2577,plain,
( c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
c_0_2044,
[final] ).
cnf(c_0_2578,plain,
( c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2045,
[final] ).
cnf(c_0_2579,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_2046,
[final] ).
cnf(c_0_2580,plain,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
c_0_2047,
[final] ).
cnf(c_0_2581,plain,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
c_0_2048,
[final] ).
cnf(c_0_2582,plain,
( X1 = X3
| ~ hBOOL(hAPP(c_fequal(X1,X2),X3)) ),
c_0_2049,
[final] ).
cnf(c_0_2583,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
c_0_2050,
[final] ).
cnf(c_0_2584,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
c_0_2051,
[final] ).
cnf(c_0_2585,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
c_0_2052,
[final] ).
cnf(c_0_2586,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2053,
[final] ).
cnf(c_0_2587,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2054,
[final] ).
cnf(c_0_2588,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
c_0_2055,
[final] ).
cnf(c_0_2589,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2056,
[final] ).
cnf(c_0_2590,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2057,
[final] ).
cnf(c_0_2591,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
c_0_2058,
[final] ).
cnf(c_0_2592,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
c_0_2059,
[final] ).
cnf(c_0_2593,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_2060,
[final] ).
cnf(c_0_2594,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
c_0_2061,
[final] ).
cnf(c_0_2595,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_2062,
[final] ).
cnf(c_0_2596,plain,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
c_0_2063,
[final] ).
cnf(c_0_2597,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
c_0_2064,
[final] ).
cnf(c_0_2598,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
c_0_2065,
[final] ).
cnf(c_0_2599,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
c_0_2066,
[final] ).
cnf(c_0_2600,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
c_0_2067,
[final] ).
cnf(c_0_2601,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_2068,
[final] ).
cnf(c_0_2602,plain,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_2069,
[final] ).
cnf(c_0_2603,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2070,
[final] ).
cnf(c_0_2604,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2071,
[final] ).
cnf(c_0_2605,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
c_0_2072,
[final] ).
cnf(c_0_2606,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
c_0_2073,
[final] ).
cnf(c_0_2607,plain,
c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool)),
c_0_2074,
[final] ).
cnf(c_0_2608,plain,
hBOOL(hAPP(c_fequal(X1,X2),X1)),
c_0_2075,
[final] ).
cnf(c_0_2609,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
c_0_2076,
[final] ).
cnf(c_0_2610,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
c_0_2077,
[final] ).
cnf(c_0_2611,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_2078,
[final] ).
cnf(c_0_2612,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
c_0_2079,
[final] ).
cnf(c_0_2613,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2080,
[final] ).
cnf(c_0_2614,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2081,
[final] ).
cnf(c_0_2615,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2082,
[final] ).
cnf(c_0_2616,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_2083,
[final] ).
cnf(c_0_2617,plain,
( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_2084,
[final] ).
cnf(c_0_2618,plain,
( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_2085,
[final] ).
cnf(c_0_2619,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2086,
[final] ).
cnf(c_0_2620,plain,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
c_0_2087,
[final] ).
cnf(c_0_2621,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2088,
[final] ).
cnf(c_0_2622,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2089,
[final] ).
cnf(c_0_2623,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_2090,
[final] ).
cnf(c_0_2624,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_2091,
[final] ).
cnf(c_0_2625,plain,
( X1 = X2
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2092,
[final] ).
cnf(c_0_2626,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
c_0_2093,
[final] ).
cnf(c_0_2627,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
c_0_2094,
[final] ).
cnf(c_0_2628,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
c_0_2095,
[final] ).
cnf(c_0_2629,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
c_0_2096,
[final] ).
cnf(c_0_2630,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_2097,
[final] ).
cnf(c_0_2631,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
c_0_2098,
[final] ).
cnf(c_0_2632,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
c_0_2099,
[final] ).
cnf(c_0_2633,plain,
c_The(c_fequal(X1,X2),X2) = X1,
c_0_2100,
[final] ).
cnf(c_0_2634,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_2101,
[final] ).
cnf(c_0_2635,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
c_0_2102,
[final] ).
cnf(c_0_2636,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_2103,
[final] ).
cnf(c_0_2637,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_2104,
[final] ).
cnf(c_0_2638,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2105,
[final] ).
cnf(c_0_2639,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_2106,
[final] ).
cnf(c_0_2640,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2107,
[final] ).
cnf(c_0_2641,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_2108,
[final] ).
cnf(c_0_2642,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2109,
[final] ).
cnf(c_0_2643,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2110,
[final] ).
cnf(c_0_2644,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_2111,
[final] ).
cnf(c_0_2645,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
c_0_2112,
[final] ).
cnf(c_0_2646,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
c_0_2113,
[final] ).
cnf(c_0_2647,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
c_0_2114,
[final] ).
cnf(c_0_2648,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
c_0_2115,
[final] ).
cnf(c_0_2649,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_2116,
[final] ).
cnf(c_0_2650,plain,
hAPP(c_COMBI(X1),X2) = X2,
c_0_2117,
[final] ).
cnf(c_0_2651,plain,
hAPP(c_COMBI(t_a),v_P) = v_P,
c_0_2118,
[final] ).
cnf(c_0_2652,plain,
c_Collect(X1,X2) = X1,
c_0_2119,
[final] ).
cnf(c_0_2653,plain,
class_HOL_Oord(tc_bool),
c_0_2120,
[final] ).
cnf(c_0_2654,plain,
class_HOL_Ominus(tc_bool),
c_0_2121,
[final] ).
cnf(c_0_2655,plain,
class_Orderings_Obot(tc_bool),
c_0_2122,
[final] ).
cnf(c_0_2656,plain,
class_Orderings_Oorder(tc_bool),
c_0_2123,
[final] ).
cnf(c_0_2657,plain,
class_Lattices_Olattice(tc_bool),
c_0_2124,
[final] ).
cnf(c_0_2658,plain,
class_Orderings_Opreorder(tc_bool),
c_0_2125,
[final] ).
cnf(c_0_2659,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
c_0_2126,
[final] ).
cnf(c_0_2660,plain,
class_Lattices_Obounded__lattice(tc_bool),
c_0_2127,
[final] ).
cnf(c_0_2661,plain,
class_Lattices_Odistrib__lattice(tc_bool),
c_0_2128,
[final] ).
cnf(c_0_2662,plain,
class_Lattices_Olower__semilattice(tc_bool),
c_0_2129,
[final] ).
cnf(c_0_2663,plain,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_2130,
[final] ).
cnf(c_0_2664,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
c_0_2131,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2132_0,axiom,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2132_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X6,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_2132]) ).
cnf(c_0_2133_0,axiom,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2133_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X5,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_2133]) ).
cnf(c_0_2134_0,axiom,
( hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10))
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_2,axiom,
( ~ hBOOL(c_in(X10,X11,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,hAPP(X1,X11)),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2135_0,axiom,
( hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11)))
| ~ hBOOL(c_in(X10,X11,X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2135_2,axiom,
( ~ hBOOL(c_in(X10,X11,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hBOOL(hAPP(hAPP(X3,X10),hAPP(X2,X11))) ),
inference(literals_permutation,[status(thm)],[c_0_2135]) ).
cnf(c_0_2136_0,axiom,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2136_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_2136]) ).
cnf(c_0_2137_0,axiom,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2137_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_2137]) ).
cnf(c_0_2138_0,axiom,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X6,X10),hAPP(X2,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2139_0,axiom,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X5,X10),hAPP(X1,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2141_0,axiom,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2141_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))) = X8 ),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2142_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OCond(X4,X5,X7),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X7,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OCond(X4,X5,X7),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X7,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X7,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OCond(X4,X5,X7),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OWhile(X4,X5),c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2143_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(c_Hoare__Mirabelle_Opeek__and(X3,X4,X2),X5,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OWhile(X4,X5),c_Hoare__Mirabelle_Opeek__and(X3,c_Fun_Ocomp(c_Not,X4,tc_bool,tc_bool,tc_Com_Ostate),X2),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2143]) ).
cnf(c_0_2144_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2144_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2145_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2145_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2146_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2146_3,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2147_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2147_3,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2147]) ).
cnf(c_0_2148_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2148_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2148]) ).
cnf(c_0_2155_0,axiom,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2155_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2155]) ).
cnf(c_0_2156_0,axiom,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2156_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2156]) ).
cnf(c_0_2160_0,axiom,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5)
| ~ hBOOL(c_in(hAPP(X1,X3),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2160_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X3),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X5))
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2160]) ).
cnf(c_0_2161_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2161_1,axiom,
( ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2161]) ).
cnf(c_0_2162_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2162_1,axiom,
( ~ hBOOL(hAPP(X1,c_Hoare__Mirabelle_Otriple_Otriple__case(X2,c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,t_b),t_b,t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(hAPP(X2,X3),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2162]) ).
cnf(c_0_2163_0,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2163_1,axiom,
( hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11))
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_2163]) ).
cnf(c_0_2164_0,axiom,
( c_Fun_Oinj__on(X1,hAPP(c_Set_Oimage(X2,X5,X3),X6),X3,X4)
| ~ c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2164_1,axiom,
( ~ c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4)
| c_Fun_Oinj__on(X1,hAPP(c_Set_Oimage(X2,X5,X3),X6),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2165_0,axiom,
( c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5)
| ~ c_Fun_Oinj__on(X1,X4,X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_1,axiom,
( ~ c_Fun_Oinj__on(X1,X3,X2,X5)
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Fun_Oinj__on(X1,X4,X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_2,axiom,
( ~ c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5)
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2165_3,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5)
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2165]) ).
cnf(c_0_2166_0,axiom,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2166_1,axiom,
( c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8)
| hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2166]) ).
cnf(c_0_2167_0,axiom,
( c_Fun_Oinj__on(c_Fun_Ocomp(X5,X1,X4,X6,X3),X2,X3,X6)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X1,X3,X4),X2),X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Fun_Ocomp(X5,X1,X4,X6,X3),X2,X3,X6)
| ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X1,X3,X4),X2),X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_2,axiom,
( ~ c_Fun_Oinj__on(X5,hAPP(c_Set_Oimage(X1,X3,X4),X2),X4,X6)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(c_Fun_Ocomp(X5,X1,X4,X6,X3),X2,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2168_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2169_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2169_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2173_0,axiom,
( hBOOL(c_in(hAPP(X1,X5),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4))
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_1,axiom,
( c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4)
| hBOOL(c_in(hAPP(X1,X5),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2173_2,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4)
| hBOOL(c_in(hAPP(X1,X5),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2176_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBB(hAPP(c_Set_Oinsert(X4),X5),X6,tc_fun(X4,tc_bool),tc_fun(X4,tc_bool),X3),X3,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X6,X3,tc_fun(X4,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2176_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,c_COMBB(hAPP(c_Set_Oinsert(X4),X5),X6,tc_fun(X4,tc_bool),tc_fun(X4,tc_bool),X3),X3,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X6,X3,tc_fun(X4,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2176]) ).
cnf(c_0_2177_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2177_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2177]) ).
cnf(c_0_2178_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2178_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X3),X4),X5,tc_fun(X3,tc_bool),tc_fun(X3,tc_bool),X2),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5,X2,tc_fun(X3,tc_bool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2178]) ).
cnf(c_0_2183_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2183_1,axiom,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X2,tc_bool)))),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X2,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2183]) ).
cnf(c_0_2186_0,axiom,
( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X1,X4,X2,tc_fun(X3,X3),X5),X5,X3)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
| c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X1,X4,X2,tc_fun(X3,X3),X5),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2194_0,axiom,
( hAPP(X2,X1) = X5
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2194_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3))
| hAPP(X2,X1) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2196_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_Set_Oimage(X1,X3,X4),X5)),hAPP(c_Set_Oimage(X1,X3,X4),X6)) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X5),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_Set_Oimage(X1,X3,X4),X5)),hAPP(c_Set_Oimage(X1,X3,X4),X6)) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X5),X6))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_Set_Oimage(X1,X3,X4),X5)),hAPP(c_Set_Oimage(X1,X3,X4),X6)) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X5),X6))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2196_3,axiom,
( ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(c_Set_Oimage(X1,X3,X4),X5)),hAPP(c_Set_Oimage(X1,X3,X4),X6)) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2197_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1))
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2202_0,axiom,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2202_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4))
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2202]) ).
cnf(c_0_2203_0,axiom,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_2,axiom,
( ~ hBOOL(c_in(X4,hAPP(X5,X1),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2204_0,axiom,
( hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6))
| ~ hBOOL(c_in(X4,hAPP(X5,X1),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_2,axiom,
( ~ hBOOL(c_in(X4,hAPP(X5,X1),X6))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X6,tc_bool)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X3,X4),X5),hAPP(c_Set_Oimage(X1,X3,X4),X6),tc_fun(X4,tc_bool)) = hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X3,X4),X5),hAPP(c_Set_Oimage(X1,X3,X4),X6),tc_fun(X4,tc_bool)) = hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_2,axiom,
( ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X3,X4),X5),hAPP(c_Set_Oimage(X1,X3,X4),X6),tc_fun(X4,tc_bool)) = hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool)))
| ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2205_3,axiom,
( ~ c_lessequals(X6,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X3,X4),X5),hAPP(c_Set_Oimage(X1,X3,X4),X6),tc_fun(X4,tc_bool)) = hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,X6,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2205]) ).
cnf(c_0_2209_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2209_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X1),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2210_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5))
| ~ hBOOL(hAPP(hAPP(X4,X1),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_2,axiom,
( ~ hBOOL(hAPP(hAPP(X4,X1),X5))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X6,tc_bool)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2212_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2212]) ).
cnf(c_0_2213_0,axiom,
( c_Fun_Ocomp(hAPP(X1,X4),hAPP(X1,X4),X3,X3,X3) = hAPP(X1,X4)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2213_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
| c_Fun_Ocomp(hAPP(X1,X4),hAPP(X1,X4),X3,X3,X3) = hAPP(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2213]) ).
cnf(c_0_2214_0,axiom,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2214_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2))
| hBOOL(c_in(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2214]) ).
cnf(c_0_2216_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2216_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2216]) ).
cnf(c_0_2217_0,axiom,
( hBOOL(c_in(X1,X3,X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_1,axiom,
( hBOOL(c_in(X1,X4,X2))
| hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2217_2,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2))
| hBOOL(c_in(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2217]) ).
cnf(c_0_2221_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2221_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2221]) ).
cnf(c_0_2222_0,axiom,
( hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2222_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2))
| hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2222]) ).
cnf(c_0_2223_0,axiom,
( c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X6,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_2,axiom,
( ~ hBOOL(c_in(X6,X1,X3))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5,tc_fun(X4,tc_bool))
| c_lessequals(hAPP(X2,X6),X5,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2224_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X2),X4,X5)
| hAPP(c_Set_Oimage(X3,X4,X5),X1) != hAPP(c_Set_Oimage(X3,X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_1,axiom,
( ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X2),X4,X5)
| X1 = X2
| hAPP(c_Set_Oimage(X3,X4,X5),X1) != hAPP(c_Set_Oimage(X3,X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2224_2,axiom,
( hAPP(c_Set_Oimage(X3,X4,X5),X1) != hAPP(c_Set_Oimage(X3,X4,X5),X2)
| ~ c_Fun_Oinj__on(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X2),X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
( hBOOL(c_in(X1,X3,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2225_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2226_0,axiom,
( hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(X5,X1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X5,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2230_0,axiom,
( c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_2,axiom,
( ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(X3,X5),X4)
| ~ hBOOL(c_in(X5,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2230_3,axiom,
( ~ hBOOL(c_in(X5,X1,X2))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(X3,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2230]) ).
cnf(c_0_2232_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2232_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2232]) ).
cnf(c_0_2234_0,axiom,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_1,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_2,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_5,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2234_6,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2) = hAPP(hAPP(X1,c_Finite__Set_Ofold1(X1,X3,X2)),c_Finite__Set_Ofold1(X1,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2234]) ).
cnf(c_0_2235_0,axiom,
( hBOOL(c_in(hAPP(X2,X1),X5,X4))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2235_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3))
| hBOOL(c_in(hAPP(X2,X1),X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2235]) ).
cnf(c_0_2236_0,axiom,
( hBOOL(c_in(hAPP(X2,X1),X5,X4))
| ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2236_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3))
| hBOOL(c_in(hAPP(X2,X1),X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2236]) ).
cnf(c_0_2237_0,axiom,
( c_Fun_Oinj__on(X1,X3,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2237_1,axiom,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| c_Fun_Oinj__on(X1,X3,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2237]) ).
cnf(c_0_2238_0,axiom,
( c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2238_1,axiom,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| c_Fun_Oinj__on(X1,X4,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2238]) ).
cnf(c_0_2239_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2239_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2239]) ).
cnf(c_0_2240_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2240_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2240]) ).
cnf(c_0_2242_0,axiom,
( hAPP(c_Set_Oimage(X3,X2,X2),X1) = X1
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(hAPP(c_Set_Oimage(X3,X2,X2),X1),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Set_Oimage(X3,X2,X2),X1) = X1
| ~ c_lessequals(hAPP(c_Set_Oimage(X3,X2,X2),X1),X1,tc_fun(X2,tc_bool))
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_2,axiom,
( ~ c_lessequals(hAPP(c_Set_Oimage(X3,X2,X2),X1),X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Set_Oimage(X3,X2,X2),X1) = X1
| ~ c_Fun_Oinj__on(X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2242_3,axiom,
( ~ c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_lessequals(hAPP(c_Set_Oimage(X3,X2,X2),X1),X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Set_Oimage(X3,X2,X2),X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2242]) ).
cnf(c_0_2243_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2243_2,axiom,
( ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2243]) ).
cnf(c_0_2244_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2244_2,axiom,
( ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2244]) ).
cnf(c_0_2246_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2246_2,axiom,
( ~ hBOOL(hAPP(X4,X1))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2246]) ).
cnf(c_0_2247_0,axiom,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_1,axiom,
( hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2247_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2247]) ).
cnf(c_0_2248_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2249_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2249_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2254_0,axiom,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3))
| X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),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_2255]) ).
cnf(c_0_2255_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2255_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2255]) ).
cnf(c_0_2256_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),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_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2256_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_0,axiom,
( hBOOL(hAPP(X4,hAPP(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2257_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5))
| hBOOL(hAPP(X4,hAPP(X1,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2257]) ).
cnf(c_0_2258_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2258_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2258]) ).
cnf(c_0_2261_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2261_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2262_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2262_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2262]) ).
cnf(c_0_2263_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2263_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2263]) ).
cnf(c_0_2264_0,axiom,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2264_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
| hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2264]) ).
cnf(c_0_2265_0,axiom,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2265_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
| hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2265]) ).
cnf(c_0_2266_0,axiom,
( hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5))
| ~ hBOOL(c_in(hAPP(X1,X2),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2266_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
| hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2266]) ).
cnf(c_0_2267_0,axiom,
( hBOOL(c_in(hAPP(X1,X6),X5,X3))
| ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_1,axiom,
( ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,tc_fun(X3,tc_bool))
| hBOOL(c_in(hAPP(X1,X6),X5,X3))
| ~ hBOOL(c_in(X6,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2267_2,axiom,
( ~ hBOOL(c_in(X6,X4,X2))
| ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,tc_fun(X3,tc_bool))
| hBOOL(c_in(hAPP(X1,X6),X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2267]) ).
cnf(c_0_2271_0,axiom,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( ~ hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( X1 = X3
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2))
| X1 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2274_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2275_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2275_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2275]) ).
cnf(c_0_2276_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2276_1,axiom,
( ~ hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2276]) ).
cnf(c_0_2277_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
| ~ hBOOL(c_in(X2,X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2277_1,axiom,
( ~ hBOOL(c_in(X2,X5,X3))
| hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2277]) ).
cnf(c_0_2278_0,axiom,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2278_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2279_0,axiom,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( X1 = X3
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( X3 = X2
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( X3 = X2
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2282_0,axiom,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_1,axiom,
( X1 = X3
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2282_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2283_0,axiom,
( c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
| ~ c_Fun_Oinj__on(X1,X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
| c_Finite__Set_Ofinite(X4,X2)
| ~ c_Fun_Oinj__on(X1,X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2283_2,axiom,
( ~ c_Fun_Oinj__on(X1,X4,X2,X3)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
| c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2284_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2284_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2286_0,axiom,
( c_Fun_Oinj__on(X1,X4,X2,X5)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2286_1,axiom,
( ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5)
| c_Fun_Oinj__on(X1,X4,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2286]) ).
cnf(c_0_2288_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2288_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2288]) ).
cnf(c_0_2289_0,axiom,
( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2289_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2289]) ).
cnf(c_0_2292_0,axiom,
( X1 = X4
| ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(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_2292]) ).
cnf(c_0_2292_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| X1 = X4
| ~ hBOOL(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_2292]) ).
cnf(c_0_2292_2,axiom,
( ~ hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(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_2292]) ).
cnf(c_0_2292_3,axiom,
( ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| ~ hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| X1 = X4
| hAPP(X5,X1) != hAPP(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2292_4,axiom,
( hAPP(X5,X1) != hAPP(X5,X4)
| ~ c_Fun_Oinj__on(X5,X2,X3,X6)
| ~ hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2293_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_2,axiom,
( ~ hBOOL(c_in(X1,X4,X5))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2293_3,axiom,
( ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(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_2293]) ).
cnf(c_0_2293_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(c_in(X1,X4,X5))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2293]) ).
cnf(c_0_2294_0,axiom,
( X1 = X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_1,axiom,
( ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(c_in(X1,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_2,axiom,
( ~ hBOOL(c_in(X1,X4,X5))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2
| ~ hBOOL(c_in(X2,X4,X5))
| hAPP(X3,X1) != hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2294_3,axiom,
( ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(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_2294]) ).
cnf(c_0_2294_4,axiom,
( hAPP(X3,X1) != hAPP(X3,X2)
| ~ hBOOL(c_in(X2,X4,X5))
| ~ hBOOL(c_in(X1,X4,X5))
| ~ c_Fun_Oinj__on(X3,X4,X5,X6)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2294]) ).
cnf(c_0_2295_0,axiom,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,X2,X3))
| ~ hBOOL(c_in(X6,X2,X3))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_1,axiom,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ hBOOL(c_in(X5,X2,X3))
| ~ hBOOL(c_in(X6,X2,X3))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_2,axiom,
( ~ hBOOL(c_in(X5,X2,X3))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6
| ~ hBOOL(c_in(X6,X2,X3))
| hAPP(X1,X5) != hAPP(X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2295_3,axiom,
( ~ hBOOL(c_in(X6,X2,X3))
| ~ hBOOL(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_2295]) ).
cnf(c_0_2295_4,axiom,
( hAPP(X1,X5) != hAPP(X1,X6)
| ~ hBOOL(c_in(X6,X2,X3))
| ~ hBOOL(c_in(X5,X2,X3))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| X5 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2295]) ).
cnf(c_0_2296_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2296_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2296]) ).
cnf(c_0_2297_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2297_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2297]) ).
cnf(c_0_2298_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2298_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_0,axiom,
( c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X2,X2),X1),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Fun_Oinj__on(X3,X1,X2,X2)
| ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X2,X2),X1),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2299]) ).
cnf(c_0_2299_2,axiom,
( ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X2,X2),X1),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_2299]) ).
cnf(c_0_2300_0,axiom,
( hBOOL(c_in(X1,X2,X4))
| ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2300_1,axiom,
( ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
| hBOOL(c_in(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2300]) ).
cnf(c_0_2301_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_2301]) ).
cnf(c_0_2301_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_2301]) ).
cnf(c_0_2301_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_2301]) ).
cnf(c_0_2302_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2306_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2309_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_1,axiom,
( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2309_2,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2309]) ).
cnf(c_0_2310_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_1,axiom,
( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2310_2,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2310]) ).
cnf(c_0_2311_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2311_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2311]) ).
cnf(c_0_2313_0,axiom,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2313_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2313]) ).
cnf(c_0_2314_0,axiom,
( hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2314_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| hAPP(X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2314]) ).
cnf(c_0_2315_0,axiom,
( c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2315_1,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool))
| c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2315]) ).
cnf(c_0_2316_0,axiom,
( c_lessequals(hAPP(c_Set_Oimage(X4,X3,X5),X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2316_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(c_Set_Oimage(X4,X3,X5),X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2316]) ).
cnf(c_0_2317_0,axiom,
( c_lessequals(hAPP(c_Set_Ovimage(X4,X5,X3),X1),hAPP(c_Set_Ovimage(X4,X5,X3),X2),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2317_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(c_Set_Ovimage(X4,X5,X3),X1),hAPP(c_Set_Ovimage(X4,X5,X3),X2),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2320_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2320_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2320]) ).
cnf(c_0_2321_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2321_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2321]) ).
cnf(c_0_2322_0,axiom,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2322_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool))
| c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2322]) ).
cnf(c_0_2323_0,axiom,
( c_lessequals(X2,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2323_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool))
| c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2323]) ).
cnf(c_0_2324_0,axiom,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2324_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2325_0,axiom,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2326_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X1)),hAPP(c_Set_Oimage(X5,X3,X4),X2)) = hAPP(c_Set_Oimage(X5,X3,X4),X2)
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2326_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X1)),hAPP(c_Set_Oimage(X5,X3,X4),X2)) = hAPP(c_Set_Oimage(X5,X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2326]) ).
cnf(c_0_2327_0,axiom,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2327_1,axiom,
( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
| hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2327]) ).
cnf(c_0_2328_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2328_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2328]) ).
cnf(c_0_2329_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,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_2329]) ).
cnf(c_0_2329_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,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_2329]) ).
cnf(c_0_2329_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X5,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2329]) ).
cnf(c_0_2330_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2330_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2331_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2332_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_1,axiom,
( ~ hBOOL(c_in(X4,X2,X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2332_2,axiom,
( ~ hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(c_in(X4,X2,X1))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2332]) ).
cnf(c_0_2334_0,axiom,
( hAPP(c_Set_Oimage(c_COMBK(X4,X5,X3),X3,X5),X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2334_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(c_Set_Oimage(c_COMBK(X4,X5,X3),X3,X5),X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2334]) ).
cnf(c_0_2335_0,axiom,
( X1 = X3
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_1,axiom,
( hBOOL(c_in(X1,X4,X2))
| X1 = X3
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2335_2,axiom,
( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2))
| X1 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2335]) ).
cnf(c_0_2337_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),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_2337]) ).
cnf(c_0_2337_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2338_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),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_2338]) ).
cnf(c_0_2338_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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_2339]) ).
cnf(c_0_2339_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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_2340]) ).
cnf(c_0_2340_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2341_0,axiom,
( c_lessequals(X4,X1,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_1,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2342_0,axiom,
( c_lessequals(X2,X5,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_1,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2343_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2343]) ).
cnf(c_0_2345_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2345_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2345]) ).
cnf(c_0_2346_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2346_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2346]) ).
cnf(c_0_2348_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_2,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))
| X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),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_2348]) ).
cnf(c_0_2352_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_lessequals(X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_3,axiom,
( ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X4,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_4,axiom,
( ~ hBOOL(c_in(X4,X1,X2))
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_5,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(c_in(X4,X1,X2))
| ~ c_lessequals(X3,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,X4,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,hAPP(c_Set_Oimage(X4,X2,X5),X1),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5)
| ~ c_lessequals(X3,hAPP(c_Set_Oimage(X4,X2,X5),X1),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_2,axiom,
( ~ c_lessequals(X3,hAPP(c_Set_Oimage(X4,X2,X5),X1),tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2355_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2355_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2356_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2356_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2356]) ).
cnf(c_0_2358_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2358_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4)
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2359_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2359_1,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)) = X2
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2359]) ).
cnf(c_0_2360_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2360_1,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2360]) ).
cnf(c_0_2361_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2361_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2362_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2363_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(X4,X3,X2))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_1,axiom,
( hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_2,axiom,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2363_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),X3),X2) = hAPP(hAPP(X1,X4),c_Finite__Set_Ofold1(X1,X3,X2))
| hBOOL(c_in(X4,X3,X2))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2364_0,axiom,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2364_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2365_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2365_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2366_0,axiom,
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2367_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ 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_2367]) ).
cnf(c_0_2367_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2367_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hAPP(c_Set_Ovimage(c_COMBK(X1,X3,X4),X4,X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2368_1,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X3,X4),X4,X3),X2) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2369_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_1,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_2,axiom,
( ~ c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2370_0,axiom,
( hBOOL(c_in(X3,X1,X2))
| c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_1,axiom,
( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| hBOOL(c_in(X3,X1,X2))
| ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2370_2,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
| c_lessequals(X1,X4,tc_fun(X2,tc_bool))
| hBOOL(c_in(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2370]) ).
cnf(c_0_2371_0,axiom,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2371_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X3),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2371]) ).
cnf(c_0_2372_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(c_COMBK(X3,X4,X2),X2,X4),X1) = hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2372]) ).
cnf(c_0_2372_1,axiom,
( hAPP(c_Set_Oimage(c_COMBK(X3,X4,X2),X2,X4),X1) = hAPP(hAPP(c_Set_Oinsert(X4),X3),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_2372]) ).
cnf(c_0_2374_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2374_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2374]) ).
cnf(c_0_2375_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2375_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x)) ),
inference(literals_permutation,[status(thm)],[c_0_2375]) ).
cnf(c_0_2376_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2376_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x)) ),
inference(literals_permutation,[status(thm)],[c_0_2376]) ).
cnf(c_0_2377_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2377_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2377]) ).
cnf(c_0_2378_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2378_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2378]) ).
cnf(c_0_2379_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2379_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2379]) ).
cnf(c_0_2380_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2380_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2380]) ).
cnf(c_0_2381_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2381_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2381]) ).
cnf(c_0_2382_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2382_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2382]) ).
cnf(c_0_2383_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_1,axiom,
( c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2383_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2383]) ).
cnf(c_0_2384_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_1,axiom,
( c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2384_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2384]) ).
cnf(c_0_2386_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2386_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2387_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2387_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2387]) ).
cnf(c_0_2388_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2388_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2388]) ).
cnf(c_0_2389_0,axiom,
( hBOOL(c_in(X4,X2,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3))
| ~ hBOOL(c_in(X4,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2389_2,axiom,
( ~ hBOOL(c_in(X4,X1,X3))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(c_in(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2389]) ).
cnf(c_0_2390_0,axiom,
( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2390_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2390]) ).
cnf(c_0_2391_0,axiom,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_1,axiom,
( hBOOL(hAPP(X3,X4))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2391_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))
| hBOOL(hAPP(X3,X4))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2392_0,axiom,
( hBOOL(c_in(X2,X4,X1))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2392_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool))
| hBOOL(c_in(X2,X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2393_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2393_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X4)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBK(X3,X4,X2),X2,X4) = X3
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2394_0,axiom,
( X1 = X2
| hBOOL(c_in(X3,X1,X4))
| hBOOL(c_in(X3,X2,X4))
| hAPP(hAPP(c_Set_Oinsert(X4),X3),X1) != hAPP(hAPP(c_Set_Oinsert(X4),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_1,axiom,
( hBOOL(c_in(X3,X1,X4))
| X1 = X2
| hBOOL(c_in(X3,X2,X4))
| hAPP(hAPP(c_Set_Oinsert(X4),X3),X1) != hAPP(hAPP(c_Set_Oinsert(X4),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_2,axiom,
( hBOOL(c_in(X3,X2,X4))
| hBOOL(c_in(X3,X1,X4))
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),X1) != hAPP(hAPP(c_Set_Oinsert(X4),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2394_3,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X3),X1) != hAPP(hAPP(c_Set_Oinsert(X4),X3),X2)
| hBOOL(c_in(X3,X2,X4))
| hBOOL(c_in(X3,X1,X4))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2395_0,axiom,
( ~ hBOOL(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_2395]) ).
cnf(c_0_2395_1,axiom,
( ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2396_0,axiom,
( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_3,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2397_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2397]) ).
cnf(c_0_2397_1,axiom,
( ~ hBOOL(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_2397]) ).
cnf(c_0_2402_0,axiom,
( c_lessequals(X3,X4,tc_fun(X1,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2402_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool))
| c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2403_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_1,axiom,
( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2403_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X3),tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2404_0,axiom,
( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3
| ~ c_Orderings_Olinorder(X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2404_1,axiom,
( ~ c_Orderings_Olinorder(X4,X5,X6)
| c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2405_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2405_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2406_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2406_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2407_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2407_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2407]) ).
cnf(c_0_2408_0,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_1,axiom,
( ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2408_2,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2409_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2409_1,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2409_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2410_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2410_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2411_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_1,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2411_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2411]) ).
cnf(c_0_2415_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2415_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2415]) ).
cnf(c_0_2416_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2416_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2416]) ).
cnf(c_0_2417_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2417_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2418_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2418_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2418_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2418_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2419_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2419_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2419_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2419_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2419]) ).
cnf(c_0_2420_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2420_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2420_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2420_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2420]) ).
cnf(c_0_2421_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2421_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2422_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2423_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_1,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2426_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2427_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2427_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2428_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_2428]) ).
cnf(c_0_2428_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_2428]) ).
cnf(c_0_2428_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_2428]) ).
cnf(c_0_2429_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2429_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2430_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2431_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2432_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2433_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2433_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2434_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2434_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2438_0,axiom,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2438_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X2,X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2438_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2439_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2439_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X3,X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2439_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2440_0,axiom,
( c_lessequals(X2,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2440_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X2,X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2440_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2441_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2441_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X3,X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2441_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X4,X1)
| c_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_2442_0,axiom,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
( c_lessequals(X1,X4,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_0,axiom,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_1,axiom,
( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4),X2)
| c_lessequals(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2448_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2448_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) != X2
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2449_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2449_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2450_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_1,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2450_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2451_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_1,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2451_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2453_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2453_2,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,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_2453]) ).
cnf(c_0_2454_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2454_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != 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_2454]) ).
cnf(c_0_2455_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != 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_2455]) ).
cnf(c_0_2458_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_1,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_4,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X3),c_Finite__Set_Olinorder__class_OMin(X1,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2459_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_1,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_4,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(X1,X3),c_Finite__Set_Olinorder__class_OMax(X2,X3),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2460_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_1,axiom,
( ~ hBOOL(c_in(X1,c_Collect(X2,X3),X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2461_0,axiom,
( c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(X3,c_Finite__Set_Olinorder__class_OMax(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2462_0,axiom,
( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_2,axiom,
( ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2463_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2463_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2464_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_2464]) ).
cnf(c_0_2464_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_2464]) ).
cnf(c_0_2464_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_2464]) ).
cnf(c_0_2465_0,axiom,
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X2,X4),X1),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2465_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X2,X4),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2465]) ).
cnf(c_0_2467_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_HOL_Ominus(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2467_1,axiom,
( ~ class_HOL_Ominus(X3)
| c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x) ),
inference(literals_permutation,[status(thm)],[c_0_2467]) ).
cnf(c_0_2468_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2468_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2469_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2470_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2471_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2471_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2471]) ).
cnf(c_0_2472_0,axiom,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X2),c_SetInterval_Oord__class_OlessThan(X3,X2),tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_1,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X2),c_SetInterval_Oord__class_OlessThan(X3,X2),tc_fun(X2,tc_bool))
| c_lessequals(X1,X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2472_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X2),c_SetInterval_Oord__class_OlessThan(X3,X2),tc_fun(X2,tc_bool))
| c_lessequals(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2472]) ).
cnf(c_0_2473_0,axiom,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2473_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2473]) ).
cnf(c_0_2474_0,axiom,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(X1,X2,X3))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2476_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(X4,X2,X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_1,axiom,
( hAPP(c_Set_Oimage(X4,X2,X3),X1) != 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_2476]) ).
cnf(c_0_2477_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Set_Oimage(X3,X2,X4),X1) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_1,axiom,
( hAPP(c_Set_Oimage(X3,X2,X4),X1) != 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_2477]) ).
cnf(c_0_2478_0,axiom,
( hBOOL(c_in(X3,X4,X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(c_Set_Oinsert(X5),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(c_in(X3,X4,X5))
| hAPP(hAPP(c_Set_Oinsert(X5),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X5),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(c_in(X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2479_0,axiom,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2479_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2479]) ).
cnf(c_0_2481_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_2,axiom,
( X5 = X4
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2481_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X5 = X4
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2481]) ).
cnf(c_0_2482_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_1,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_2,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2483_0,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_1,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_2,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2483_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2483]) ).
cnf(c_0_2484_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_2,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2484_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2485_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X2))
| hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_1,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X2))
| hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_2,axiom,
( ~ c_Orderings_Olinorder(X1,X3,X4)
| hBOOL(hAPP(hAPP(X3,X2),X2))
| hBOOL(hAPP(hAPP(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2486_0,axiom,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2487_0,axiom,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2488_0,axiom,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_1,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2489_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_1,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2489_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2489]) ).
cnf(c_0_2490_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X4),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X4),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2490_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2490]) ).
cnf(c_0_2491_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X4),X2),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X4),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2491_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2491]) ).
cnf(c_0_2492_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2492_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X4),X1),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2492]) ).
cnf(c_0_2493_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2495_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_2495]) ).
cnf(c_0_2495_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_2495]) ).
cnf(c_0_2495_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_2495]) ).
cnf(c_0_2496_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_2496]) ).
cnf(c_0_2496_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_2496]) ).
cnf(c_0_2496_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_2496]) ).
cnf(c_0_2497_0,axiom,
( hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),X5)
| ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2497_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)
| hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2497]) ).
cnf(c_0_2498_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_2498]) ).
cnf(c_0_2498_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_2498]) ).
cnf(c_0_2498_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_2498]) ).
cnf(c_0_2499_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2499_1,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2499]) ).
cnf(c_0_2501_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_2501]) ).
cnf(c_0_2501_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_2501]) ).
cnf(c_0_2501_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_2501]) ).
cnf(c_0_2501_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_2501]) ).
cnf(c_0_2502_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_2502]) ).
cnf(c_0_2502_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_2502]) ).
cnf(c_0_2502_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_2502]) ).
cnf(c_0_2502_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_2502]) ).
cnf(c_0_2503_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_2503]) ).
cnf(c_0_2503_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_2503]) ).
cnf(c_0_2505_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2505_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2505]) ).
cnf(c_0_2506_0,axiom,
( c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2506_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2507_0,axiom,
( c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2507_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2508_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2509_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2510_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_2510]) ).
cnf(c_0_2511_0,axiom,
( c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X3),c_SetInterval_Oord__class_OlessThan(X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X3),c_SetInterval_Oord__class_OlessThan(X2,X3),tc_fun(X3,tc_bool))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_SetInterval_Oord__class_OlessThan(X1,X3),c_SetInterval_Oord__class_OlessThan(X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2513_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2513_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2514_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2515_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_1,axiom,
( hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2516_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_1,axiom,
( hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2516_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(X1,X2),X1,X2))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2516]) ).
cnf(c_0_2519_0,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2519_1,axiom,
( ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2520_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2520_1,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X4),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2520]) ).
cnf(c_0_2521_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2521_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2521]) ).
cnf(c_0_2522_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2522_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2522]) ).
cnf(c_0_2523_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2523_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2523]) ).
cnf(c_0_2524_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2524_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2524]) ).
cnf(c_0_2525_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,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_2525]) ).
cnf(c_0_2525_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2525_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2525]) ).
cnf(c_0_2526_0,axiom,
( hBOOL(c_in(X2,c_Collect(X1,X3),X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2526_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2529_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(c_in(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2529_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2529]) ).
cnf(c_0_2530_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2530_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2530]) ).
cnf(c_0_2531_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2531_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2531]) ).
cnf(c_0_2532_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_2532]) ).
cnf(c_0_2532_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_2532]) ).
cnf(c_0_2532_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_2532]) ).
cnf(c_0_2533_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_2533]) ).
cnf(c_0_2533_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_2533]) ).
cnf(c_0_2533_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_2533]) ).
cnf(c_0_2537_0,axiom,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2537_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1)
| c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2537]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2540_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2540_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2541_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_2541]) ).
cnf(c_0_2541_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_2541]) ).
cnf(c_0_2541_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_2541]) ).
cnf(c_0_2541_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_2541]) ).
cnf(c_0_2542_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_2542]) ).
cnf(c_0_2542_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_2542]) ).
cnf(c_0_2542_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_2542]) ).
cnf(c_0_2542_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_2542]) ).
cnf(c_0_2543_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_2543]) ).
cnf(c_0_2543_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_2543]) ).
cnf(c_0_2543_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_2543]) ).
cnf(c_0_2543_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_2543]) ).
cnf(c_0_2545_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2546_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2550_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_2550]) ).
cnf(c_0_2550_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_2550]) ).
cnf(c_0_2551_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_2551]) ).
cnf(c_0_2551_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_2551]) ).
cnf(c_0_2552_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2553_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2554_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2555_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2555]) ).
cnf(c_0_2555_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2555]) ).
cnf(c_0_2556_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2556]) ).
cnf(c_0_2556_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2556]) ).
cnf(c_0_2557_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2557_1,axiom,
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2558_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2558_1,axiom,
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2558]) ).
cnf(c_0_2559_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2559_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2560_0,axiom,
( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2561_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2562_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2563_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_2563]) ).
cnf(c_0_2563_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_2563]) ).
cnf(c_0_2563_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_2563]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2564_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_2564]) ).
cnf(c_0_2565_0,axiom,
( hBOOL(c_in(X2,X1,X3))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(c_in(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2568_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2569_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X1) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X1) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X2),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2570_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2570_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X2),X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2570]) ).
cnf(c_0_2571_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2571_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2571]) ).
cnf(c_0_2572_0,axiom,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) != X2
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2572_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X2) != X2
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2572]) ).
cnf(c_0_2573_0,axiom,
( c_lessequals(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2573_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X1),X2) != X1
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2573]) ).
cnf(c_0_2577_0,axiom,
( c_lessequals(X1,X2,X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2577_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2577]) ).
cnf(c_0_2578_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_2,axiom,
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2579_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2579_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2579]) ).
cnf(c_0_2582_0,axiom,
( X1 = X3
| ~ hBOOL(hAPP(c_fequal(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2582_1,axiom,
( ~ hBOOL(hAPP(c_fequal(X1,X2),X3))
| X1 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2589_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2589_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2589]) ).
cnf(c_0_2590_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_1,axiom,
( c_Collect(X1,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2591_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2591_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_Collect(X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2592_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2593_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2594_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2594_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2594]) ).
cnf(c_0_2595_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2595_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2595]) ).
cnf(c_0_2602_0,axiom,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2602_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2603_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2603_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != 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_2603]) ).
cnf(c_0_2603_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2603]) ).
cnf(c_0_2604_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2604_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != 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_2604]) ).
cnf(c_0_2604_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2604]) ).
cnf(c_0_2611_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2611_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2611]) ).
cnf(c_0_2612_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2612_1,axiom,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2612]) ).
cnf(c_0_2613_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2613_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2613]) ).
cnf(c_0_2614_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2614_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2615_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2615_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2616_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2616_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2617_0,axiom,
( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2617_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2617]) ).
cnf(c_0_2618_0,axiom,
( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2618_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2618]) ).
cnf(c_0_2619_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2621_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2621_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2621]) ).
cnf(c_0_2622_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2622_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2622]) ).
cnf(c_0_2623_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2623_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2623]) ).
cnf(c_0_2624_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2625_0,axiom,
( X1 = X2
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2625_1,axiom,
( c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2625_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2626_0,axiom,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2626_1,axiom,
( c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2627_0,axiom,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2627_1,axiom,
( c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2627]) ).
cnf(c_0_2628_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_1,axiom,
( c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2629_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_1,axiom,
( c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2630_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_2630]) ).
cnf(c_0_2630_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_2630]) ).
cnf(c_0_2630_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_2630]) ).
cnf(c_0_2634_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2634_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2634]) ).
cnf(c_0_2635_0,axiom,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2635_1,axiom,
( ~ class_HOL_Ominus(X1)
| class_HOL_Ominus(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2636_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2636_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2637_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2637_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2638_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2639_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2639_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2640_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2640_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2641_0,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2641_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2642_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2642_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2643_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2643_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2643]) ).
cnf(c_0_2644_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2644_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2644]) ).
cnf(c_0_2649_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2308_0,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_2308]) ).
cnf(c_0_2412_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2413_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2414_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2414]) ).
cnf(c_0_2527_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2586_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2587_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2597_0,axiom,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2597]) ).
cnf(c_0_2598_0,axiom,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2598]) ).
cnf(c_0_2599_0,axiom,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2599]) ).
cnf(c_0_2600_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2600]) ).
cnf(c_0_2605_0,axiom,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2605]) ).
cnf(c_0_2606_0,axiom,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2631_0,axiom,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2632_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2645_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2645]) ).
cnf(c_0_2646_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2646]) ).
cnf(c_0_2647_0,axiom,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2647]) ).
cnf(c_0_2648_0,axiom,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
inference(literals_permutation,[status(thm)],[c_0_2648]) ).
cnf(c_0_2149_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
inference(literals_permutation,[status(thm)],[c_0_2150]) ).
cnf(c_0_2151_0,axiom,
c_COMBS(X1,X2,X3,X4,X5,X6) = hAPP(hAPP(X1,X3),hAPP(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2151]) ).
cnf(c_0_2152_0,axiom,
c_COMBS(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2153_0,axiom,
c_COMBC(X1,X2,X3,X4,X5,X6) = hAPP(hAPP(X1,X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2153]) ).
cnf(c_0_2154_0,axiom,
c_COMBC(v_P,v_Q,v_R,t_a,t_b,t_c) = hAPP(hAPP(v_P,v_R),v_Q),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2157_0,axiom,
hAPP(c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4),X6) = hAPP(c_Set_Oimage(X1,X3,X4),hAPP(c_Set_Oimage(X2,X5,X3),X6)),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2158_0,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X5,X2),X6)) = hAPP(c_Set_Oimage(c_COMBB(X1,X4,X2,X3,X5),X5,X3),X6),
inference(literals_permutation,[status(thm)],[c_0_2158]) ).
cnf(c_0_2159_0,axiom,
hAPP(c_Set_Ovimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4),X6) = hAPP(c_Set_Ovimage(X2,X5,X3),hAPP(c_Set_Ovimage(X1,X3,X4),X6)),
inference(literals_permutation,[status(thm)],[c_0_2159]) ).
cnf(c_0_2170_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2171_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2171]) ).
cnf(c_0_2172_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2172]) ).
cnf(c_0_2174_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Ovimage(X1,X2,X3),X5,tc_fun(X3,tc_bool),tc_fun(X2,tc_bool),X6),X6,tc_fun(X2,tc_bool)) = hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X3,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2175_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Oimage(X1,X2,X3),X5,tc_fun(X2,tc_bool),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)) = hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X2,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2179_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,X3,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(X5,X1,X3,tc_fun(X6,tc_bool),X2),X2,tc_fun(X6,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2179]) ).
cnf(c_0_2180_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(X2,X3,X4,tc_fun(X5,tc_bool),X6),X6,tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X3,X6,X4),X1),X2,X4,tc_fun(X5,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2180]) ).
cnf(c_0_2181_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2181]) ).
cnf(c_0_2182_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2182]) ).
cnf(c_0_2184_0,axiom,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
inference(literals_permutation,[status(thm)],[c_0_2184]) ).
cnf(c_0_2185_0,axiom,
c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X4),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2187_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3) = hAPP(X1,hAPP(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
inference(literals_permutation,[status(thm)],[c_0_2190]) ).
cnf(c_0_2191_0,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
inference(literals_permutation,[status(thm)],[c_0_2191]) ).
cnf(c_0_2192_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSKIP,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
inference(literals_permutation,[status(thm)],[c_0_2192]) ).
cnf(c_0_2193_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X1,tc_fun(X5,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,X1,tc_fun(X5,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2195_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)) = hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2198_0,axiom,
hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2201_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4),
inference(literals_permutation,[status(thm)],[c_0_2201]) ).
cnf(c_0_2206_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X1,tc_bool))),X4) = X4,
inference(literals_permutation,[status(thm)],[c_0_2206]) ).
cnf(c_0_2207_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_2207]) ).
cnf(c_0_2208_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_2208]) ).
cnf(c_0_2215_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1))),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2218_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)) = hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5)),
inference(literals_permutation,[status(thm)],[c_0_2218]) ).
cnf(c_0_2219_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)) = hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5)),
inference(literals_permutation,[status(thm)],[c_0_2219]) ).
cnf(c_0_2220_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)) = hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5)),
inference(literals_permutation,[status(thm)],[c_0_2220]) ).
cnf(c_0_2228_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2231_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),hAPP(X4,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2231]) ).
cnf(c_0_2233_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4),
inference(literals_permutation,[status(thm)],[c_0_2233]) ).
cnf(c_0_2241_0,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_2241]) ).
cnf(c_0_2245_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2245]) ).
cnf(c_0_2250_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2252_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2259_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_2259]) ).
cnf(c_0_2260_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2268_0,axiom,
c_Hoare__Mirabelle_Otriple_Otriple__case(X1,c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),X5,X6) = hAPP(hAPP(hAPP(X1,X2),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_0,axiom,
c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5),X5,X6) = hAPP(hAPP(hAPP(X1,X2),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_2269]) ).
cnf(c_0_2270_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool)) = hAPP(c_Set_Ovimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2273_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2285_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2285]) ).
cnf(c_0_2287_0,axiom,
c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2287]) ).
cnf(c_0_2290_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_2290]) ).
cnf(c_0_2291_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = X2,
inference(literals_permutation,[status(thm)],[c_0_2291]) ).
cnf(c_0_2305_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2307_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2312_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
inference(literals_permutation,[status(thm)],[c_0_2312]) ).
cnf(c_0_2318_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2319_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2319]) ).
cnf(c_0_2333_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2333]) ).
cnf(c_0_2336_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2344_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2344]) ).
cnf(c_0_2347_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_2347]) ).
cnf(c_0_2349_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2350_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X1,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2354_0,axiom,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2357_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2373_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2373]) ).
cnf(c_0_2385_0,axiom,
hAPP(c_Set_Oimage(c_COMBK(X1,X2,X3),X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2398_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2398]) ).
cnf(c_0_2399_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X2,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2400_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2401_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2424_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2425_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2425]) ).
cnf(c_0_2435_0,axiom,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2436_0,axiom,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2437_0,axiom,
hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2446_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2452_0,axiom,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2456_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2457_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2466_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2466]) ).
cnf(c_0_2475_0,axiom,
c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3,
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2480_0,axiom,
c_Fun_Oinj__on(c_COMBI(X1),X2,X1,X1),
inference(literals_permutation,[status(thm)],[c_0_2480]) ).
cnf(c_0_2494_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_2494]) ).
cnf(c_0_2500_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2504_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2512_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2517_0,axiom,
c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2517]) ).
cnf(c_0_2518_0,axiom,
c_The(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2528_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2534_0,axiom,
hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2534]) ).
cnf(c_0_2535_0,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2535]) ).
cnf(c_0_2536_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2536]) ).
cnf(c_0_2538_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
inference(literals_permutation,[status(thm)],[c_0_2538]) ).
cnf(c_0_2544_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(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2547_0,axiom,
c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2548_0,axiom,
c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3) = c_Finite__Set_Ofold1(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2566_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2566]) ).
cnf(c_0_2567_0,axiom,
c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2574_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_2574]) ).
cnf(c_0_2575_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2576_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Collect(c_fequal(X1,X2),X2),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2580_0,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_2580]) ).
cnf(c_0_2581_0,axiom,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2583_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2584_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2585_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2588_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2596_0,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
inference(literals_permutation,[status(thm)],[c_0_2596]) ).
cnf(c_0_2601_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2607_0,axiom,
c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2608_0,axiom,
hBOOL(hAPP(c_fequal(X1,X2),X1)),
inference(literals_permutation,[status(thm)],[c_0_2608]) ).
cnf(c_0_2609_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2609]) ).
cnf(c_0_2610_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2610]) ).
cnf(c_0_2620_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2620]) ).
cnf(c_0_2633_0,axiom,
c_The(c_fequal(X1,X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2633]) ).
cnf(c_0_2650_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_2650]) ).
cnf(c_0_2651_0,axiom,
hAPP(c_COMBI(t_a),v_P) = v_P,
inference(literals_permutation,[status(thm)],[c_0_2651]) ).
cnf(c_0_2652_0,axiom,
c_Collect(X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2653_0,axiom,
class_HOL_Oord(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2653]) ).
cnf(c_0_2654_0,axiom,
class_HOL_Ominus(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2654]) ).
cnf(c_0_2655_0,axiom,
class_Orderings_Obot(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2655]) ).
cnf(c_0_2656_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2656]) ).
cnf(c_0_2657_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2657]) ).
cnf(c_0_2658_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2658]) ).
cnf(c_0_2659_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2659]) ).
cnf(c_0_2660_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2660]) ).
cnf(c_0_2661_0,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2661]) ).
cnf(c_0_2662_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2662]) ).
cnf(c_0_2663_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2663]) ).
cnf(c_0_2664_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2664]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_002,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_2_003,negated_conjecture,
! [X1,X2,X3] :
( hBOOL(hAPP(hAPP(v_Q,X3),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X3,X1,X2)),X2))
| ~ hBOOL(hAPP(hAPP(v_P,X3),X1)) ),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_3_004,negated_conjecture,
! [X1,X2,X3] :
( hBOOL(hAPP(hAPP(v_Q,X3),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X3,X1,X2)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X3),X1)) ),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_4_005,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_5_006,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
c_0_1 ).
fof(c_0_6_007,negated_conjecture,
! [X1,X2,X3] :
( hBOOL(hAPP(hAPP(v_Q,X3),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X3,X1,X2)),X2))
| ~ hBOOL(hAPP(hAPP(v_P,X3),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_7_008,negated_conjecture,
! [X1,X2,X3] :
( hBOOL(hAPP(hAPP(v_Q,X3),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X3,X1,X2)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X3),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_8_009,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
c_0_4 ).
fof(c_0_9_010,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
c_0_5 ).
fof(c_0_10_011,negated_conjecture,
! [X4,X5,X6] :
( hBOOL(hAPP(hAPP(v_Q,X6),X5))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X6,X4,X5)),X5))
| ~ hBOOL(hAPP(hAPP(v_P,X6),X4)) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_11_012,negated_conjecture,
! [X4,X5,X6] :
( hBOOL(hAPP(hAPP(v_Q,X6),X5))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X6,X4,X5)),X4))
| ~ hBOOL(hAPP(hAPP(v_P,X6),X4)) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
cnf(c_0_12_013,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_014,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14_015,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X1,X2,X3)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15_016,negated_conjecture,
( hBOOL(hAPP(hAPP(v_P_H,v_Z(X1,X2,X3)),X2))
| hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16_017,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
c_0_12,
[final] ).
cnf(c_0_17_018,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
c_0_13,
[final] ).
cnf(c_0_18_019,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X1,X2,X3)),X3)) ),
c_0_14,
[final] ).
cnf(c_0_19_020,negated_conjecture,
( hBOOL(hAPP(hAPP(v_P_H,v_Z(X1,X2,X3)),X2))
| hBOOL(hAPP(hAPP(v_Q,X1),X3))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2)) ),
c_0_15,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1128,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_16) ).
cnf(c_1522,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1128]) ).
cnf(c_1536,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1522]) ).
cnf(c_1539,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1536]) ).
cnf(c_1544,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1539]) ).
cnf(c_4838,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1544]) ).
cnf(c_1087,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X3,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X5,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X6,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X2,X3,X4,X5,X0,X6)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_2147_1) ).
cnf(c_4756,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X3,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X5,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X6,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X2,X3,X4,X5,X0,X6)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(copy,[status(esa)],[c_1087]) ).
cnf(c_4757,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X3,X4,X5)))
| hBOOL(hAPP(hAPP(X6,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X2,X3,X4,X5,X0,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X5,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(rewriting,[status(thm)],[c_4756]) ).
cnf(c_4865,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(X2,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,X0,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X2,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(resolution,[status(thm)],[c_4838,c_4757]) ).
cnf(c_4866,plain,
( ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(X2,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,X0,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X2,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(rewriting,[status(thm)],[c_4865]) ).
cnf(c_1129,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_17) ).
cnf(c_1524,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1129]) ).
cnf(c_1537,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1524]) ).
cnf(c_1538,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1537]) ).
cnf(c_1545,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1538]) ).
cnf(c_4840,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(copy,[status(esa)],[c_1545]) ).
cnf(c_5478,plain,
( hBOOL(hAPP(hAPP(v_Q_H,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))) ),
inference(resolution,[status(thm)],[c_4866,c_4840]) ).
cnf(c_5479,plain,
( hBOOL(hAPP(hAPP(v_Q_H,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))) ),
inference(rewriting,[status(thm)],[c_5478]) ).
cnf(c_1126,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_18) ).
cnf(c_1518,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1126]) ).
cnf(c_1534,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1518]) ).
cnf(c_1541,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1534]) ).
cnf(c_1542,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1541]) ).
cnf(c_4834,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(copy,[status(esa)],[c_1542]) ).
cnf(c_5984,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))) ),
inference(resolution,[status(thm)],[c_5479,c_4834]) ).
cnf(c_5985,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))) ),
inference(rewriting,[status(thm)],[c_5984]) ).
cnf(c_1127,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_19) ).
cnf(c_1520,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1127]) ).
cnf(c_1535,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1520]) ).
cnf(c_1540,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1535]) ).
cnf(c_1543,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1540]) ).
cnf(c_4836,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1)) ),
inference(copy,[status(esa)],[c_1543]) ).
cnf(c_5998,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H))) ),
inference(resolution,[status(thm)],[c_5985,c_4836]) ).
cnf(c_5999,plain,
( ~ hBOOL(hAPP(hAPP(v_P,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)))
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H))) ),
inference(rewriting,[status(thm)],[c_5998]) ).
cnf(c_1098,plain,
( ~ hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X0,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X0,X3,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X0,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_2144_0) ).
cnf(c_4778,plain,
( ~ hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X0,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X0,X3,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X0,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(copy,[status(esa)],[c_1098]) ).
cnf(c_4868,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,X0,X1)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(resolution,[status(thm)],[c_4838,c_4778]) ).
cnf(c_4871,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,X0,X1)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(rewriting,[status(thm)],[c_4868]) ).
cnf(c_5380,plain,
~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H))),
inference(resolution,[status(thm)],[c_4871,c_4840]) ).
cnf(c_5381,plain,
~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q_H))),
inference(rewriting,[status(thm)],[c_5380]) ).
cnf(c_6038,plain,
~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))),
inference(resolution,[status(thm)],[c_5999,c_5381]) ).
cnf(c_6039,plain,
~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))),
inference(rewriting,[status(thm)],[c_6038]) ).
cnf(c_1080,plain,
( hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X0,X2,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X0,X2,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X3,X2,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p',c_0_2155_1) ).
cnf(c_4742,plain,
( hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X0,X2,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X0,X2,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,X3,X2,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(copy,[status(esa)],[c_1080]) ).
cnf(c_4860,plain,
hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))),
inference(resolution,[status(thm)],[c_4838,c_4742]) ).
cnf(c_4863,plain,
hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))),
inference(rewriting,[status(thm)],[c_4860]) ).
cnf(c_6059,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6039,c_4863]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV825-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 15:56:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.18/0.49 % Orienting using strategy Equiv(ClausalAll)
% 0.18/0.49 % Orientation found
% 0.18/0.49 % 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/sandbox2/tmp/iprover_proof_13b258.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_643dd4 | grep -v "SZS"
% 0.18/0.51
% 0.18/0.51 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.18/0.51
% 0.18/0.51 %
% 0.18/0.51 % ------ iProver source info
% 0.18/0.51
% 0.18/0.51 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.18/0.51 % git: non_committed_changes: true
% 0.18/0.51 % git: last_make_outside_of_git: true
% 0.18/0.51
% 0.18/0.51 %
% 0.18/0.51 % ------ Input Options
% 0.18/0.51
% 0.18/0.51 % --out_options all
% 0.18/0.51 % --tptp_safe_out true
% 0.18/0.51 % --problem_path ""
% 0.18/0.51 % --include_path ""
% 0.18/0.51 % --clausifier .//eprover
% 0.18/0.51 % --clausifier_options --tstp-format
% 0.18/0.51 % --stdin false
% 0.18/0.51 % --dbg_backtrace false
% 0.18/0.51 % --dbg_dump_prop_clauses false
% 0.18/0.51 % --dbg_dump_prop_clauses_file -
% 0.18/0.51 % --dbg_out_stat false
% 0.18/0.51
% 0.18/0.51 % ------ General Options
% 0.18/0.51
% 0.18/0.51 % --fof false
% 0.18/0.51 % --time_out_real 150.
% 0.18/0.51 % --time_out_prep_mult 0.2
% 0.18/0.51 % --time_out_virtual -1.
% 0.18/0.51 % --schedule none
% 0.18/0.51 % --ground_splitting input
% 0.18/0.52 % --splitting_nvd 16
% 0.18/0.52 % --non_eq_to_eq false
% 0.18/0.52 % --prep_gs_sim true
% 0.18/0.52 % --prep_unflatten false
% 0.18/0.52 % --prep_res_sim true
% 0.18/0.52 % --prep_upred true
% 0.18/0.52 % --res_sim_input true
% 0.18/0.52 % --clause_weak_htbl true
% 0.18/0.52 % --gc_record_bc_elim false
% 0.18/0.52 % --symbol_type_check false
% 0.18/0.52 % --clausify_out false
% 0.18/0.52 % --large_theory_mode false
% 0.18/0.52 % --prep_sem_filter none
% 0.18/0.52 % --prep_sem_filter_out false
% 0.18/0.52 % --preprocessed_out false
% 0.18/0.52 % --sub_typing false
% 0.18/0.52 % --brand_transform false
% 0.18/0.52 % --pure_diseq_elim true
% 0.18/0.52 % --min_unsat_core false
% 0.18/0.52 % --pred_elim true
% 0.18/0.52 % --add_important_lit false
% 0.18/0.52 % --soft_assumptions false
% 0.18/0.52 % --reset_solvers false
% 0.18/0.52 % --bc_imp_inh []
% 0.18/0.52 % --conj_cone_tolerance 1.5
% 0.18/0.52 % --prolific_symb_bound 500
% 0.18/0.52 % --lt_threshold 2000
% 0.18/0.52
% 0.18/0.52 % ------ SAT Options
% 0.18/0.52
% 0.18/0.52 % --sat_mode false
% 0.18/0.52 % --sat_fm_restart_options ""
% 0.18/0.52 % --sat_gr_def false
% 0.18/0.52 % --sat_epr_types true
% 0.18/0.52 % --sat_non_cyclic_types false
% 0.18/0.52 % --sat_finite_models false
% 0.18/0.52 % --sat_fm_lemmas false
% 0.18/0.52 % --sat_fm_prep false
% 0.18/0.52 % --sat_fm_uc_incr true
% 0.18/0.52 % --sat_out_model small
% 0.18/0.52 % --sat_out_clauses false
% 0.18/0.52
% 0.18/0.52 % ------ QBF Options
% 0.18/0.52
% 0.18/0.52 % --qbf_mode false
% 0.18/0.52 % --qbf_elim_univ true
% 0.18/0.52 % --qbf_sk_in true
% 0.18/0.52 % --qbf_pred_elim true
% 0.18/0.52 % --qbf_split 32
% 0.18/0.52
% 0.18/0.52 % ------ BMC1 Options
% 0.18/0.52
% 0.18/0.52 % --bmc1_incremental false
% 0.18/0.52 % --bmc1_axioms reachable_all
% 0.18/0.52 % --bmc1_min_bound 0
% 0.18/0.52 % --bmc1_max_bound -1
% 0.18/0.52 % --bmc1_max_bound_default -1
% 0.18/0.52 % --bmc1_symbol_reachability true
% 0.18/0.52 % --bmc1_property_lemmas false
% 0.18/0.52 % --bmc1_k_induction false
% 0.18/0.52 % --bmc1_non_equiv_states false
% 0.18/0.52 % --bmc1_deadlock false
% 0.18/0.52 % --bmc1_ucm false
% 0.18/0.52 % --bmc1_add_unsat_core none
% 0.18/0.52 % --bmc1_unsat_core_children false
% 0.18/0.52 % --bmc1_unsat_core_extrapolate_axioms false
% 0.18/0.52 % --bmc1_out_stat full
% 0.18/0.52 % --bmc1_ground_init false
% 0.18/0.52 % --bmc1_pre_inst_next_state false
% 0.18/0.52 % --bmc1_pre_inst_state false
% 0.18/0.52 % --bmc1_pre_inst_reach_state false
% 0.18/0.52 % --bmc1_out_unsat_core false
% 0.18/0.52 % --bmc1_aig_witness_out false
% 0.18/0.52 % --bmc1_verbose false
% 0.18/0.52 % --bmc1_dump_clauses_tptp false
% 8.10/8.31 % --bmc1_dump_unsat_core_tptp false
% 8.10/8.31 % --bmc1_dump_file -
% 8.10/8.31 % --bmc1_ucm_expand_uc_limit 128
% 8.10/8.31 % --bmc1_ucm_n_expand_iterations 6
% 8.10/8.31 % --bmc1_ucm_extend_mode 1
% 8.10/8.31 % --bmc1_ucm_init_mode 2
% 8.10/8.31 % --bmc1_ucm_cone_mode none
% 8.10/8.31 % --bmc1_ucm_reduced_relation_type 0
% 8.10/8.31 % --bmc1_ucm_relax_model 4
% 8.10/8.31 % --bmc1_ucm_full_tr_after_sat true
% 8.10/8.31 % --bmc1_ucm_expand_neg_assumptions false
% 8.10/8.31 % --bmc1_ucm_layered_model none
% 8.10/8.31 % --bmc1_ucm_max_lemma_size 10
% 8.10/8.31
% 8.10/8.31 % ------ AIG Options
% 8.10/8.31
% 8.10/8.31 % --aig_mode false
% 8.10/8.31
% 8.10/8.31 % ------ Instantiation Options
% 8.10/8.31
% 8.10/8.31 % --instantiation_flag true
% 8.10/8.31 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 8.10/8.31 % --inst_solver_per_active 750
% 8.10/8.31 % --inst_solver_calls_frac 0.5
% 8.10/8.31 % --inst_passive_queue_type priority_queues
% 8.10/8.31 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 8.10/8.31 % --inst_passive_queues_freq [25;2]
% 8.10/8.31 % --inst_dismatching true
% 8.10/8.31 % --inst_eager_unprocessed_to_passive true
% 8.10/8.31 % --inst_prop_sim_given true
% 8.10/8.31 % --inst_prop_sim_new false
% 8.10/8.31 % --inst_orphan_elimination true
% 8.10/8.31 % --inst_learning_loop_flag true
% 8.10/8.31 % --inst_learning_start 3000
% 8.10/8.31 % --inst_learning_factor 2
% 8.10/8.31 % --inst_start_prop_sim_after_learn 3
% 8.10/8.31 % --inst_sel_renew solver
% 8.10/8.31 % --inst_lit_activity_flag true
% 8.10/8.31 % --inst_out_proof true
% 8.10/8.31
% 8.10/8.31 % ------ Resolution Options
% 8.10/8.31
% 8.10/8.31 % --resolution_flag true
% 8.10/8.31 % --res_lit_sel kbo_max
% 8.10/8.31 % --res_to_prop_solver none
% 8.10/8.31 % --res_prop_simpl_new false
% 8.10/8.31 % --res_prop_simpl_given false
% 8.10/8.31 % --res_passive_queue_type priority_queues
% 8.10/8.31 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 8.10/8.31 % --res_passive_queues_freq [15;5]
% 8.10/8.31 % --res_forward_subs full
% 8.10/8.31 % --res_backward_subs full
% 8.10/8.31 % --res_forward_subs_resolution true
% 8.10/8.31 % --res_backward_subs_resolution true
% 8.10/8.31 % --res_orphan_elimination false
% 8.10/8.31 % --res_time_limit 1000.
% 8.10/8.31 % --res_out_proof true
% 8.10/8.31 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_13b258.s
% 8.10/8.31 % --modulo true
% 8.10/8.31
% 8.10/8.31 % ------ Combination Options
% 8.10/8.31
% 8.10/8.31 % --comb_res_mult 1000
% 8.10/8.31 % --comb_inst_mult 300
% 8.10/8.31 % ------
% 8.10/8.31
% 8.10/8.31 % ------ Parsing...% successful
% 8.10/8.31
% 8.10/8.31 % ------ 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 %
% 8.10/8.31
% 8.10/8.31 % ------ Proving...
% 8.10/8.31 % ------ Problem Properties
% 8.10/8.31
% 8.10/8.31 %
% 8.10/8.31 % EPR false
% 8.10/8.31 % Horn false
% 8.10/8.31 % Has equality true
% 8.10/8.31
% 8.10/8.31 % % ------ Input Options Time Limit: Unbounded
% 8.10/8.31
% 8.10/8.31
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 Compiling...
% 8.10/8.31 Loading plugin: done.
% 8.10/8.31 % % ------ Current options:
% 8.10/8.31
% 8.10/8.31 % ------ Input Options
% 8.10/8.31
% 8.10/8.31 % --out_options all
% 8.10/8.31 % --tptp_safe_out true
% 8.10/8.31 % --problem_path ""
% 8.10/8.31 % --include_path ""
% 8.10/8.31 % --clausifier .//eprover
% 8.10/8.31 % --clausifier_options --tstp-format
% 8.10/8.31 % --stdin false
% 8.10/8.31 % --dbg_backtrace false
% 8.10/8.31 % --dbg_dump_prop_clauses false
% 8.10/8.31 % --dbg_dump_prop_clauses_file -
% 8.10/8.31 % --dbg_out_stat false
% 8.10/8.31
% 8.10/8.31 % ------ General Options
% 8.10/8.31
% 8.10/8.31 % --fof false
% 8.10/8.31 % --time_out_real 150.
% 8.10/8.31 % --time_out_prep_mult 0.2
% 8.10/8.31 % --time_out_virtual -1.
% 8.10/8.31 % --schedule none
% 8.10/8.31 % --ground_splitting input
% 8.10/8.31 % --splitting_nvd 16
% 8.10/8.31 % --non_eq_to_eq false
% 8.10/8.31 % --prep_gs_sim true
% 8.10/8.31 % --prep_unflatten false
% 8.10/8.31 % --prep_res_sim true
% 8.10/8.32 % --prep_upred true
% 8.10/8.32 % --res_sim_input true
% 8.10/8.32 % --clause_weak_htbl true
% 8.10/8.32 % --gc_record_bc_elim false
% 8.10/8.32 % --symbol_type_check false
% 8.10/8.32 % --clausify_out false
% 8.10/8.32 % --large_theory_mode false
% 8.10/8.32 % --prep_sem_filter none
% 8.10/8.32 % --prep_sem_filter_out false
% 8.10/8.32 % --preprocessed_out false
% 8.10/8.32 % --sub_typing false
% 8.10/8.32 % --brand_transform false
% 8.10/8.32 % --pure_diseq_elim true
% 8.10/8.32 % --min_unsat_core false
% 8.10/8.32 % --pred_elim true
% 8.10/8.32 % --add_important_lit false
% 8.10/8.32 % --soft_assumptions false
% 8.10/8.32 % --reset_solvers false
% 8.10/8.32 % --bc_imp_inh []
% 8.10/8.32 % --conj_cone_tolerance 1.5
% 8.10/8.32 % --prolific_symb_bound 500
% 8.10/8.32 % --lt_threshold 2000
% 8.10/8.32
% 8.10/8.32 % ------ SAT Options
% 8.10/8.32
% 8.10/8.32 % --sat_mode false
% 8.10/8.32 % --sat_fm_restart_options ""
% 8.10/8.32 % --sat_gr_def false
% 8.10/8.32 % --sat_epr_types true
% 8.10/8.32 % --sat_non_cyclic_types false
% 8.10/8.32 % --sat_finite_models false
% 8.10/8.32 % --sat_fm_lemmas false
% 8.10/8.32 % --sat_fm_prep false
% 8.10/8.32 % --sat_fm_uc_incr true
% 8.10/8.32 % --sat_out_model small
% 8.10/8.32 % --sat_out_clauses false
% 8.10/8.32
% 8.10/8.32 % ------ QBF Options
% 8.10/8.32
% 8.10/8.32 % --qbf_mode false
% 8.10/8.32 % --qbf_elim_univ true
% 8.10/8.32 % --qbf_sk_in true
% 8.10/8.32 % --qbf_pred_elim true
% 8.10/8.32 % --qbf_split 32
% 8.10/8.32
% 8.10/8.32 % ------ BMC1 Options
% 8.10/8.32
% 8.10/8.32 % --bmc1_incremental false
% 8.10/8.32 % --bmc1_axioms reachable_all
% 8.10/8.32 % --bmc1_min_bound 0
% 8.10/8.32 % --bmc1_max_bound -1
% 8.10/8.32 % --bmc1_max_bound_default -1
% 8.10/8.32 % --bmc1_symbol_reachability true
% 8.10/8.32 % --bmc1_property_lemmas false
% 8.10/8.32 % --bmc1_k_induction false
% 8.10/8.32 % --bmc1_non_equiv_states false
% 8.10/8.32 % --bmc1_deadlock false
% 8.10/8.32 % --bmc1_ucm false
% 8.10/8.32 % --bmc1_add_unsat_core none
% 8.10/8.32 % --bmc1_unsat_core_children false
% 8.10/8.32 % --bmc1_unsat_core_extrapolate_axioms false
% 8.10/8.32 % --bmc1_out_stat full
% 8.10/8.32 % --bmc1_ground_init false
% 8.10/8.32 % --bmc1_pre_inst_next_state false
% 8.10/8.32 % --bmc1_pre_inst_state false
% 8.10/8.32 % --bmc1_pre_inst_reach_state false
% 8.10/8.32 % --bmc1_out_unsat_core false
% 8.10/8.32 % --bmc1_aig_witness_out false
% 8.10/8.32 % --bmc1_verbose false
% 8.10/8.32 % --bmc1_dump_clauses_tptp false
% 8.10/8.32 % --bmc1_dump_unsat_core_tptp false
% 8.10/8.32 % --bmc1_dump_file -
% 8.10/8.32 % --bmc1_ucm_expand_uc_limit 128
% 8.10/8.32 % --bmc1_ucm_n_expand_iterations 6
% 8.10/8.32 % --bmc1_ucm_extend_mode 1
% 150.29/150.52 % --bmc1_ucm_init_mode 2
% 150.29/150.52 % --bmc1_ucm_cone_mode none
% 150.29/150.52 % --bmc1_ucm_reduced_relation_type 0
% 150.29/150.52 % --bmc1_ucm_relax_model 4
% 150.29/150.52 % --bmc1_ucm_full_tr_after_sat true
% 150.29/150.52 % --bmc1_ucm_expand_neg_assumptions false
% 150.29/150.52 % --bmc1_ucm_layered_model none
% 150.29/150.52 % --bmc1_ucm_max_lemma_size 10
% 150.29/150.52
% 150.29/150.52 % ------ AIG Options
% 150.29/150.52
% 150.29/150.52 % --aig_mode false
% 150.29/150.52
% 150.29/150.52 % ------ Instantiation Options
% 150.29/150.52
% 150.29/150.52 % --instantiation_flag true
% 150.29/150.52 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.29/150.52 % --inst_solver_per_active 750
% 150.29/150.52 % --inst_solver_calls_frac 0.5
% 150.29/150.52 % --inst_passive_queue_type priority_queues
% 150.29/150.52 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.29/150.52 % --inst_passive_queues_freq [25;2]
% 150.29/150.52 % --inst_dismatching true
% 150.29/150.52 % --inst_eager_unprocessed_to_passive true
% 150.29/150.52 % --inst_prop_sim_given true
% 150.29/150.52 % --inst_prop_sim_new false
% 150.29/150.52 % --inst_orphan_elimination true
% 150.29/150.52 % --inst_learning_loop_flag true
% 150.29/150.52 % --inst_learning_start 3000
% 150.29/150.52 % --inst_learning_factor 2
% 150.29/150.52 % --inst_start_prop_sim_after_learn 3
% 150.29/150.52 % --inst_sel_renew solver
% 150.29/150.52 % --inst_lit_activity_flag true
% 150.29/150.52 % --inst_out_proof true
% 150.29/150.52
% 150.29/150.52 % ------ Resolution Options
% 150.29/150.52
% 150.29/150.52 % --resolution_flag true
% 150.29/150.52 % --res_lit_sel kbo_max
% 150.29/150.52 % --res_to_prop_solver none
% 150.29/150.52 % --res_prop_simpl_new false
% 150.29/150.52 % --res_prop_simpl_given false
% 150.29/150.52 % --res_passive_queue_type priority_queues
% 150.29/150.52 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.29/150.52 % --res_passive_queues_freq [15;5]
% 150.29/150.52 % --res_forward_subs full
% 150.29/150.52 % --res_backward_subs full
% 150.29/150.52 % --res_forward_subs_resolution true
% 150.29/150.52 % --res_backward_subs_resolution true
% 150.29/150.52 % --res_orphan_elimination false
% 150.29/150.52 % --res_time_limit 1000.
% 150.29/150.52 % --res_out_proof true
% 150.29/150.52 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_13b258.s
% 150.29/150.52 % --modulo true
% 150.29/150.52
% 150.29/150.52 % ------ Combination Options
% 150.29/150.52
% 150.29/150.52 % --comb_res_mult 1000
% 150.29/150.52 % --comb_inst_mult 300
% 150.29/150.52 % ------
% 150.29/150.52
% 150.29/150.52
% 150.29/150.52
% 150.29/150.52 % ------ Proving...
% 150.29/150.52 %
% 150.29/150.52
% 150.29/150.52
% 150.29/150.52 % Time Out Real
% 150.29/150.52
% 150.29/150.52 % ------ Statistics
% 150.29/150.52
% 150.29/150.52 % ------ General
% 150.29/150.52
% 150.29/150.52 % num_of_input_clauses: 1130
% 150.29/150.52 % num_of_input_neg_conjectures: 4
% 150.29/150.52 % num_of_splits: 0
% 150.29/150.52 % num_of_split_atoms: 0
% 150.29/150.52 % num_of_sem_filtered_clauses: 0
% 150.29/150.52 % num_of_subtypes: 0
% 150.29/150.52 % monotx_restored_types: 0
% 150.29/150.52 % sat_num_of_epr_types: 0
% 150.29/150.52 % sat_num_of_non_cyclic_types: 0
% 150.29/150.52 % sat_guarded_non_collapsed_types: 0
% 150.29/150.52 % is_epr: 0
% 150.29/150.52 % is_horn: 0
% 150.29/150.52 % has_eq: 1
% 150.29/150.52 % num_pure_diseq_elim: 0
% 150.29/150.52 % simp_replaced_by: 0
% 150.29/150.52 % res_preprocessed: 8
% 150.29/150.52 % prep_upred: 0
% 150.29/150.52 % prep_unflattend: 0
% 150.29/150.52 % pred_elim_cands: 0
% 150.29/150.52 % pred_elim: 0
% 150.29/150.52 % pred_elim_cl: 0
% 150.29/150.52 % pred_elim_cycles: 0
% 150.29/150.52 % forced_gc_time: 0
% 150.29/150.52 % gc_basic_clause_elim: 0
% 150.29/150.52 % parsing_time: 0.057
% 150.29/150.52 % sem_filter_time: 0.
% 150.29/150.52 % pred_elim_time: 0.
% 150.29/150.52 % out_proof_time: 0.
% 150.29/150.52 % monotx_time: 0.
% 150.29/150.52 % subtype_inf_time: 0.
% 150.29/150.52 % unif_index_cands_time: 0.398
% 150.29/150.52 % unif_index_add_time: 0.051
% 150.29/150.52 % total_time: 150.017
% 150.29/150.52 % num_of_symbols: 109
% 150.29/150.52 % num_of_terms: 1744255
% 150.29/150.52
% 150.29/150.52 % ------ Propositional Solver
% 150.29/150.52
% 150.29/150.52 % prop_solver_calls: 13
% 150.29/150.52 % prop_fast_solver_calls: 24
% 150.29/150.52 % prop_num_of_clauses: 18711
% 150.29/150.52 % prop_preprocess_simplified: 28770
% 150.29/150.52 % prop_fo_subsumed: 0
% 150.29/150.52 % prop_solver_time: 0.004
% 150.29/150.52 % prop_fast_solver_time: 0.
% 150.29/150.52 % prop_unsat_core_time: 0.
% 150.29/150.52
% 150.29/150.52 % ------ QBF
% 150.29/150.52
% 150.29/150.52 % qbf_q_res: 0
% 150.29/150.52 % qbf_num_tautologies: 0
% 150.29/150.52 % qbf_prep_cycles: 0
% 150.29/150.52
% 150.29/150.52 % ------ BMC1
% 150.29/150.52
% 150.29/150.52 % bmc1_current_bound: -1
% 150.29/150.52 % bmc1_last_solved_bound: -1
% 150.29/150.52 % bmc1_unsat_core_size: -1
% 150.29/150.52 % bmc1_unsat_core_parents_size: -1
% 150.29/150.52 % bmc1_merge_next_fun: 0
% 150.29/150.52 % bmc1_unsat_core_clauses_time: 0.
% 150.29/150.52
% 150.29/150.52 % ------ Instantiation
% 150.29/150.52
% 150.29/150.52 % inst_num_of_clauses: 1097
% 150.29/150.52 % inst_num_in_passive: 697
% 150.29/150.52 % inst_num_in_active: 298
% 150.29/150.52 % inst_num_in_unprocessed: 102
% 150.29/150.52 % inst_num_of_loops: 299
% 150.29/150.52 % inst_num_of_learning_restarts: 1
% 150.29/150.52 % inst_num_moves_active_passive: 0
% 150.29/150.52 % inst_lit_activity: 30
% 150.29/150.52 % inst_lit_activity_moves: 0
% 150.29/150.52 % inst_num_tautologies: 0
% 150.29/150.52 % inst_num_prop_implied: 0
% 150.29/150.52 % inst_num_existing_simplified: 0
% 150.29/150.52 % inst_num_eq_res_simplified: 0
% 150.29/150.52 % inst_num_child_elim: 0
% 150.29/150.52 % inst_num_of_dismatching_blockings: 0
% 150.29/150.52 % inst_num_of_non_proper_insts: 120
% 150.29/150.52 % inst_num_of_duplicates: 183
% 150.29/150.52 % inst_inst_num_from_inst_to_res: 0
% 150.29/150.52 % inst_dismatching_checking_time: 0.108
% 150.29/150.52
% 150.29/150.52 % ------ Resolution
% 150.29/150.52
% 150.29/150.52 % res_num_of_clauses: 497334
% 150.29/150.52 % res_num_in_passive: 496086
% 150.29/150.52 % res_num_in_active: 7914
% 150.29/150.52 % res_num_of_loops: 11136
% 150.29/150.52 % res_forward_subset_subsumed: 25159
% 150.29/150.52 % res_backward_subset_subsumed: 7486
% 150.29/150.52 % res_forward_subsumed: 3629
% 150.29/150.52 % res_backward_subsumed: 3
% 150.29/150.52 % res_forward_subsumption_resolution: 102
% 150.29/150.52 % res_backward_subsumption_resolution: 0
% 150.29/150.52 % res_clause_to_clause_subsumption: 577651
% 150.29/150.52 % res_orphan_elimination: 0
% 150.29/150.52 % res_tautology_del: 4883
% 150.29/150.52 % res_num_eq_res_simplified: 0
% 150.29/150.52 % res_num_sel_changes: 0
% 150.29/150.52 % res_moves_from_active_to_pass: 0
% 150.29/150.52
% 150.29/150.52 % Status Unknown
% 150.34/150.62 % Orienting using strategy ClausalAll
% 150.34/150.62 % Orientation found
% 150.34/150.62 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_13b258.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ec1d79.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_baa021 | grep -v "SZS"
% 150.34/150.65
% 150.34/150.65 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.34/150.65
% 150.34/150.65 %
% 150.34/150.65 % ------ iProver source info
% 150.34/150.65
% 150.34/150.65 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.34/150.65 % git: non_committed_changes: true
% 150.34/150.65 % git: last_make_outside_of_git: true
% 150.34/150.65
% 150.34/150.65 %
% 150.34/150.65 % ------ Input Options
% 150.34/150.65
% 150.34/150.65 % --out_options all
% 150.34/150.65 % --tptp_safe_out true
% 150.34/150.65 % --problem_path ""
% 150.34/150.65 % --include_path ""
% 150.34/150.65 % --clausifier .//eprover
% 150.34/150.65 % --clausifier_options --tstp-format
% 150.34/150.65 % --stdin false
% 150.34/150.65 % --dbg_backtrace false
% 150.34/150.65 % --dbg_dump_prop_clauses false
% 150.34/150.65 % --dbg_dump_prop_clauses_file -
% 150.34/150.65 % --dbg_out_stat false
% 150.34/150.65
% 150.34/150.65 % ------ General Options
% 150.34/150.65
% 150.34/150.65 % --fof false
% 150.34/150.65 % --time_out_real 150.
% 150.34/150.65 % --time_out_prep_mult 0.2
% 150.34/150.65 % --time_out_virtual -1.
% 150.34/150.65 % --schedule none
% 150.34/150.65 % --ground_splitting input
% 150.34/150.65 % --splitting_nvd 16
% 150.34/150.65 % --non_eq_to_eq false
% 150.34/150.65 % --prep_gs_sim true
% 150.34/150.65 % --prep_unflatten false
% 150.34/150.65 % --prep_res_sim true
% 150.34/150.65 % --prep_upred true
% 150.34/150.65 % --res_sim_input true
% 150.34/150.65 % --clause_weak_htbl true
% 150.34/150.65 % --gc_record_bc_elim false
% 150.34/150.65 % --symbol_type_check false
% 150.34/150.65 % --clausify_out false
% 150.34/150.65 % --large_theory_mode false
% 150.34/150.65 % --prep_sem_filter none
% 150.34/150.65 % --prep_sem_filter_out false
% 150.34/150.65 % --preprocessed_out false
% 150.34/150.65 % --sub_typing false
% 150.34/150.65 % --brand_transform false
% 150.34/150.65 % --pure_diseq_elim true
% 150.34/150.65 % --min_unsat_core false
% 150.34/150.65 % --pred_elim true
% 150.34/150.65 % --add_important_lit false
% 150.34/150.65 % --soft_assumptions false
% 150.34/150.65 % --reset_solvers false
% 150.34/150.65 % --bc_imp_inh []
% 150.34/150.65 % --conj_cone_tolerance 1.5
% 150.34/150.65 % --prolific_symb_bound 500
% 150.34/150.65 % --lt_threshold 2000
% 150.34/150.65
% 150.34/150.65 % ------ SAT Options
% 150.34/150.65
% 150.34/150.65 % --sat_mode false
% 150.34/150.65 % --sat_fm_restart_options ""
% 150.34/150.65 % --sat_gr_def false
% 150.34/150.65 % --sat_epr_types true
% 150.34/150.65 % --sat_non_cyclic_types false
% 150.34/150.65 % --sat_finite_models false
% 150.34/150.65 % --sat_fm_lemmas false
% 150.34/150.65 % --sat_fm_prep false
% 150.34/150.65 % --sat_fm_uc_incr true
% 150.34/150.65 % --sat_out_model small
% 150.34/150.65 % --sat_out_clauses false
% 150.34/150.65
% 150.34/150.65 % ------ QBF Options
% 150.34/150.65
% 150.34/150.65 % --qbf_mode false
% 150.34/150.65 % --qbf_elim_univ true
% 150.34/150.65 % --qbf_sk_in true
% 150.34/150.65 % --qbf_pred_elim true
% 150.34/150.65 % --qbf_split 32
% 150.34/150.65
% 150.34/150.65 % ------ BMC1 Options
% 150.34/150.65
% 150.34/150.65 % --bmc1_incremental false
% 150.34/150.65 % --bmc1_axioms reachable_all
% 150.34/150.65 % --bmc1_min_bound 0
% 150.34/150.65 % --bmc1_max_bound -1
% 150.34/150.65 % --bmc1_max_bound_default -1
% 150.34/150.65 % --bmc1_symbol_reachability true
% 150.34/150.65 % --bmc1_property_lemmas false
% 150.34/150.65 % --bmc1_k_induction false
% 150.34/150.65 % --bmc1_non_equiv_states false
% 150.34/150.65 % --bmc1_deadlock false
% 150.34/150.65 % --bmc1_ucm false
% 150.34/150.65 % --bmc1_add_unsat_core none
% 150.34/150.65 % --bmc1_unsat_core_children false
% 150.34/150.65 % --bmc1_unsat_core_extrapolate_axioms false
% 150.34/150.65 % --bmc1_out_stat full
% 150.34/150.65 % --bmc1_ground_init false
% 150.34/150.65 % --bmc1_pre_inst_next_state false
% 150.34/150.65 % --bmc1_pre_inst_state false
% 150.34/150.65 % --bmc1_pre_inst_reach_state false
% 150.34/150.65 % --bmc1_out_unsat_core false
% 150.34/150.65 % --bmc1_aig_witness_out false
% 150.34/150.65 % --bmc1_verbose false
% 150.34/150.65 % --bmc1_dump_clauses_tptp false
% 155.69/155.92 % --bmc1_dump_unsat_core_tptp false
% 155.69/155.92 % --bmc1_dump_file -
% 155.69/155.92 % --bmc1_ucm_expand_uc_limit 128
% 155.69/155.92 % --bmc1_ucm_n_expand_iterations 6
% 155.69/155.92 % --bmc1_ucm_extend_mode 1
% 155.69/155.92 % --bmc1_ucm_init_mode 2
% 155.69/155.92 % --bmc1_ucm_cone_mode none
% 155.69/155.92 % --bmc1_ucm_reduced_relation_type 0
% 155.69/155.92 % --bmc1_ucm_relax_model 4
% 155.69/155.92 % --bmc1_ucm_full_tr_after_sat true
% 155.69/155.92 % --bmc1_ucm_expand_neg_assumptions false
% 155.69/155.92 % --bmc1_ucm_layered_model none
% 155.69/155.92 % --bmc1_ucm_max_lemma_size 10
% 155.69/155.92
% 155.69/155.92 % ------ AIG Options
% 155.69/155.92
% 155.69/155.92 % --aig_mode false
% 155.69/155.92
% 155.69/155.92 % ------ Instantiation Options
% 155.69/155.92
% 155.69/155.92 % --instantiation_flag true
% 155.69/155.92 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 155.69/155.92 % --inst_solver_per_active 750
% 155.69/155.92 % --inst_solver_calls_frac 0.5
% 155.69/155.92 % --inst_passive_queue_type priority_queues
% 155.69/155.92 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 155.69/155.92 % --inst_passive_queues_freq [25;2]
% 155.69/155.92 % --inst_dismatching true
% 155.69/155.92 % --inst_eager_unprocessed_to_passive true
% 155.69/155.92 % --inst_prop_sim_given true
% 155.69/155.92 % --inst_prop_sim_new false
% 155.69/155.92 % --inst_orphan_elimination true
% 155.69/155.92 % --inst_learning_loop_flag true
% 155.69/155.92 % --inst_learning_start 3000
% 155.69/155.92 % --inst_learning_factor 2
% 155.69/155.92 % --inst_start_prop_sim_after_learn 3
% 155.69/155.92 % --inst_sel_renew solver
% 155.69/155.92 % --inst_lit_activity_flag true
% 155.69/155.92 % --inst_out_proof true
% 155.69/155.92
% 155.69/155.92 % ------ Resolution Options
% 155.69/155.92
% 155.69/155.92 % --resolution_flag true
% 155.69/155.92 % --res_lit_sel kbo_max
% 155.69/155.92 % --res_to_prop_solver none
% 155.69/155.92 % --res_prop_simpl_new false
% 155.69/155.92 % --res_prop_simpl_given false
% 155.69/155.92 % --res_passive_queue_type priority_queues
% 155.69/155.92 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 155.69/155.92 % --res_passive_queues_freq [15;5]
% 155.69/155.92 % --res_forward_subs full
% 155.69/155.92 % --res_backward_subs full
% 155.69/155.92 % --res_forward_subs_resolution true
% 155.69/155.92 % --res_backward_subs_resolution true
% 155.69/155.92 % --res_orphan_elimination false
% 155.69/155.92 % --res_time_limit 1000.
% 155.69/155.92 % --res_out_proof true
% 155.69/155.92 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_13b258.s
% 155.69/155.92 % --modulo true
% 155.69/155.92
% 155.69/155.92 % ------ Combination Options
% 155.69/155.92
% 155.69/155.92 % --comb_res_mult 1000
% 155.69/155.92 % --comb_inst_mult 300
% 155.69/155.92 % ------
% 155.69/155.92
% 155.69/155.92 % ------ Parsing...% successful
% 155.69/155.92
% 155.69/155.92 % ------ 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 %
% 155.69/155.92
% 155.69/155.92 % ------ Proving...
% 155.69/155.92 % ------ Problem Properties
% 155.69/155.92
% 155.69/155.92 %
% 155.69/155.92 % EPR false
% 155.69/155.92 % Horn false
% 155.69/155.92 % Has equality true
% 155.69/155.92
% 155.69/155.92 % % ------ Input Options Time Limit: Unbounded
% 155.69/155.92
% 155.69/155.92
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 Compiling...
% 155.69/155.92 Loading plugin: done.
% 155.69/155.92 % % ------ Current options:
% 155.69/155.92
% 155.69/155.92 % ------ Input Options
% 155.69/155.92
% 155.69/155.92 % --out_options all
% 155.69/155.92 % --tptp_safe_out true
% 155.69/155.92 % --problem_path ""
% 155.69/155.92 % --include_path ""
% 155.69/155.92 % --clausifier .//eprover
% 155.69/155.92 % --clausifier_options --tstp-format
% 155.69/155.92 % --stdin false
% 155.69/155.92 % --dbg_backtrace false
% 155.69/155.92 % --dbg_dump_prop_clauses false
% 155.69/155.92 % --dbg_dump_prop_clauses_file -
% 155.69/155.92 % --dbg_out_stat false
% 155.69/155.92
% 155.69/155.92 % ------ General Options
% 155.69/155.92
% 155.69/155.92 % --fof false
% 155.69/155.92 % --time_out_real 150.
% 155.69/155.92 % --time_out_prep_mult 0.2
% 155.69/155.92 % --time_out_virtual -1.
% 155.69/155.92 % --schedule none
% 155.69/155.92 % --ground_splitting input
% 155.69/155.92 % --splitting_nvd 16
% 155.69/155.92 % --non_eq_to_eq false
% 155.69/155.92 % --prep_gs_sim true
% 155.69/155.92 % --prep_unflatten false
% 155.69/155.92 % --prep_res_sim true
% 155.69/155.92 % --prep_upred true
% 155.69/155.92 % --res_sim_input true
% 155.69/155.92 % --clause_weak_htbl true
% 155.69/155.92 % --gc_record_bc_elim false
% 155.69/155.92 % --symbol_type_check false
% 155.69/155.92 % --clausify_out false
% 155.69/155.92 % --large_theory_mode false
% 155.69/155.92 % --prep_sem_filter none
% 155.69/155.92 % --prep_sem_filter_out false
% 155.69/155.92 % --preprocessed_out false
% 155.69/155.92 % --sub_typing false
% 155.69/155.92 % --brand_transform false
% 155.69/155.92 % --pure_diseq_elim true
% 155.69/155.92 % --min_unsat_core false
% 155.69/155.92 % --pred_elim true
% 155.69/155.92 % --add_important_lit false
% 155.69/155.92 % --soft_assumptions false
% 155.69/155.92 % --reset_solvers false
% 155.69/155.92 % --bc_imp_inh []
% 155.69/155.92 % --conj_cone_tolerance 1.5
% 155.69/155.92 % --prolific_symb_bound 500
% 155.69/155.92 % --lt_threshold 2000
% 155.69/155.92
% 155.69/155.92 % ------ SAT Options
% 155.69/155.92
% 155.69/155.92 % --sat_mode false
% 155.69/155.92 % --sat_fm_restart_options ""
% 155.69/155.92 % --sat_gr_def false
% 155.69/155.92 % --sat_epr_types true
% 155.69/155.92 % --sat_non_cyclic_types false
% 155.69/155.92 % --sat_finite_models false
% 155.69/155.92 % --sat_fm_lemmas false
% 155.69/155.92 % --sat_fm_prep false
% 155.69/155.92 % --sat_fm_uc_incr true
% 155.69/155.92 % --sat_out_model small
% 155.69/155.92 % --sat_out_clauses false
% 155.69/155.92
% 155.69/155.92 % ------ QBF Options
% 155.69/155.92
% 155.69/155.92 % --qbf_mode false
% 155.69/155.92 % --qbf_elim_univ true
% 155.69/155.92 % --qbf_sk_in true
% 155.69/155.92 % --qbf_pred_elim true
% 155.69/155.92 % --qbf_split 32
% 155.69/155.92
% 155.69/155.92 % ------ BMC1 Options
% 155.69/155.92
% 155.69/155.92 % --bmc1_incremental false
% 155.69/155.92 % --bmc1_axioms reachable_all
% 155.69/155.92 % --bmc1_min_bound 0
% 155.69/155.92 % --bmc1_max_bound -1
% 155.69/155.92 % --bmc1_max_bound_default -1
% 155.69/155.92 % --bmc1_symbol_reachability true
% 155.69/155.92 % --bmc1_property_lemmas false
% 155.69/155.92 % --bmc1_k_induction false
% 155.69/155.92 % --bmc1_non_equiv_states false
% 155.69/155.92 % --bmc1_deadlock false
% 155.69/155.92 % --bmc1_ucm false
% 155.69/155.92 % --bmc1_add_unsat_core none
% 155.69/155.92 % --bmc1_unsat_core_children false
% 155.69/155.92 % --bmc1_unsat_core_extrapolate_axioms false
% 155.69/155.92 % --bmc1_out_stat full
% 155.69/155.92 % --bmc1_ground_init false
% 155.69/155.92 % --bmc1_pre_inst_next_state false
% 155.69/155.92 % --bmc1_pre_inst_state false
% 155.69/155.92 % --bmc1_pre_inst_reach_state false
% 155.69/155.92 % --bmc1_out_unsat_core false
% 155.69/155.92 % --bmc1_aig_witness_out false
% 155.69/155.92 % --bmc1_verbose false
% 155.69/155.92 % --bmc1_dump_clauses_tptp false
% 155.69/155.92 % --bmc1_dump_unsat_core_tptp false
% 155.69/155.92 % --bmc1_dump_file -
% 155.69/155.92 % --bmc1_ucm_expand_uc_limit 128
% 155.69/155.92 % --bmc1_ucm_n_expand_iterations 6
% 155.69/155.92 % --bmc1_ucm_extend_mode 1
% 155.69/155.92 % --bmc1_ucm_init_mode 2
% 155.69/155.92 % --bmc1_ucm_cone_mode none
% 155.69/155.92 % --bmc1_ucm_reduced_relation_type 0
% 155.69/155.92 % --bmc1_ucm_relax_model 4
% 155.69/155.92 % --bmc1_ucm_full_tr_after_sat true
% 155.69/155.92 % --bmc1_ucm_expand_neg_assumptions false
% 155.69/155.92 % --bmc1_ucm_layered_model none
% 155.69/155.92 % --bmc1_ucm_max_lemma_size 10
% 155.72/156.01
% 155.72/156.01 % ------ AIG Options
% 155.72/156.01
% 155.72/156.01 % --aig_mode false
% 155.72/156.01
% 155.72/156.01 % ------ Instantiation Options
% 155.72/156.01
% 155.72/156.01 % --instantiation_flag true
% 155.72/156.01 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 155.72/156.01 % --inst_solver_per_active 750
% 155.72/156.01 % --inst_solver_calls_frac 0.5
% 155.72/156.01 % --inst_passive_queue_type priority_queues
% 155.72/156.01 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 155.72/156.01 % --inst_passive_queues_freq [25;2]
% 155.72/156.01 % --inst_dismatching true
% 155.72/156.01 % --inst_eager_unprocessed_to_passive true
% 155.72/156.01 % --inst_prop_sim_given true
% 155.72/156.01 % --inst_prop_sim_new false
% 155.72/156.01 % --inst_orphan_elimination true
% 155.72/156.01 % --inst_learning_loop_flag true
% 155.72/156.01 % --inst_learning_start 3000
% 155.72/156.01 % --inst_learning_factor 2
% 155.72/156.01 % --inst_start_prop_sim_after_learn 3
% 155.72/156.01 % --inst_sel_renew solver
% 155.72/156.01 % --inst_lit_activity_flag true
% 155.72/156.01 % --inst_out_proof true
% 155.72/156.01
% 155.72/156.01 % ------ Resolution Options
% 155.72/156.01
% 155.72/156.01 % --resolution_flag true
% 155.72/156.01 % --res_lit_sel kbo_max
% 155.72/156.01 % --res_to_prop_solver none
% 155.72/156.01 % --res_prop_simpl_new false
% 155.72/156.01 % --res_prop_simpl_given false
% 155.72/156.01 % --res_passive_queue_type priority_queues
% 155.72/156.01 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 155.72/156.01 % --res_passive_queues_freq [15;5]
% 155.72/156.01 % --res_forward_subs full
% 155.72/156.01 % --res_backward_subs full
% 155.72/156.01 % --res_forward_subs_resolution true
% 155.72/156.01 % --res_backward_subs_resolution true
% 155.72/156.01 % --res_orphan_elimination false
% 155.72/156.01 % --res_time_limit 1000.
% 155.72/156.01 % --res_out_proof true
% 155.72/156.01 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_13b258.s
% 155.72/156.01 % --modulo true
% 155.72/156.01
% 155.72/156.01 % ------ Combination Options
% 155.72/156.01
% 155.72/156.01 % --comb_res_mult 1000
% 155.72/156.01 % --comb_inst_mult 300
% 155.72/156.01 % ------
% 155.72/156.01
% 155.72/156.01
% 155.72/156.01
% 155.72/156.01 % ------ Proving...
% 155.72/156.01 %
% 155.72/156.01
% 155.72/156.01
% 155.72/156.01 % Resolution empty clause
% 155.72/156.01
% 155.72/156.01 % ------ Statistics
% 155.72/156.01
% 155.72/156.01 % ------ General
% 155.72/156.01
% 155.72/156.01 % num_of_input_clauses: 1130
% 155.72/156.01 % num_of_input_neg_conjectures: 4
% 155.72/156.01 % num_of_splits: 0
% 155.72/156.01 % num_of_split_atoms: 0
% 155.72/156.01 % num_of_sem_filtered_clauses: 0
% 155.72/156.01 % num_of_subtypes: 0
% 155.72/156.01 % monotx_restored_types: 0
% 155.72/156.01 % sat_num_of_epr_types: 0
% 155.72/156.01 % sat_num_of_non_cyclic_types: 0
% 155.72/156.01 % sat_guarded_non_collapsed_types: 0
% 155.72/156.01 % is_epr: 0
% 155.72/156.01 % is_horn: 0
% 155.72/156.01 % has_eq: 1
% 155.72/156.01 % num_pure_diseq_elim: 0
% 155.72/156.01 % simp_replaced_by: 0
% 155.72/156.01 % res_preprocessed: 8
% 155.72/156.01 % prep_upred: 0
% 155.72/156.01 % prep_unflattend: 0
% 155.72/156.01 % pred_elim_cands: 0
% 155.72/156.01 % pred_elim: 0
% 155.72/156.01 % pred_elim_cl: 0
% 155.72/156.01 % pred_elim_cycles: 0
% 155.72/156.01 % forced_gc_time: 0
% 155.72/156.01 % gc_basic_clause_elim: 0
% 155.72/156.01 % parsing_time: 0.079
% 155.72/156.01 % sem_filter_time: 0.
% 155.72/156.01 % pred_elim_time: 0.
% 155.72/156.01 % out_proof_time: 0.003
% 155.72/156.01 % monotx_time: 0.
% 155.72/156.01 % subtype_inf_time: 0.
% 155.72/156.01 % unif_index_cands_time: 0.
% 155.72/156.01 % unif_index_add_time: 0.001
% 155.72/156.01 % total_time: 5.375
% 155.72/156.01 % num_of_symbols: 109
% 155.72/156.01 % num_of_terms: 6787
% 155.72/156.01
% 155.72/156.01 % ------ Propositional Solver
% 155.72/156.01
% 155.72/156.01 % prop_solver_calls: 1
% 155.72/156.01 % prop_fast_solver_calls: 24
% 155.72/156.01 % prop_num_of_clauses: 1174
% 155.72/156.01 % prop_preprocess_simplified: 3354
% 155.72/156.01 % prop_fo_subsumed: 0
% 155.72/156.01 % prop_solver_time: 0.
% 155.72/156.01 % prop_fast_solver_time: 0.
% 155.72/156.01 % prop_unsat_core_time: 0.
% 155.72/156.01
% 155.72/156.01 % ------ QBF
% 155.72/156.01
% 155.72/156.01 % qbf_q_res: 0
% 155.72/156.01 % qbf_num_tautologies: 0
% 155.72/156.01 % qbf_prep_cycles: 0
% 155.72/156.01
% 155.72/156.01 % ------ BMC1
% 155.72/156.01
% 155.72/156.01 % bmc1_current_bound: -1
% 155.72/156.01 % bmc1_last_solved_bound: -1
% 155.72/156.01 % bmc1_unsat_core_size: -1
% 155.72/156.01 % bmc1_unsat_core_parents_size: -1
% 155.72/156.01 % bmc1_merge_next_fun: 0
% 155.72/156.01 % bmc1_unsat_core_clauses_time: 0.
% 155.72/156.01
% 155.72/156.01 % ------ Instantiation
% 155.72/156.01
% 155.72/156.01 % inst_num_of_clauses: 990
% 155.72/156.01 % inst_num_in_passive: 0
% 155.72/156.01 % inst_num_in_active: 0
% 155.72/156.01 % inst_num_in_unprocessed: 1130
% 155.72/156.01 % inst_num_of_loops: 0
% 155.72/156.01 % inst_num_of_learning_restarts: 0
% 155.72/156.01 % inst_num_moves_active_passive: 0
% 155.72/156.01 % inst_lit_activity: 0
% 155.72/156.01 % inst_lit_activity_moves: 0
% 155.72/156.01 % inst_num_tautologies: 0
% 155.72/156.01 % inst_num_prop_implied: 0
% 155.72/156.01 % inst_num_existing_simplified: 0
% 155.72/156.01 % inst_num_eq_res_simplified: 0
% 155.72/156.01 % inst_num_child_elim: 0
% 155.72/156.01 % inst_num_of_dismatching_blockings: 0
% 155.72/156.01 % inst_num_of_non_proper_insts: 0
% 155.72/156.01 % inst_num_of_duplicates: 0
% 155.72/156.01 % inst_inst_num_from_inst_to_res: 0
% 155.72/156.01 % inst_dismatching_checking_time: 0.
% 155.72/156.01
% 155.72/156.01 % ------ Resolution
% 155.72/156.01
% 155.72/156.01 % res_num_of_clauses: 1530
% 155.72/156.01 % res_num_in_passive: 424
% 155.72/156.01 % res_num_in_active: 483
% 155.72/156.01 % res_num_of_loops: 61
% 155.72/156.01 % res_forward_subset_subsumed: 608
% 155.72/156.01 % res_backward_subset_subsumed: 1
% 155.72/156.01 % res_forward_subsumed: 12
% 155.72/156.01 % res_backward_subsumed: 0
% 155.72/156.01 % res_forward_subsumption_resolution: 1
% 155.72/156.01 % res_backward_subsumption_resolution: 0
% 155.72/156.01 % res_clause_to_clause_subsumption: 212
% 155.72/156.01 % res_orphan_elimination: 0
% 155.72/156.01 % res_tautology_del: 0
% 155.72/156.01 % res_num_eq_res_simplified: 0
% 155.72/156.01 % res_num_sel_changes: 0
% 155.72/156.01 % res_moves_from_active_to_pass: 0
% 155.72/156.01
% 155.72/156.01 % Status Unsatisfiable
% 155.72/156.01 % SZS status Unsatisfiable
% 155.72/156.01 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------